From f3df93d58db2eed8d2730d5defe11179ba904591 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 4 Oct 2020 21:29:02 +0200 Subject: [PATCH 01/28] Set up elsearticle template with meta data - paper.tex + main file to generate the PDF version from + rough structure of the paper + set static/elsearticle.cls as the document class - tex/ folder + glossary.tex => holds terms listed in glossary + meta.tex => add meta data (incl. abstract) of the paper + preamble.tex => holds LaTeX imports and document-wide settings + references.bib => holds BibTeX data of sources * set static/elsarticle-harv.bst as quoting style --- paper.tex | 22 + static/elsarticle-harv.bst | 1597 ++++++++++++++++++++++++++++++++++++ static/elsarticle.cls | 1056 ++++++++++++++++++++++++ tex/glossary.tex | 1 + tex/meta.tex | 47 ++ tex/preamble.tex | 2 + tex/references.bib | 0 7 files changed, 2725 insertions(+) create mode 100644 paper.tex create mode 100644 static/elsarticle-harv.bst create mode 100644 static/elsarticle.cls create mode 100644 tex/glossary.tex create mode 100644 tex/meta.tex create mode 100644 tex/preamble.tex create mode 100644 tex/references.bib diff --git a/paper.tex b/paper.tex new file mode 100644 index 0000000..a7f42bd --- /dev/null +++ b/paper.tex @@ -0,0 +1,22 @@ +\documentclass[preprint,review,12pt]{static/elsarticle} + +\input{tex/preamble} + +\begin{document} + +\input{tex/meta} +\newpage + +Lorem ipsum. +\newpage + +\input{tex/glossary} +\newpage + +\appendix +\newpage + +\bibliographystyle{static/elsarticle-harv} +\bibliography{tex/references} + +\end{document} \ No newline at end of file diff --git a/static/elsarticle-harv.bst b/static/elsarticle-harv.bst new file mode 100644 index 0000000..3eaac4d --- /dev/null +++ b/static/elsarticle-harv.bst @@ -0,0 +1,1597 @@ +%% +%% This is file `elsarticle-harv.bst' (Version 2.1), +%% +%% Copyright 2009-2019 Elsevier Ltd +%% +%% This file is part of the 'Elsarticle Bundle'. +%% --------------------------------------------- +%% +%% It may be distributed under the conditions of the LaTeX Project Public +%% License, either version 1.2 of this license or (at your option) any +%% later version. The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.2 or later is part of all distributions of LaTeX +%% version 1999/12/01 or later. +%% +%% $Id: elsarticle-harv.bst 163 2019-01-14 09:54:24Z rishi $ +%% +%% $URL: http://lenova.river-valley.com/svn/elsarticle/trunk/elsarticle-harv.bst $ +%% + +ENTRY + { address + archive + author + booktitle + chapter + collaboration + edition + editor + howpublished + institution + journal + key + month + note + number + organization + pages + publisher + school + series + title + type + volume + year + url + doi + eprint + pubmed + } + {} + { label extra.label sort.label short.list } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +STRINGS { urlprefix doiprefix eprintprefix pubmedprefix } + +FUNCTION {init.web.variables} +{ + "\URLprefix " 'urlprefix := + "\DOIprefix" 'doiprefix := + "\ArXivprefix " 'eprintprefix := + "\Pubmedprefix " 'pubmedprefix := +} + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} +STRINGS { s t} +FUNCTION {output.comma} +{ ", " * write$} + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ". " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { ", " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} +FUNCTION {output.commanull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { ", " * write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} +FUNCTION {output.book.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} +FUNCTION {add.blank} +{ " " * before.all 'output.state := +} + +FUNCTION {date.block} +{ + new.block +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "\textit{" swap$ * "}" * } + if$ +} +FUNCTION {tie.or.space.prefix} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ +} + +FUNCTION {capitalize} +{ "u" change.case$ "t" change.case$ } + +FUNCTION {space.word} +{ " " swap$ * " " * } + % Here are the language-specific definitions for explicit words. + % Each function has a name bbl.xxx where xxx is the English word. + % The language selected here is ENGLISH +FUNCTION {bbl.and} +{ "and"} + +FUNCTION {bbl.etal} +{ "et~al." } + +FUNCTION {bbl.editors} +{ "Eds." } + +FUNCTION {bbl.editor} +{ "Ed." } + +FUNCTION {bbl.edby} +{ "edited by" } + +FUNCTION {bbl.edition} +{ "ed." } + +FUNCTION {bbl.volume} +{ "volume" } + +FUNCTION {bbl.of} +{ "of" } + +FUNCTION {bbl.number} +{ "number" } + +FUNCTION {bbl.nr} +{ "no." } + +FUNCTION {bbl.in} +{ "in" } + +FUNCTION {bbl.pages} +{ "pp." } + +FUNCTION {bbl.page} +{ "p." } + +FUNCTION {bbl.chapter} +{ "chapter" } + +FUNCTION {bbl.techrep} +{ "Technical Report" } + +FUNCTION {bbl.mthesis} +{ "Master's thesis" } + +FUNCTION {bbl.phdthesis} +{ "Ph.D. thesis" } + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + +MACRO {acmcs} {"ACM Comput. Surv."} + +MACRO {acta} {"Acta Inf."} + +MACRO {cacm} {"Commun. ACM"} + +MACRO {ibmjrd} {"IBM J. Res. Dev."} + +MACRO {ibmsj} {"IBM Syst.~J."} + +MACRO {ieeese} {"IEEE Trans. Software Eng."} + +MACRO {ieeetc} {"IEEE Trans. Comput."} + +MACRO {ieeetcad} + {"IEEE Trans. Comput. Aid. Des."} + +MACRO {ipl} {"Inf. Process. Lett."} + +MACRO {jacm} {"J.~ACM"} + +MACRO {jcss} {"J.~Comput. Syst. Sci."} + +MACRO {scp} {"Sci. Comput. Program."} + +MACRO {sicomp} {"SIAM J. Comput."} + +MACRO {tocs} {"ACM Trans. Comput. Syst."} + +MACRO {tods} {"ACM Trans. Database Syst."} + +MACRO {tog} {"ACM Trans. Graphic."} + +MACRO {toms} {"ACM Trans. Math. Software"} + +MACRO {toois} {"ACM Trans. Office Inf. Syst."} + +MACRO {toplas} {"ACM Trans. Progr. Lang. Syst."} + +MACRO {tcs} {"Theor. Comput. Sci."} + +FUNCTION {bibinfo.check} +{ swap$ + duplicate$ missing$ + { + pop$ pop$ + "" + } + { duplicate$ empty$ + { + swap$ pop$ + } + { swap$ + "\bibinfo{" swap$ * "}{" * swap$ * "}" * + } + if$ + } + if$ +} +FUNCTION {bibinfo.warn} +{ swap$ + duplicate$ missing$ + { + swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ + "" + } + { duplicate$ empty$ + { + swap$ "empty " swap$ * " in " * cite$ * warning$ + } + { swap$ + pop$ + } + if$ + } + if$ +} + +STRINGS { bibinfo} + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 'bibinfo := + duplicate$ empty$ 'skip$ { + 's := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}{, jj}{, f{.}.}" + format.name$ + bibinfo bibinfo.check + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + "," * + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { + " " * bbl.etal * + } + { " " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ + } if$ +} +FUNCTION {format.names.ed} +{ + format.names +} +FUNCTION {format.key} +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.authors} +{ author "author" format.names + duplicate$ empty$ 'skip$ + { collaboration "collaboration" bibinfo.check + duplicate$ empty$ 'skip$ + { " (" swap$ * ")" * } + if$ + * + } + if$ +} + +FUNCTION {get.bbl.editor} +{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ } + +FUNCTION {format.editors} +{ editor "editor" format.names duplicate$ empty$ 'skip$ + { + " " * + get.bbl.editor + capitalize + "(" swap$ * ")" * + * + } + if$ +} +FUNCTION {format.note} +{ + note empty$ + { "" } + { note #1 #1 substring$ + duplicate$ "{" = + 'skip$ + { output.state mid.sentence = + { "l" } + { "u" } + if$ + change.case$ + } + if$ + note #2 global.max$ substring$ * "note" bibinfo.check + } + if$ +} + +FUNCTION {format.title} +{ title + duplicate$ empty$ 'skip$ + { "t" change.case$ } + if$ + "title" bibinfo.check +} +FUNCTION {format.full.names} +{'s := + "" 't := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{vv~}{ll}" format.name$ + 't := + nameptr #1 > + { + namesleft #1 > + { ", " * t * } + { + s nameptr "{ll}" format.name$ duplicate$ "others" = + { 't := } + { pop$ } + if$ + t "others" = + { + " " * bbl.etal * + } + { + bbl.and + space.word * t * + } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {author.editor.key.full} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.full.names } + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {author.key.full} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.full.names } + if$ +} + +FUNCTION {editor.key.full} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.full.names } + if$ +} + +FUNCTION {make.full.names} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.full + { type$ "proceedings" = + 'editor.key.full + 'author.key.full + if$ + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[{" write$ + label write$ + ")" make.full.names duplicate$ short.list = + { pop$ } + { * } + if$ + "}]{" * write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {n.dashify} +{ + 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {word.in} +{ bbl.in %capitalize + ":" * + " " * } + +FUNCTION {format.date} +{ year "year" bibinfo.check duplicate$ empty$ + { + } + 'skip$ + if$ + extra.label * + before.all 'output.state := + ", " swap$ * +} +FUNCTION {format.btitle} +{ title "title" bibinfo.check + duplicate$ empty$ 'skip$ + { + } + if$ +} +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { bbl.volume volume tie.or.space.prefix + "volume" bibinfo.check * * + series "series" bibinfo.check + duplicate$ empty$ 'pop$ + { swap$ bbl.of space.word * swap$ + emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { series empty$ + { number "number" bibinfo.check } + { output.state mid.sentence = + { bbl.number } + { bbl.number capitalize } + if$ + number tie.or.space.prefix "number" bibinfo.check * * + bbl.in space.word * + series "series" bibinfo.check * + } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition duplicate$ empty$ 'skip$ + { + output.state mid.sentence = + { "l" } + { "t" } + if$ change.case$ + "edition" bibinfo.check + " " * bbl.edition * + } + if$ +} +INTEGERS { multiresult } +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} +%FUNCTION {format.pages} +%{ pages duplicate$ empty$ 'skip$ +% { duplicate$ multi.page.check +% { +% n.dashify +% } +% { +% } +% if$ +% "pages" bibinfo.check +% } +% if$ +%} + +FUNCTION {format.pages} +{ pages duplicate$ empty$ 'skip$ + { duplicate$ multi.page.check + { + bbl.pages swap$ + n.dashify + } + { + bbl.page swap$ + } + if$ + tie.or.space.prefix + "pages" bibinfo.check + * * + } + if$ +} + +FUNCTION {format.journal.pages} +{ pages duplicate$ empty$ 'pop$ + { swap$ duplicate$ empty$ + { pop$ pop$ format.pages } + { + ", " * + swap$ + n.dashify + "pages" bibinfo.check + * + } + if$ + } + if$ +} +FUNCTION {format.vol.num.pages} +{ volume field.or.null + duplicate$ empty$ 'skip$ + { + "volume" bibinfo.check + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + { "" } + { type empty$ + { bbl.chapter } + { type "l" change.case$ + "type" bibinfo.check + } + if$ + chapter tie.or.space.prefix + "chapter" bibinfo.check + * * + } + if$ +} + +FUNCTION {format.booktitle} +{ + booktitle "booktitle" bibinfo.check +} +FUNCTION {format.in.ed.booktitle} +{ format.booktitle duplicate$ empty$ 'skip$ + { + editor "editor" format.names.ed duplicate$ empty$ 'pop$ + { + " " * + get.bbl.editor + capitalize + "(" swap$ * "), " * + * swap$ + * } + if$ + word.in swap$ * + } + if$ +} +FUNCTION {format.thesis.type} +{ type duplicate$ empty$ + 'pop$ + { swap$ pop$ + "t" change.case$ "type" bibinfo.check + } + if$ +} +FUNCTION {format.tr.number} +{ number "number" bibinfo.check + type duplicate$ empty$ + { pop$ bbl.techrep } + 'skip$ + if$ + "type" bibinfo.check + swap$ duplicate$ empty$ + { pop$ "t" change.case$ } + { tie.or.space.prefix * * } + if$ +} +FUNCTION {format.article.crossref} +{ + word.in + " \cite{" * crossref * "}" * +} +FUNCTION {format.book.crossref} +{ volume duplicate$ empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + pop$ word.in + } + { bbl.volume + capitalize + swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word * + } + if$ + " \cite{" * crossref * "}" * +} +FUNCTION {format.incoll.inproc.crossref} +{ + word.in + " \cite{" * crossref * "}" * +} +FUNCTION {format.org.or.pub} +{ 't := + "" + address empty$ t empty$ and + 'skip$ + { + t empty$ + { address "address" bibinfo.check * + } + { t * + address empty$ + 'skip$ + { ", " * address "address" bibinfo.check * } + if$ + } + if$ + } + if$ +} +FUNCTION {format.publisher.address} +{ publisher "publisher" bibinfo.check format.org.or.pub +} + +FUNCTION {format.organization.address} +{ organization "organization" bibinfo.check format.org.or.pub +} + +FUNCTION {print.url} + {url duplicate$ empty$ + { pop$ "" } + { new.sentence + urlprefix "\url{" * swap$ * "}" * + } + if$ + } + +FUNCTION {print.doi} + {doi duplicate$ empty$ + { pop$ "" } + { new.sentence + doiprefix "\doi{" * swap$ * "}" * + } + if$ + } + +FUNCTION {print.eprint} + {eprint duplicate$ empty$ + { pop$ "" } + { new.sentence + duplicate$ "\href{http://arxiv.org/abs/" swap$ * "}{{\tt arXiv:" * swap$ * "}}" * } + if$ + } + +FUNCTION {print.pubmed} + {pubmed duplicate$ empty$ + { pop$ "" } + { new.sentence + pubmedprefix "\Pubmed{" * swap$ * "}" * + } + if$ + } + +FUNCTION {webpage} +{ "%Type = Webpage" write$ + output.bibitem + format.authors "author" output.check + author format.key output + author empty$ + { + format.title "title" output.check + new.block + format.date "year" output.check + date.block + } + { + format.date "year" output.check + date.block + format.title "title" output.check + new.block +} + if$ + print.url output + fin.entry +} + + +FUNCTION {article} +{ "%Type = Article" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + crossref missing$ + { + journal + "journal" bibinfo.check + "journal" output.check + add.blank + format.vol.num.pages output + } + { format.article.crossref output.nonnull + } + if$ + format.journal.pages + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {book} +{ "%Type = Book" write$ + output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + format.date "year" output.check + date.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + format.edition output + new.sentence + format.publisher.address output + } + { + new.block + format.book.crossref output.nonnull + } + if$ + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {booklet} +{ "%Type = Booklet" write$ + output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + howpublished "howpublished" bibinfo.check output + address "address" bibinfo.check output + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {inbook} +{ "%Type = Inbook" write$ + output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + format.date "year" output.check + date.block + format.btitle "title" output.check + format.edition output + crossref missing$ + { + format.publisher.address output + format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + } + { + format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.pages "pages" output.check + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {incollection} +{ "%Type = Incollection" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.book.check + new.sentence + crossref missing$ + { format.in.ed.booktitle "booktitle" output.book.check + format.edition output + format.publisher.address output + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + format.pages "pages" output.check + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {inproceedings} +{ "%Type = Inproceedings" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.book.check + new.sentence + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + new.sentence + publisher empty$ + { format.organization.address output } + { organization "organization" bibinfo.check output + format.publisher.address output + } + if$ +% format.bvolume output +% format.number.series output +% format.pages output + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + format.pages "pages" output.check + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ "%Type = Manual" write$ + output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.btitle "title" output.check + format.edition output + organization address new.block.checkb + organization "organization" bibinfo.check output + address "address" bibinfo.check output + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {mastersthesis} +{ "%Type = Masterthesis" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.btitle + "title" output.check + new.block + bbl.mthesis format.thesis.type output.nonnull + school "school" bibinfo.warn output + address "address" bibinfo.check output + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {misc} +{ "%Type = Misc" write$ + output.bibitem + format.authors output + author format.key output + format.date "year" output.check + date.block + format.title output + new.block + howpublished "howpublished" bibinfo.check output + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {phdthesis} +{ "%Type = Phdthesis" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.btitle + "title" output.check + new.block + bbl.phdthesis format.thesis.type output.nonnull + school "school" bibinfo.warn output + address "address" bibinfo.check output + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {proceedings} +{ "%Type = Proceedings" write$ + output.bibitem + format.editors output + editor format.key output + format.date "year" output.check + date.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + new.sentence + publisher empty$ + { format.organization.address output } + { organization "organization" bibinfo.check output + format.publisher.address output + } + if$ + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {techreport} +{ "%Type = Techreport" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.btitle + "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" bibinfo.warn output + address "address" bibinfo.check output + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note output + fin.entry +} + +FUNCTION {unpublished} +{ "%Type = Unpublished" write$ + output.bibitem + format.authors "author" output.check + author format.key output + format.date "year" output.check + date.block + format.title "title" output.check + new.block + print.url output + print.doi output + print.eprint output + print.pubmed output + format.note "note" output.check + fin.entry +} + +FUNCTION {default.type} { misc } +READ +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} +INTEGERS { len } +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} +FUNCTION {format.lab.names} +{ 's := + "" 't := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ + " " * bbl.etal * + } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { + " " * bbl.etal * + } + { bbl.and space.word * s #2 "{vv~}{ll}" format.name$ + * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.label} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.short.authors} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.label + 'author.key.label + if$ + } + if$ + 'short.list := +} + +FUNCTION {calc.label} +{ calc.short.authors + short.list + "(" + * + year duplicate$ empty$ + short.list key field.or.null = or + { pop$ "" } + 'skip$ + if$ + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr + "{ll{ }}{ f{ }}{ jj{ }}" + format.name$ 't := + nameptr #1 > + { + " " * + namesleft #1 = t "others" = and + { "zzzzz" * } + { t sortify * } + if$ + } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} +FUNCTION {editor.sort} +{ editor empty$ + { key empty$ + { "to sort, need editor or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ +} +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.sort + 'author.sort + if$ + } + if$ + #1 entry.max$ substring$ + 'sort.label := + sort.label + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} +SORT +STRINGS { last.label next.extra } +INTEGERS { last.extra.num number.label } +FUNCTION {initialize.extra.label.stuff} +{ #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'last.extra.num := + #0 'number.label := +} +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ + number.label #1 + 'number.label := +} +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + extra.label 'next.extra := + extra.label + duplicate$ empty$ + 'skip$ +% { "{\natexlab{" swap$ * "}}" * } + { "" swap$ * "" * } + if$ + 'extra.label := + label extra.label * 'label := +} +EXECUTE {initialize.extra.label.stuff} +ITERATE {forward.pass} +REVERSE {reverse.pass} +FUNCTION {bib.sort.order} +{ sort.label + " " + * + year field.or.null sortify + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} +ITERATE {bib.sort.order} +SORT +FUNCTION {begin.bib} +{ preamble$ empty$ + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{" number.label int.to.str$ * "}" * + write$ newline$ + "\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi" + write$ newline$ + "\providecommand{\url}[1]{\texttt{#1}}" + write$ newline$ + "\providecommand{\href}[2]{#2}" + write$ newline$ + "\providecommand{\path}[1]{#1}" + write$ newline$ + "\providecommand{\DOIprefix}{doi:}" + write$ newline$ + "\providecommand{\ArXivprefix}{arXiv:}" + write$ newline$ + "\providecommand{\URLprefix}{URL: }" + write$ newline$ + "\providecommand{\Pubmedprefix}{pmid:}" + write$ newline$ + "\providecommand{\doi}[1]{\href{http://dx.doi.org/#1}{\path{#1}}}" + write$ newline$ + "\providecommand{\Pubmed}[1]{\href{pmid:#1}{\path{#1}}}" + write$ newline$ + "\providecommand{\bibinfo}[2]{#2}" + write$ newline$ + "\ifx\xfnm\relax \def\xfnm[#1]{\unskip,\space#1}\fi" + write$ newline$ +} +EXECUTE {begin.bib} +EXECUTE {init.state.consts} +EXECUTE {init.web.variables} +ITERATE {call.type$} +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} +EXECUTE {end.bib} +%% End of customized bst file +%% +%% End of file `elsarticle-harv.bst'. +%% +%% Change log: +%% ----------- +%% 22.04.2011 +%% +%% 10.08.2012 +%% a. doi, url, eprint, pmid added +%% b. Bibtype `webpage' defined +%% +%% 30.08.2012 +%% a. collaboration added. +%% + diff --git a/static/elsarticle.cls b/static/elsarticle.cls new file mode 100644 index 0000000..53a1072 --- /dev/null +++ b/static/elsarticle.cls @@ -0,0 +1,1056 @@ +%% +%% This is file `elsarticle.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% elsarticle.dtx (with options: `class') +%% +%% Copyright 2007-2019 Elsevier Ltd +%% +%% This file is part of the 'Elsarticle Bundle'. +%% ------------------------------------------- +%% +%% It may be distributed under the conditions of the LaTeX Project Public +%% License, either version 1.2 of this license or (at your option) any +%% later version. The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.2 or later is part of all distributions of LaTeX +%% version 1999/12/01 or later. +%% +%% The list of all files belonging to the 'Elsarticle Bundle' is +%% given in the file `manifest.txt'. +%% +%% +%% +%% + \def\RCSfile{elsarticle}% + \def\RCSversion{3.2}% + \def\RCSdate{2019/02/25}% + \def\@shortjnl{\relax} + \def\@journal{Elsevier Ltd} + \def\@company{Elsevier Ltd} + \def\@issn{000-0000} + \def\@shortjid{elsarticle} +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{\@shortjid}[\RCSdate, \RCSversion: \@journal] +\def\ABD{\AtBeginDocument} +\newif\ifpreprint \preprintfalse +\newif\ifnonatbib \nonatbibfalse +\newif\iflongmktitle \longmktitlefalse +\newif\ifnopreprintline \nopreprintlinefalse +\newif\ifdoubleblind \doubleblindfalse + +\def\@blstr{1} +\newdimen\@bls +\@bls=\baselineskip + +\def\@finalWarning{% + *****************************************************\MessageBreak + This document is typeset in the CRC style which\MessageBreak + is not suitable for submission.\MessageBreak + \MessageBreak + Please typeset again using 'preprint' option\MessageBreak + for creating PDF suitable for submission.\MessageBreak + ******************************************************\MessageBreak +} + +\DeclareOption{preprint}{\global\preprinttrue + \gdef\@blstr{1}\xdef\jtype{0}% + \AtBeginDocument{\@twosidefalse\@mparswitchfalse}} +\DeclareOption{nopreprintline}{\global\nopreprintlinetrue} +\DeclareOption{final}{\gdef\@blstr{1}\global\preprintfalse} +\DeclareOption{review}{\global\preprinttrue\gdef\@blstr{1.5}} +\DeclareOption{authoryear}{\xdef\@biboptions{round,authoryear}} +\DeclareOption{number}{\xdef\@biboptions{numbers}} +\DeclareOption{numbers}{\xdef\@biboptions{numbers}} +\DeclareOption{nonatbib}{\global\nonatbibtrue} +\DeclareOption{longtitle}{\global\longmktitletrue} +\DeclareOption{5p}{\xdef\jtype{5}\global\preprintfalse + \ExecuteOptions{twocolumn}} + \def\jtype{0} +\DeclareOption{3p}{\xdef\jtype{3}\global\preprintfalse} +\DeclareOption{1p}{\xdef\jtype{1}\global\preprintfalse + \AtBeginDocument{\@twocolumnfalse}} +\DeclareOption{times}{\IfFileExists{txfonts.sty}% + {\AtEndOfClass{\RequirePackage{txfonts}% + \gdef\ttdefault{cmtt}% + \let\iint\relax + \let\iiint\relax + \let\iiiint\relax + \let\idotsint\relax + \let\openbox\relax}}{\AtEndOfClass{\RequirePackage{times}}}} + +\DeclareOption{endfloat}{\IfFileExists{endfloat.sty} + {\AtEndOfClass{\RequirePackage[markers]{endfloat}}}{}} +\DeclareOption{endfloats}{\IfFileExists{endfloat.sty} + {\AtEndOfClass{\RequirePackage[markers]{endfloat}}}{}} +\DeclareOption{numafflabel} + {\AtBeginDocument{\def\theaffn{\arabic{affn}}}} %*% +\DeclareOption{lefttitle} + {\AtBeginDocument{\def\elsarticletitlealign{flushleft}}} %*% +\DeclareOption{centertitle} + {\AtBeginDocument{\def\elsarticletitlealign{center}}} %*% +\DeclareOption{reversenotenum} + {\AtBeginDocument{\def\theaffn{\arabic{affn}} + \def\thefnote{\alph{fnote}}}} +\DeclareOption{doubleblind}{\doubleblindtrue} + +\ExecuteOptions{a4paper,10pt,oneside,onecolumn,number,preprint,centertitle} +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} +\ProcessOptions +\LoadClass{article} +\RequirePackage{graphicx} +\let\comma\@empty +\let\tnotesep\@empty +\let\@title\@empty + +\def\useelstitle{} + +\def\title#1{\g@addto@macro\@title{#1% + \global\let\tnoteref\@gobble}% + \g@addto@macro\useelstitle{#1}} + +\def\elsLabel#1{\@bsphack\protected@write\@auxout{}% + {\string\Newlabel{#1}{\@currentlabel}}\@esphack} +\def\Newlabel#1#2{\expandafter\xdef\csname X@#1\endcsname{#2}} + +\def\elsRef#1{\@ifundefined{X@#1}{0}{\csname X@#1\endcsname}} + +\let\@tnotemark\@empty + +\ifdoubleblind + \def\tnotemark[#1]{} +\else + \def\tnotemark[#1]{\@for\mytmark:=#1\do{% + \expandafter\ifcase\elsRef{\mytmark}\or$^{\star}$\or + $^{,\star\star}$\fi + }% +} +\fi + +\def\tnoteref#1{\tnotemark[{#1}]} +\let\@tnotes\@empty +\newcounter{tnote} +\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{% + \stepcounter{tnote}\elsLabel{#1}% + \def\thefootnote{\ifcase\c@tnote\or$\star$\or$\star\star$\fi}% + \footnotetext{#2}}} + +\let\@nonumnotes\@empty +\def\nonumnote#1{\g@addto@macro\@nonumnotes{% + \let\thefootnote\relax\footnotetext{#1}}} + +\newcounter{fnote} +\def\thefnote{\arabic{fnote}} +\def\fnmark[#1]{\let\comma\@empty + \def\@fnmark{\@for\@@fnmark:=#1\do{% + \edef\fnotenum{\@ifundefined{X@\@@fnmark}{1}{\elsRef{\@@fnmark}}}% + \unskip\comma\fnotenum\let\comma,}}% +} + +\def\fnref#1{\fnmark[#1]} + +\let\@fnotes\@empty\let\@fnmark\@empty +\def\fntext[#1]#2{\g@addto@macro\@fnotes{% + \refstepcounter{fnote}\elsLabel{#1}% + \def\thefootnote{\c@fnote}% + \global\setcounter{footnote}{\c@fnote}% + \footnotetext{#2}}} + +\def\cormark[#1]{\edef\cnotenum{\elsRef{#1}}% + \unskip\textsuperscript{\sep\ifcase\cnotenum\or + $\ast$\or$\ast\ast$\fi\hspace{-1pt}}\let\sep=,} + +\let\@cormark\@empty +\let\@cornotes\@empty +\newcounter{cnote} +\def\cortext[#1]#2{\g@addto@macro\@cornotes{% + \refstepcounter{cnote}\elsLabel{#1}% + \def\thefootnote{\ifcase\thecnote\or$\ast$\or + $\ast\ast$\fi}% + \footnotetext{#2}}} + +\let\@corref\@empty +\def\corref#1{\edef\cnotenum{\elsRef{#1}}% + \edef\@corref{\ifcase\cnotenum\or + $\ast$\or$\ast\ast$\fi\hskip-1pt}} + +\def\resetTitleCounters{\c@cnote=0 + \c@fnote=0 \c@tnote=0 \c@footnote=0} + +\let\eadsep\@empty +\def\@elseads{} +\let\@elsuads\@empty +\let\@cormark\@empty +\def\hashchar{\expandafter\@gobble\string\~} +\def\underscorechar{\expandafter\@gobble\string\_} +\def\lbracechar{\expandafter\@gobble\string\{} +\def\rbracechar{\expandafter\@gobble\string\}} + +\gdef\ead{\@ifnextchar[{\@uad}{\@ead}} +\gdef\@ead#1{\bgroup + \def\_{\underscorechar}% + \def\{{\lbracechar}% + \def~{\hashchar}% + \def\}{\rbracechar}% + \edef\tmp{\the\@eadauthor}% + \immediate\write\@auxout{\string\emailauthor + {#1}{\expandafter\strip@prefix\meaning\tmp}}% + \egroup +} +\newcounter{ead} +\gdef\emailauthor#1#2{\stepcounter{ead}% + \g@addto@macro\@elseads{\raggedright% + \let\corref\@gobble\def\@@tmp{#1}% + \eadsep{\ttfamily\expandafter\strip@prefix\meaning\@@tmp} + (#2)\def\eadsep{\unskip,\space}}% +} +\gdef\@uad[#1]#2{\bgroup + \def~{\hashchar}% + \def\_{\underscorechar}% + \def~{\hashchar}% + \def\}{\rbracechar}% + \edef\tmp{\the\@eadauthor} + \immediate\write\@auxout{\string\urlauthor + {#2}{\expandafter\strip@prefix\meaning\tmp}}% + \egroup +} +\gdef\urlauthor#1#2{\g@addto@macro\@elsuads{\let\corref\@gobble% + \def\@@tmp{#1}\raggedright\eadsep + {\ttfamily\expandafter\strip@prefix\meaning\@@tmp}\space(#2)% + \def\eadsep{\unskip,\space}}% +} + +\def\elsauthors{} +\def\useauthors{} +\def\elsprelimauthors{} + +\def\pprinttitle{} +\let\authorsep\@empty +\let\prelimauthorsep\@empty +\let\sep\@empty +\newcounter{author} +\def\author{\@ifnextchar[{\@@author}{\@author}} + +\newtoks\@eadauthor +\def\@@author[#1]#2{% + \g@addto@macro\elsprelimauthors{% + \prelimauthorsep#2% + \def\prelimauthorsep{\unskip,\space}}% + \g@addto@macro\elsauthors{% + \def\baselinestretch{1}% + \authorsep#2\unskip\textsuperscript{%#1% + \@for\@@affmark:=#1\do{% + \edef\affnum{\@ifundefined{X@\@@affmark}{1}{\elsRef{\@@affmark}}}% + \unskip\sep\affnum\let\sep=,}% + \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi + \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi + }% + \def\authorsep{\unskip,\space}% + \global\let\sep\@empty\global\let\@corref\@empty + \global\let\@fnmark\@empty}% + \@eadauthor={#2}% + \g@addto@macro\useauthors{#2; }% +} + +\def\@author#1{% + \g@addto@macro\elsprelimauthors{% + \prelimauthorsep#1% + \def\prelimauthorsep{\unskip,\space}}% + \g@addto@macro\elsauthors{\normalsize% + \def\baselinestretch{1}% + \upshape\authorsep#1\unskip\textsuperscript{% + \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi + \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi + }% + \def\authorsep{\unskip,\space}% + \global\let\@fnmark\@empty + \global\let\@corref\@empty \global\let\sep\@empty}% + \@eadauthor={#1}% + \g@addto@macro\useauthors{#1; }% +} + +\AtBeginDocument{% + \@ifpackageloaded{hyperref}{% + \expandafter\gdef\csname Hy@title\endcsname{\useelstitle}% + \expandafter\gdef\csname Hy@author\endcsname{\useauthors}% + }{} +} + +\def\elsaddress{} +\def\addsep{\par\vskip6pt} +\def\address{\@ifnextchar[{\@@address}{\@address}} + +\def\@alph#1{% + \ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or + l\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or + y\or z% + \or aa\or ab\or ac\or ad\or ae\or af\or ag\or ah\or ai\or aj\or + ak\or al\or am\or an\or ao\or ap\or aq\or ar\or as\or at\or au\or + av\or aw\or ax\or ay\or az% + \or ba\or bb\or bc\or bd\or be\or bf\or bg\or bh\or bi\or bj\or + bk\or bl\or bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or bu\or + bv\or bw\or bx\or by\or bz% + \or ca\or cb\or cc\or cd\or ce\or cf\or cg\or ch\or ci\or cj\or + ck\or cl\or cm\or cn\or co\or cp\or cq\or cr\or cs\or ct\or cu\or + cv\or cw\or cx\or cy\or cz% + \or da\or db\or dc\or dd\or de\or df\or dg\or dh\or di\or dj\or + dk\or dl\or dm\or dn\or do\or dp\or dq\or dr\or ds\or dt\or du\or + dv\or dw\or dx\or dy\or dz% + \or ea\or eb\or ec\or ed\or ee\or ef\or eg\or eh\or ei\or ej\or + ek\or el\or em\or en\or eo\or ep\or eq\or er\or es\or et\or eu\or + ev\or ew\or ex\or ey\or ez% + \or fa\or fb\or fc\or fd\or fe\or ff\or fg\or fh\or fi\or fj\or + fk\or fl\or fm\or fn\or fo\or fp\or fq\or fr\or fs\or ft\or fu\or + fv\or fw\or fx\or fy\or fz% + \or ga\or gb\or gc\or gd\or ge\or gf\or gg\or gh\or gi\or gj\or + gk\or gl\or gm\or gn\or go\or gp\or gq\or gr\or gs\or gt\or gu\or + gv\or gw\or gx\or gy\or gz% + \else\@ctrerr\fi} + +\newcounter{affn} +\renewcommand\theaffn{\alph{affn}} + +\long\def\@@address[#1]#2{\g@addto@macro\elsaddress{% + \def\baselinestretch{1}% + \refstepcounter{affn} + \xdef\@currentlabel{\theaffn} + \elsLabel{#1}% + \textsuperscript{\theaffn}#2\par}} + +\long\def\@address#1{\g@addto@macro\elsauthors{% + \def\baselinestretch{1}% + \addsep\footnotesize\itshape#1\def\addsep{\par\vskip6pt}% + \def\authorsep{\par\vskip8pt}}} + +\newbox\absbox +\let\@elsarticleabstitle\@empty %*% +\def\abstracttitle#1{\gdef\@elsarticleabstitle{#1}} %*% +\abstracttitle{Abstract} %*% +\renewenvironment{abstract}{\global\setbox\absbox=\vbox\bgroup + \hsize=\textwidth\def\baselinestretch{1}% + \noindent\unskip\textbf{\@elsarticleabstitle} %*% + \par\medskip\noindent\unskip\ignorespaces} + {\egroup} + +\newbox\elsarticlehighlightsbox +\newbox\elsarticlegrabsbox +\def\@elsarticlehighlightstitle{Highlights} +\def\@elsarticlegrabstitle{Graphical Abstract} +\newif\ifelsprelimpagegrabs\global\elsprelimpagegrabsfalse +\newif\ifelsprelimpagehl\global\elsprelimpagehlfalse +\def\elsarticleprelims{% + \ifelsprelimpagegrabs\relax% + \thispagestyle{empty}% + \unvbox\elsarticlegrabsbox% + \pagebreak\clearpage% + \fi% + \ifelsprelimpagehl\relax% + \thispagestyle{empty} + \unvbox\elsarticlehighlightsbox% + \pagebreak\clearpage% + \setcounter{page}{1}% + \fi% +} +\newenvironment{highlights}{% + \global\elsprelimpagehltrue% + \global\setbox\elsarticlehighlightsbox=\vbox\bgroup + \hsize=\textwidth\def\baselinestretch{1}% + \noindent\unskip{\Large\@elsarticlehighlightstitle}%*% + \par\vskip12pt\noindent\unskip\ignorespaces\textbf{\@title}% + \ifx\elsprelimauthors\@empty\relax\else% + \par\vskip6pt\noindent\unskip\ignorespaces\elsprelimauthors% + \fi% + \par\medskip\noindent\unskip\ignorespaces + \begin{itemize} + } + {\end{itemize} + \egroup} +\newenvironment{graphicalabstract}{% + \global\elsprelimpagegrabstrue% + \global\setbox\elsarticlegrabsbox=\vbox\bgroup + \hsize=\textwidth\def\baselinestretch{1}% + \noindent\unskip{\Large\@elsarticlegrabstitle}%*% + \par\vskip12pt\noindent\unskip\ignorespaces\textbf{\@title}% + \ifx\elsprelimauthors\@empty\relax\else% + \par\vskip6pt\noindent\unskip\ignorespaces\elsprelimauthors% + \fi% + \par\medskip\noindent\unskip\ignorespaces} + {\egroup} + +\newbox\keybox +\let\@elsarticlekwdtitle\@empty %*% +\def\keywordtitle#1{\gdef\@elsarticlekwdtitle{#1}} %*% +\def\keywordtitlesep#1{\gdef\@elsarticlekeywordtitlesep{#1}} %*% +\keywordtitle{Keywords} %*% +\keywordtitlesep{:\ } +\def\keyword{% + \def\sep{\unskip, }% + \def\MSC{\@ifnextchar[{\@MSC}{\@MSC[2000]}} + \def\@MSC[##1]{\par\leavevmode\hbox {\it ##1~MSC:\space}}% + \def\PACS{\par\leavevmode\hbox {\it PACS:\space}}% + \def\JEL{\par\leavevmode\hbox {\it JEL:\space}}% + \global\setbox\keybox=\vbox\bgroup\hsize=\textwidth + \normalsize\normalfont\def\baselinestretch{1} + \parskip\z@ + \noindent\textit{\@elsarticlekwdtitle\@elsarticlekeywordtitlesep} + \raggedright % Keywords are not justified. + \ignorespaces} +\def\endkeyword{\par \egroup} + +\newdimen\Columnwidth +\Columnwidth=\columnwidth + +\def\printFirstPageNotes{% + \iflongmktitle + \let\columnwidth=\textwidth + \fi +\ifdoubleblind +\else + \ifx\@tnotes\@empty\else\@tnotes\fi + \ifx\@nonumnotes\@empty\else\@nonumnotes\fi + \ifx\@cornotes\@empty\else\@cornotes\fi + \ifx\@elseads\@empty\relax\else + \let\thefootnote\relax + \footnotetext{\ifnum\theead=1\relax + \textit{Email address:\space}\else + \textit{Email addresses:\space}\fi + \@elseads}\fi + \ifx\@elsuads\@empty\relax\else + \let\thefootnote\relax + \footnotetext{\textit{URL:\space}% + \@elsuads}\fi +\fi + \ifx\@fnotes\@empty\else\@fnotes\fi + \iflongmktitle\if@twocolumn + \let\columnwidth=\Columnwidth\fi\fi +} + +%% Pushing text to begin on newpage %*% +\def\newpage@after@title{title} +\def\newpage@after@author{author} +\def\newpage@after@abstract{abstract} +\def\newpageafter#1% + {\gdef\@elsarticlenewpageafter{#1}} + +\long\def\pprintMaketitle{\clearpage + \iflongmktitle\if@twocolumn\let\columnwidth=\textwidth\fi\fi + \resetTitleCounters + \def\baselinestretch{1}% + \printFirstPageNotes + \begin{\elsarticletitlealign}% + \thispagestyle{pprintTitle}% + \def\baselinestretch{1}% + \Large\@title\par\vskip18pt% + \ifx\@elsarticlenewpageafter\newpage@after@title% %*% + \newpage + \fi% + \ifdoubleblind + \vspace*{2pc} + \else + \normalsize\elsauthors\par\vskip10pt + \footnotesize\itshape\elsaddress\par\vskip36pt + \fi + \ifx\@elsarticlenewpageafter\newpage@after@author% %*% + \newpage + \fi% + \hrule\vskip12pt + \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi + \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi + \hrule\vskip12pt + \ifx\@elsarticlenewpageafter\newpage@after@abstract% %*% + \newpage + \fi% + \end{\elsarticletitlealign}% + \gdef\thefootnote{\arabic{footnote}}% + } + +\def\printWarning{% + \mbox{}\par\vfill\par\bgroup + \fboxsep12pt\fboxrule1pt + \hspace*{.18\textwidth} + \fcolorbox{gray50}{gray10}{\box\warnbox} + \egroup\par\vfill\thispagestyle{empty} + \setcounter{page}{0} + \clearpage} + +\long\def\finalMaketitle{% + \resetTitleCounters + \def\baselinestretch{1}% + \MaketitleBox + \thispagestyle{pprintTitle}% + \gdef\thefootnote{\arabic{footnote}}% + } + +\long\def\MaketitleBox{% + \resetTitleCounters + \def\baselinestretch{1}% + \begin{\elsarticletitlealign}% + \def\baselinestretch{1}% + \Large\@title\par\vskip18pt + \ifdoubleblind + \vspace*{2pc} + \else + \normalsize\elsauthors\par\vskip10pt + \footnotesize\itshape\elsaddress\par\vskip36pt + \fi + \hrule\vskip12pt + \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi + \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi + \hrule\vskip12pt + \end{\elsarticletitlealign}% +} + +\def\FNtext#1{\par\bgroup\footnotesize#1\egroup} +\newdimen\space@left +\def\alarm#1{\typeout{******************************}% + \typeout{#1}% + \typeout{******************************}% +} + +\def\titlespancalculator#1#2#3#4{% + % break count + \@tempcnta=#4\relax% + % pagebreakcount increment + \advance\@tempcnta by 1\relax% + % title page height + \@tempdima=#1\relax% + % Page height - title page notes height (only for first break) + % Page height - textheight (for remaining breaks) + % Page height - title page notes height + \@tempdimb=#2\relax% + % Remaining title page height + \advance\@tempdima -\the\@tempdimb% + % Checks if remaining title page + % height less than textheight + \ifdim\the\@tempdima>#3\relax% + \titlespancalculator% + {\the\@tempdima}{#3}{#3}{\the\@tempcnta}%Break again + \else% + % Save break count and exit. + \xdef\savetitlepagespan{\the\@tempcnta}% + \fi% +}% + +\long\def\myfor#1#2#3{% + \@tempcnta=#1\relax% + \ifnum#1<#2\relax% + \advance\@tempcnta by 1\relax% + #3% + \myfor{\the\@tempcnta}{#2}{#3}% + \fi} + +\long\def\getSpaceLeft{%\global\@twocolumnfalse% + \global\setbox0=\vbox{\hsize=\textwidth\MaketitleBox}% + \global\setbox1=\vbox{\hsize=\textwidth + \let\footnotetext\FNtext + \printFirstPageNotes}% + \xdef\noteheight{\the\ht1}% + \xdef\titleheight{\the\ht0}% + \@tempdima=\vsize + \advance\@tempdima-\noteheight + \advance\@tempdima-1\baselineskip + \xdef\savefpageheight{\the\@tempdima}% + \setbox2=\vbox{\titlespancalculator{\titleheight}% + {\savefpageheight}{\textheight}{0}}% +} + + \skip\footins=24pt + +\newbox\els@boxa +\newbox\els@boxb + +\ifpreprint + \def\maketitle{\elsarticleprelims\pprintMaketitle} + \else + \ifnum\jtype=1 + \def\maketitle{% + \elsarticleprelims% + \iflongmktitle\getSpaceLeft + \ifdim\noteheight>0pt% + \advance\@tempdima-1.35\baselineskip + \fi% + \global\setbox\els@boxa=\vsplit0 to \@tempdima + \box\els@boxa\par\resetTitleCounters + \thispagestyle{pprintTitle}% + \printFirstPageNotes + \ifnum\savetitlepagespan>1\relax% + \myfor{2}{\savetitlepagespan}{% + \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima + \box\els@boxb} + \else% + \fi% + \box0% + \else + \finalMaketitle\printFirstPageNotes + \fi + \gdef\thefootnote{\arabic{footnote}}}% + \else + \ifnum\jtype=5 + \def\maketitle{% + \elsarticleprelims% + \iflongmktitle\getSpaceLeft + \ifdim\noteheight>0pt% + \advance\@tempdima-1.35\baselineskip + \fi% + \global\setbox\els@boxa=\vsplit0 to \@tempdima + \box\els@boxa\par\resetTitleCounters + \thispagestyle{pprintTitle}% + \printFirstPageNotes + \ifnum\savetitlepagespan>1\relax% + \myfor{2}{\savetitlepagespan}{% + \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima + \twocolumn[\box\els@boxb]} + \else% + \fi% + \twocolumn[\box0]%\printFirstPageNotes + \else + \twocolumn[\finalMaketitle]\printFirstPageNotes + \fi + \gdef\thefootnote{\arabic{footnote}}} + \else + \if@twocolumn + \def\maketitle{% + \elsarticleprelims% + \iflongmktitle\getSpaceLeft + \ifdim\noteheight>0pt% + \advance\@tempdima-1.35\baselineskip + \fi% + \global\setbox\els@boxa=\vsplit0 to \@tempdima + \box\els@boxa\par\resetTitleCounters + \thispagestyle{pprintTitle}% + \printFirstPageNotes + \ifnum\savetitlepagespan>1\relax% + \myfor{2}{\savetitlepagespan}{% + \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima + \twocolumn[\box\els@boxb]} + \else% + \fi% + \twocolumn[\box0]% + \else + \twocolumn[\finalMaketitle]\printFirstPageNotes + \fi + \gdef\thefootnote{\arabic{footnote}}}% + \else + \def\maketitle{% + \elsarticleprelims% + \iflongmktitle\getSpaceLeft + \ifdim\noteheight>0pt% + \advance\@tempdima-1.35\baselineskip + \fi% + \global\setbox\els@boxa=\vsplit0 to \@tempdima + \box\els@boxa\par\resetTitleCounters + \thispagestyle{pprintTitle}% + \printFirstPageNotes + \ifnum\savetitlepagespan>1\relax% + \myfor{2}{\savetitlepagespan}{% + \global\setbox\els@boxb=\vsplit0 to \textheight%\@tempdima + \box\els@boxb} + \else% + \fi% + \box0% + \else + \elsarticleprelims% + \finalMaketitle\printFirstPageNotes + \fi + \gdef\thefootnote{\arabic{footnote}}}% + \fi + \fi + \fi +\fi + +\let\@elsarticlemyfooter\@empty +\let\@elsarticlemyfooteralign\@empty +\def\@elsarticlemyfooteralignleft{L} +\def\@elsarticlemyfooteralignright{R} +\def\@elsarticlemyfooteraligncenter{C} + +\def\myfooter[#1]#2 %*% + {\gdef\@elsarticlemyfooteralign{#1} + \gdef\@elsarticlemyfooter{#2}} + +\def\myfooterfont#1{\gdef\@myfooterfont{#1}} +\myfooterfont{\footnotesize\itshape} +\def\ps@pprintTitle{% + \let\@oddhead\@empty + \let\@evenhead\@empty + \def\@oddfoot + {\hbox to \textwidth% + {\ifnopreprintline\relax\else + \@myfooterfont% + \ifx\@elsarticlemyfooteralign\@elsarticlemyfooteraligncenter% + \hfil\@elsarticlemyfooter\hfil% + \else% + \ifx\@elsarticlemyfooteralign\@elsarticlemyfooteralignleft% + \@elsarticlemyfooter\hfill{}% + \else% + \ifx\@elsarticlemyfooteralign\@elsarticlemyfooteralignright% + {}\hfill\@elsarticlemyfooter% + \else% + Preprint submitted to \ifx\@journal\@empty% + Elsevier% + \else\@journal\fi\hfill\@date\fi% + \fi% + \fi% + \fi% + } + }% + \let\@evenfoot\@oddfoot} +\def\@seccntDot{.} +\def\@seccntformat#1{\csname the#1\endcsname\@seccntDot\hskip 0.5em} + +\renewcommand\section{\@startsection {section}{1}{\z@}% + {18\p@ \@plus 6\p@ \@minus 3\p@}% + {9\p@ \@plus 6\p@ \@minus 3\p@}% + {\normalsize\bfseries\boldmath}} +\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% + {12\p@ \@plus 6\p@ \@minus 3\p@}% + {3\p@ \@plus 6\p@ \@minus 3\p@}% + {\normalfont\normalsize\itshape}} +\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {12\p@ \@plus 6\p@ \@minus 3\p@}% + {\p@}% + {\normalfont\normalsize\itshape}} + +\def\paragraph{\secdef{\els@aparagraph}{\els@bparagraph}} +\def\els@aparagraph[#1]#2{\elsparagraph[#1]{#2.}} +\def\els@bparagraph#1{\elsparagraph*{#1.}} + +\newcommand\elsparagraph{\@startsection{paragraph}{4}{0\z@}% + {10\p@ \@plus 6\p@ \@minus 3\p@}% + {-6\p@}% + {\normalfont\itshape}} +\newdimen\leftMargin +\leftMargin=2em +\newtoks\@enLab %\newtoks\@enfont +\def\@enQmark{?} +\def\@enLabel#1#2{% + \edef\@enThe{\noexpand#1{\@enumctr}}% + \@enLab\expandafter{\the\@enLab\csname the\@enumctr\endcsname}% + \@enloop} +\def\@enSpace{\afterassignment\@enSp@ce\let\@tempa= } +\def\@enSp@ce{\@enLab\expandafter{\the\@enLab\space}\@enloop} +\def\@enGroup#1{\@enLab\expandafter{\the\@enLab{#1}}\@enloop} +\def\@enOther#1{\@enLab\expandafter{\the\@enLab#1}\@enloop} +\def\@enloop{\futurelet\@entemp\@enloop@} +\def\@enloop@{% + \ifx A\@entemp \def\@tempa{\@enLabel\Alph }\else + \ifx a\@entemp \def\@tempa{\@enLabel\alph }\else + \ifx i\@entemp \def\@tempa{\@enLabel\roman }\else + \ifx I\@entemp \def\@tempa{\@enLabel\Roman }\else + \ifx 1\@entemp \def\@tempa{\@enLabel\arabic}\else + \ifx \@sptoken\@entemp \let\@tempa\@enSpace \else + \ifx \bgroup\@entemp \let\@tempa\@enGroup \else + \ifx \@enum@\@entemp \let\@tempa\@gobble \else + \let\@tempa\@enOther + \fi\fi\fi\fi\fi\fi\fi\fi + \@tempa} +\newlength{\@sep} \newlength{\@@sep} +\setlength{\@sep}{.5\baselineskip plus.2\baselineskip + minus.2\baselineskip} +\setlength{\@@sep}{.1\baselineskip plus.01\baselineskip + minus.05\baselineskip} +\providecommand{\sfbc}{\rmfamily\upshape} +\providecommand{\sfn}{\rmfamily\upshape} +\def\@enfont{\ifnum \@enumdepth >1\let\@nxt\sfn \else\let\@nxt\sfbc \fi\@nxt} +\def\enumerate{% + \ifnum \@enumdepth >3 \@toodeep\else + \advance\@enumdepth \@ne + \edef\@enumctr{enum\romannumeral\the\@enumdepth}\fi + \@ifnextchar[{\@@enum@}{\@enum@}} +\def\@@enum@[#1]{% + \@enLab{}\let\@enThe\@enQmark + \@enloop#1\@enum@ + \ifx\@enThe\@enQmark\@warning{The counter will not be printed.% + ^^J\space\@spaces\@spaces\@spaces The label is: \the\@enLab}\fi + \expandafter\edef\csname label\@enumctr\endcsname{\the\@enLab}% + \expandafter\let\csname the\@enumctr\endcsname\@enThe + \csname c@\@enumctr\endcsname7 + \expandafter\settowidth + \csname leftmargin\romannumeral\@enumdepth\endcsname + {\the\@enLab\hskip\labelsep}% + \@enum@} +\def\@enum@{\list{{\@enfont\csname label\@enumctr\endcsname}}% + {\usecounter{\@enumctr}\def\makelabel##1{\hss\llap{##1}}% + \ifnum \@enumdepth>1\setlength{\topsep}{\@@sep}\else + \setlength{\topsep}{\@sep}\fi + \ifnum \@enumdepth>1\setlength{\itemsep}{0pt plus1pt minus1pt}% + \else \setlength{\itemsep}{\@@sep}\fi + %\setlength\leftmargin{\leftMargin}%%%{1.8em} + \setlength{\parsep}{0pt plus1pt minus1pt}% + \setlength{\parskip}{0pt plus1pt minus1pt} + }} + +\def\endenumerate{\par\ifnum \@enumdepth >1\addvspace{\@@sep}\else + \addvspace{\@sep}\fi \endlist} + +\def\sitem{\@noitemargtrue\@item[\@itemlabel *]} + +\def\itemize{\@ifnextchar[{\@Itemize}{\@Itemize[]}} + +\def\@Itemize[#1]{\def\next{#1}% + \ifnum \@itemdepth >\thr@@\@toodeep\else + \advance\@itemdepth\@ne + \ifx\next\@empty\else\expandafter\def\csname + labelitem\romannumeral\the\@itemdepth\endcsname{#1}\fi% + \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% + \expandafter\list\csname\@itemitem\endcsname + {\def\makelabel##1{\hss\llap{##1}}}% + \fi} +\def\newdefinition#1{% + \@ifnextchar[{\@odfn{#1}}{\@ndfn{#1}}}%] +\def\@ndfn#1#2{% + \@ifnextchar[{\@xndfn{#1}{#2}}{\@yndfn{#1}{#2}}} +\def\@xndfn#1#2[#3]{% + \expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@newctr{#1}[#3]% + \expandafter\xdef\csname the#1\endcsname{% + \expandafter\noexpand\csname the#3\endcsname \@dfncountersep + \@dfncounter{#1}}% + \global\@namedef{#1}{\@dfn{#1}{#2}}% + \global\@namedef{end#1}{\@enddefinition}}} +\def\@yndfn#1#2{% + \expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@dfncounter{#1}}% + \global\@namedef{#1}{\@dfn{#1}{#2}}% + \global\@namedef{end#1}{\@enddefinition}}} +\def\@odfn#1[#2]#3{% + \@ifundefined{c@#2}{\@nocounterr{#2}}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{the#1}{\@nameuse{the#2}} + \global\@namedef{#1}{\@dfn{#2}{#3}}% + \global\@namedef{end#1}{\@enddefinition}}}} +\def\@dfn#1#2{% + \refstepcounter{#1}% + \@ifnextchar[{\@ydfn{#1}{#2}}{\@xdfn{#1}{#2}}} +\def\@xdfn#1#2{% + \@begindefinition{#2}{\csname the#1\endcsname}\ignorespaces} +\def\@ydfn#1#2[#3]{% + \@opargbegindefinition{#2}{\csname the#1\endcsname}{#3}\ignorespaces} +\def\@dfncounter#1{\noexpand\arabic{#1}} +\def\@dfncountersep{.} +\def\@begindefinition#1#2{\trivlist + \item[\hskip\labelsep{\bfseries #1\ #2.}]\upshape} +\def\@opargbegindefinition#1#2#3{\trivlist + \item[\hskip\labelsep{\bfseries #1\ #2\ (#3).}]\upshape} +\def\@enddefinition{\endtrivlist} + +\def\@begintheorem#1#2{\trivlist + \let\baselinestretch\@blstr + \item[\hskip \labelsep{\bfseries #1\ #2.}]\itshape} +\def\@opargbegintheorem#1#2#3{\trivlist + \let\baselinestretch\@blstr + \item[\hskip \labelsep{\bfseries #1\ #2\ (#3).}]\itshape} + +\def\newproof#1{% + \@ifnextchar[{\@oprf{#1}}{\@nprf{#1}}} +\def\@nprf#1#2{% + \@ifnextchar[{\@xnprf{#1}{#2}}{\@ynprf{#1}{#2}}} +\def\@xnprf#1#2[#3]{% + \expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@newctr{#1}[#3]% + \expandafter\xdef\csname the#1\endcsname{% + \expandafter\noexpand\csname the#3\endcsname \@prfcountersep + \@prfcounter{#1}}% + \global\@namedef{#1}{\@prf{#1}{#2}}% + \global\@namedef{end#1}{\@endproof}}} +\def\@ynprf#1#2{% + \expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@prfcounter{#1}}% + \global\@namedef{#1}{\@prf{#1}{#2}}% + \global\@namedef{end#1}{\@endproof}}} +\def\@oprf#1[#2]#3{% + \@ifundefined{c@#2}{\@nocounterr{#2}}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{the#1}{\@nameuse{the#2}}% + \global\@namedef{#1}{\@prf{#2}{#3}}% + \global\@namedef{end#1}{\@endproof}}}} +\def\@prf#1#2{% + \refstepcounter{#1}% + \@ifnextchar[{\@yprf{#1}{#2}}{\@xprf{#1}{#2}}} +\def\@xprf#1#2{% + \@beginproof{#2}{\csname the#1\endcsname}\ignorespaces} +\def\@yprf#1#2[#3]{% + \@opargbeginproof{#2}{\csname the#1\endcsname}{#3}\ignorespaces} +\def\@prfcounter#1{\noexpand\arabic{#1}} +\def\@prfcountersep{.} +\def\@beginproof#1#2{\trivlist\let\baselinestretch\@blstr + \item[\hskip \labelsep{\scshape #1.}]\rmfamily} +\def\@opargbeginproof#1#2#3{\trivlist\let\baselinestretch\@blstr + \item[\hskip \labelsep{\scshape #1\ (#3).}]\rmfamily} +\def\@endproof{\endtrivlist} +\newcommand*{\qed}{\hbox{}\hfill$\Box$} + +\@ifundefined{@biboptions}{\xdef\@biboptions{numbers}}{} +\InputIfFileExists{\jobname.spl}{}{} +\ifnonatbib\relax\else + \RequirePackage[\@biboptions]{natbib} +\fi +\newwrite\splwrite +\immediate\openout\splwrite=\jobname.spl +\def\biboptions#1{\def\next{#1}\immediate\write\splwrite{% + \string\g@addto@macro\string\@biboptions{% + ,\expandafter\strip@prefix\meaning\next}}} + +\let\baselinestretch=\@blstr +\ifnum\jtype=1 + \RequirePackage{geometry} + \geometry{twoside, + paperwidth=210mm, + paperheight=297mm, + textheight=562pt, + textwidth=384pt, + centering, + headheight=50pt, + headsep=12pt, + footskip=12pt, + footnotesep=24pt plus 2pt minus 12pt, + } + \global\let\bibfont=\footnotesize + \global\bibsep=0pt + \if@twocolumn\global\@twocolumnfalse\fi +\else\ifnum\jtype=3 + \RequirePackage{geometry} + \geometry{twoside, + paperwidth=210mm, + paperheight=297mm, + textheight=622pt, + textwidth=468pt, + centering, + headheight=50pt, + headsep=12pt, + footskip=18pt, + footnotesep=24pt plus 2pt minus 12pt, + columnsep=2pc + } + \global\let\bibfont=\footnotesize + \global\bibsep=0pt + \if@twocolumn\input{fleqn.clo}\fi +\else\ifnum\jtype=5 + \RequirePackage{geometry} + \geometry{twoside, + paperwidth=210mm, + paperheight=297mm, + textheight=682pt, + textwidth=522pt, + centering, + headheight=50pt, + headsep=12pt, + footskip=18pt, + footnotesep=24pt plus 2pt minus 12pt, + columnsep=18pt + }% + \global\let\bibfont=\footnotesize + \global\bibsep=0pt + \input{fleqn.clo} + \global\@twocolumntrue +%% +%% End of option '5p' +%% +\fi\fi\fi +\def\journal#1{\gdef\@journal{#1}} + \let\@journal\@empty +\newenvironment{frontmatter}{}{\maketitle} + +\long\def\@makecaption#1#2{% + \vskip\abovecaptionskip\footnotesize + \sbox\@tempboxa{#1: #2}% + \ifdim \wd\@tempboxa >\hsize + #1: #2\par + \else + \global \@minipagefalse + \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip\belowcaptionskip} + +\AtBeginDocument{\@ifpackageloaded{hyperref} + {\def\@linkcolor{blue} + \def\@anchorcolor{blue} + \def\@citecolor{blue} + \def\@filecolor{blue} + \def\@urlcolor{blue} + \def\@menucolor{blue} + \def\@pagecolor{blue} +\begingroup + \@makeother\`% + \@makeother\=% + \edef\x{% + \edef\noexpand\x{% + \endgroup + \noexpand\toks@{% + \catcode 96=\noexpand\the\catcode`\noexpand\`\relax + \catcode 61=\noexpand\the\catcode`\noexpand\=\relax + }% + }% + \noexpand\x + }% +\x +\@makeother\` +\@makeother\= +}{}} +%% +\def\appendixname{Appendix } +\renewcommand\appendix{\par + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \setcounter{equation}{0} + \gdef\thefigure{\@Alph\c@section.\arabic{figure}}% + \gdef\thetable{\@Alph\c@section.\arabic{table}}% + \gdef\thesection{\appendixname~\@Alph\c@section}% + \@addtoreset{equation}{section}% + \gdef\theequation{\@Alph\c@section.\arabic{equation}}% + \addtocontents{toc}{\string\let\string\numberline\string\tmptocnumberline}{}{} +} + +%%%% \numberline width calculation for appendix. +\newdimen\appnamewidth +\def\tmptocnumberline#1{% + \setbox0=\hbox{\appendixname} + \appnamewidth=\wd0 + \addtolength\appnamewidth{2.5pc} + \hb@xt@\appnamewidth{#1\hfill} +} + +%% Added for work with amsrefs.sty + +\@ifpackageloaded{amsrefs}% + {} + {%\let\bibsection\relax% + \AtBeginDocument{\def\cites@b#1#2,#3{% + \begingroup[% + \toks@{\InnerCite{#2}#1}% + \ifx\@empty#3\@xp\@gobble\fi + \cites@c#3% +}}} +%% +%% Added for avoiding clash with cleveref.sty +\@ifpackageloaded{cleveref}% + {} + {\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{% + \refstepcounter{tnote}% + \immediate\write\@auxout{\string\Newlabel{#1}{\thetnote}} + \def\thefootnote{\ifcase\c@tnote\or$\star$\or$\star\star$\fi}% + \footnotetext{#2}}} +%%% + \def\fntext[#1]#2{\g@addto@macro\@fnotes{% + \refstepcounter{fnote}% + \immediate\write\@auxout{\string\Newlabel{#1}{\thefnote}} + \def\thefootnote{\thefnote}% + \global\setcounter{footnote}{\c@fnote}% + \footnotetext{#2}}} +%%% + \def\cortext[#1]#2{\g@addto@macro\@cornotes{% + \refstepcounter{cnote}% + \immediate\write\@auxout{\string\Newlabel{#1}{\thecnote}} + \def\thefootnote{\ifcase\c@cnote\or$\ast$\or + $\ast\ast$\fi}% + \footnotetext{#2}}} +} + +\def\textmarker#1#2{\textcolor{#1}{#2}}%*% +\endinput +%% +%% End of file `elsarticle.cls'. diff --git a/tex/glossary.tex b/tex/glossary.tex new file mode 100644 index 0000000..5a69948 --- /dev/null +++ b/tex/glossary.tex @@ -0,0 +1 @@ +\printglossaries \ No newline at end of file diff --git a/tex/meta.tex b/tex/meta.tex new file mode 100644 index 0000000..d944b33 --- /dev/null +++ b/tex/meta.tex @@ -0,0 +1,47 @@ +\begin{frontmatter} + +\journal{Transportation Research Part E} +\title{Real-time Demand Forecasting for an Urban Delivery Platform} + +\author[WHU]{Alexander Hess\fnref{emails}} +\author[WHU]{Stefan Spinler\fnref{emails}} +\author[MIT]{Matthias Winkenbach\fnref{emails}} +\address[WHU]{ +WHU - Otto Beisheim School of Management, +Burgplatz 2, 56179 Vallendar, Germany +} +\address[MIT]{ +Massachusetts Institute of Technology, +77 Massachusetts Avenue, Cambridge, MA 02139, United States +} +\fntext[email]{ +Emails: + alexander.hess@whu.edu, + stefan.spinler@whu.edu, + mwinkenb@mit.edu +} + +\begin{abstract} +Meal delivery platforms like Uber Eats shape the landscape in cities around the world. +This paper addresses forecasting demand into the short-term future. +We propose an approach incorporating + both classical forecasting + and machine learning methods. +Model evaluation and selection is adapted to demand typical for such a platform + (i.e., intermittent with a double-seasonal pattern). +The results of an empirical study with a European meal delivery service show + that machine learning models become competitive + once the average daily demand passes a threshold. +As a main contribution, the paper explains + how a forecasting system must be set up + to enable predictive routing. +\end{abstract} + +\begin{keyword} +demand forecasting \sep +intermittent demand \sep +machine learning \sep +urban delivery platform +\end{keyword} + +\end{frontmatter} \ No newline at end of file diff --git a/tex/preamble.tex b/tex/preamble.tex new file mode 100644 index 0000000..7fcd468 --- /dev/null +++ b/tex/preamble.tex @@ -0,0 +1,2 @@ +\usepackage[acronym]{glossaries} +\makeglossaries \ No newline at end of file diff --git a/tex/references.bib b/tex/references.bib new file mode 100644 index 0000000..e69de29 From 1d054b978044811e15585c211c8327d44f2b8231 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 4 Oct 2020 21:35:46 +0200 Subject: [PATCH 02/28] Hide built artifacts --- .gitignore | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100644 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..28766eb --- /dev/null +++ b/.gitignore @@ -0,0 +1,9 @@ +*.acn +*.aux +*.bbl +*.blg +*.glo +*.ist +*.log +*.spl +*.synctex.gz From 526135106faf8a82b1c828abe7a806162de04230 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 4 Oct 2020 21:47:28 +0200 Subject: [PATCH 03/28] Add section titles --- paper.tex | 7 ++++++- tex/1_intro.tex | 2 ++ tex/2_lit/1_intro.tex | 2 ++ tex/3_mod/1_intro.tex | 2 ++ tex/4_stu/1_intro.tex | 2 ++ tex/5_con/1_intro.tex | 2 ++ 6 files changed, 16 insertions(+), 1 deletion(-) create mode 100644 tex/1_intro.tex create mode 100644 tex/2_lit/1_intro.tex create mode 100644 tex/3_mod/1_intro.tex create mode 100644 tex/4_stu/1_intro.tex create mode 100644 tex/5_con/1_intro.tex diff --git a/paper.tex b/paper.tex index a7f42bd..d445c71 100644 --- a/paper.tex +++ b/paper.tex @@ -7,7 +7,12 @@ \input{tex/meta} \newpage -Lorem ipsum. +\input{tex/1_intro} +\input{tex/2_lit/1_intro} +\input{tex/3_mod/1_intro} +\input{tex/4_stu/1_intro} +\input{tex/5_con/1_intro} + \newpage \input{tex/glossary} diff --git a/tex/1_intro.tex b/tex/1_intro.tex new file mode 100644 index 0000000..3c74279 --- /dev/null +++ b/tex/1_intro.tex @@ -0,0 +1,2 @@ +\section{Introduction} +\label{intro} \ No newline at end of file diff --git a/tex/2_lit/1_intro.tex b/tex/2_lit/1_intro.tex new file mode 100644 index 0000000..e875a28 --- /dev/null +++ b/tex/2_lit/1_intro.tex @@ -0,0 +1,2 @@ +\section{Literature Review} +\label{lit} \ No newline at end of file diff --git a/tex/3_mod/1_intro.tex b/tex/3_mod/1_intro.tex new file mode 100644 index 0000000..bf72f24 --- /dev/null +++ b/tex/3_mod/1_intro.tex @@ -0,0 +1,2 @@ +\section{Model Formulation} +\label{mod} \ No newline at end of file diff --git a/tex/4_stu/1_intro.tex b/tex/4_stu/1_intro.tex new file mode 100644 index 0000000..4a28425 --- /dev/null +++ b/tex/4_stu/1_intro.tex @@ -0,0 +1,2 @@ +\section{Empirical Study: A Meal Delivery Platform in Europe} +\label{stu} \ No newline at end of file diff --git a/tex/5_con/1_intro.tex b/tex/5_con/1_intro.tex new file mode 100644 index 0000000..42126bd --- /dev/null +++ b/tex/5_con/1_intro.tex @@ -0,0 +1,2 @@ +\section{Conclusion} +\label{con} \ No newline at end of file From 5578802e37ba27d923c398052cb9022ca3d9bd93 Mon Sep 17 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z#0EzhV{=-WNz`60SN-qdV&}f%b5!}G(W5xs;@j?Vevb(4d$#|Tjq!s1g@Wj5KrQir z@{Sfz4}c*Ez{_QX2h_Cjfyp2`_U2M zXYMCY>DA6w@2{~CF? ai Date: Sun, 4 Oct 2020 22:24:38 +0200 Subject: [PATCH 05/28] Add Introduction section --- tex/1_intro.tex | 102 ++++++++++++++++++++++++++++++++++++++++++++- tex/glossary.tex | 11 +++++ tex/preamble.tex | 9 +++- tex/references.bib | 85 +++++++++++++++++++++++++++++++++++++ 4 files changed, 205 insertions(+), 2 deletions(-) diff --git a/tex/1_intro.tex b/tex/1_intro.tex index 3c74279..87d0171 100644 --- a/tex/1_intro.tex +++ b/tex/1_intro.tex @@ -1,2 +1,102 @@ \section{Introduction} -\label{intro} \ No newline at end of file +\label{intro} + +In recent years, many meal delivery platform providers (e.g., Uber Eats, + GrubHub, DoorDash, Deliveroo) with different kinds of business models have + entered the markets in cities around the world. +A study by \cite{hirschberg2016} estimates the global market size to surpass + 20 billion Dollars by 2025. +A common feature of these platforms is that they do not operate kitchens but + focus on marketing their partner restaurants' meals, unifying all order + related processes in simple smartphone apps, and managing the delivery via + a fleet of either employees or crowd-sourced sub-contractors. + +Various kind of urban delivery platforms (UDP) have received attention in + recent scholarly publications. +\cite{hou2018} look into heuristics to simultaneously optimize courier + scheduling and routing in general, while \cite{masmoudi2018} do so + for the popular dial-a-ride problem and \cite{wang2018} investigate + the effect of different fulfillment strategies in the context of urban + meal delivery. +\cite{ehmke2018} and \cite{alcaraz2019} focus their research on the routing + aspect, which is commonly modeled as a so-called vehicle routing problem + (\gls{vrp}). + +Not covered in the recent literature is research focusing on the demand + forecasting problem a UDP faces. +Due to the customers' fragmented locations and the majority of the orders + occurring ad-hoc for immediate delivery in the case of a meal delivery + platform, forecasting demand for the near future (i.e., several hours) + and distinct locations of the city in real-time is an essential factor + in achieving timely fulfillment. +In general, demand forecasting is a well-researched discipline with a + decades-long history in scholarly journals as summarized, for example, by + \cite{de2006}. +Even some meal delivery platforms themselves publish their practices: For + example, \cite{bell2018} provide a general overview of supply and demand + forecasting at Uber and benchmarks of the methods used while + \cite{laptev2017} investigate how extreme events can be incorporated. + +The conditions such platforms face are not limited to meal delivery: + Any entity that performs ad-hoc requested point-to-point transportation at + scale in an urban area benefits from a robust forecasting system. +Examples include ride-hailing, such as the original Uber offering, or bicycle + courier services. +The common characteristics are: +\begin{itemize} +\item \textbf{Geospatial Slicing}: + Forecasts for distinct parts of a city in parallel +\item \textbf{Temporal Slicing}: + Forecasts on a sub-daily basis (e.g., 60-minute windows) +\item \textbf{Order Sparsity}: + The historical order time series exhibit an intermittent pattern +\item \textbf{Double Seasonality}: + Demand varies with the day of the week and the time of day +\end{itemize} +Whereas the first two points can be assumed to vary with the concrete + application's requirements, it is the last two that pose challenges for + forecasting a platform's demand: +Intermittent demand (i.e., many observations in the historic order time series + exhibit no demand at all) renders most of the commonly applied error + metrics useless. +Moreover, many of the established forecasting methods can only handle a single + and often low seasonality (i.e., repeated regular pattern), if at all. + +In this paper, we develop a rigorous methodology as to how to build and + evaluate a robust forecasting system for an urban delivery platform + (\gls{udp}) that offers ad-hoc point-to-point transportation of any kind. +We implement such a system with a broad set of commonly used forecasting + methods. +We not only apply established (i.e., "classical") time series methods but also + machine learning (\gls{ml}) models that have gained traction in recent + years due to advancements in computing power and availability of larger + amounts of data. +In that regard, the classical methods serve as benchmarks for the ML methods. +Our system is trained on and evaluated with a dataset obtained from an + undisclosed industry partner that, during the timeframe of our study, was + active in several European countries and, in particular, in France. +Its primary business strategy is the delivery of meals from upper-class + restaurants to customers in their home or work places via bicycles. +In this empirical study, we identify the best-performing methods. +Thus, we answer the following research questions: +\begin{enumerate} +\item[\textbf{Q1}:] + Which forecasting methods work best under what circumstances? +\item[\textbf{Q2}:] + How do classical forecasting methods compare with ML models? +\item[\textbf{Q3}:] + How does the forecast accuracy change with more historic data available? +\item[\textbf{Q4}:] + Can real-time information on demand be exploited? +\item[\textbf{Q5}:] + Can external data (e.g., weather data) improve the forecast accuracy? +\end{enumerate} +To the best of our knowledge, no such study has yet been published in a + scholarly journal. + +The subsequent Section \ref{lit} reviews the literature on the forecasting + methods included in the system. +Section \ref{mod} introduces our forecasting system, and Section \ref{stu} + discusses the results obtained in the empirical study. +Lastly, Section \ref{con} summarizes our findings and concludes + with an outlook on further research opportunities. \ No newline at end of file diff --git a/tex/glossary.tex b/tex/glossary.tex index 5a69948..b34e1b9 100644 --- a/tex/glossary.tex +++ b/tex/glossary.tex @@ -1 +1,12 @@ +% Abbreviations for technical terms. +\newglossaryentry{ml}{ + name=ML, description={Machine Learning} +} +\newglossaryentry{udp}{ + name=UDP, description={Urban Delivery Platform} +} +\newglossaryentry{vrp}{ + name=VRP, description={Vehicle Routing Problem} +} + \printglossaries \ No newline at end of file diff --git a/tex/preamble.tex b/tex/preamble.tex index 7fcd468..bc34c42 100644 --- a/tex/preamble.tex +++ b/tex/preamble.tex @@ -1,2 +1,9 @@ +% Use the document width more effectively. +\usepackage[margin=2.5cm]{geometry} + \usepackage[acronym]{glossaries} -\makeglossaries \ No newline at end of file +\makeglossaries + +% Make opening quotes look different than closing quotes. +\usepackage[english=american]{csquotes} +\MakeOuterQuote{"} \ No newline at end of file diff --git a/tex/references.bib b/tex/references.bib index e69de29..be2c815 100644 --- a/tex/references.bib +++ b/tex/references.bib @@ -0,0 +1,85 @@ +@article{alcaraz2019, +title={Rich vehicle routing problem with last-mile outsourcing decisions}, +author={Alcaraz, Juan J and Caballero-Arnaldos, Luis and Vales-Alonso, Javier}, +year={2019}, +journal={Transportation Research Part E: Logistics and Transportation Review}, +volume={129}, +pages={263--286} +} + +@misc{bell2018, +title = {Forecasting at Uber: An Introduction}, +author={Bell, Franziska and Smyl, Slawek}, +year={2018}, +howpublished = {\url{https://eng.uber.com/forecasting-introduction/}}, +note = {Accessed: 2020-10-01} +} + +@article{de2006, +title={25 Years of Time Series Forecasting}, +author={De Gooijer, Jan and Hyndman, Rob}, +year={2006}, +journal={International Journal of Forecasting}, +volume={22}, +number={3}, +pages={443--473} +} + +@article{ehmke2018, +title={Optimizing for total costs in vehicle routing in urban areas}, +author={Ehmke, Jan Fabian and Campbell, Ann M and Thomas, Barrett W}, +year={2018}, +journal={Transportation Research Part E: Logistics and Transportation Review}, +volume={116}, +pages={242--265} +} + +@misc{hirschberg2016, +title = {McKinsey: The changing market for food delivery}, +author={Hirschberg, Carsten and Rajko, Alexander and Schumacher, Thomas + and Wrulich, Martin}, +year={2016}, +howpublished = "\url{https://www.mckinsey.com/industries/high-tech/ + our-insights/the-changing-market-for-food-delivery}", +note = {Accessed: 2020-10-01} +} + +@article{hou2018, +title={Ride-matching and routing optimisation: Models and a large + neighbourhood search heuristic}, +author={Hou, Liwen and Li, Dong and Zhang, Dali}, +year={2018}, +journal={Transportation Research Part E: Logistics and Transportation Review}, +volume={118}, +pages={143--162} +} + +@misc{laptev2017, +title = {Engineering Extreme Event Forecasting + at Uber with Recurrent Neural Networks}, +author={Laptev, Nikolay and Smyl, Slawek and Shanmugam, Santhosh}, +year={2017}, +howpublished = {\url{https://eng.uber.com/neural-networks/}}, +note = {Accessed: 2020-10-01} +} + +@article{masmoudi2018, +title={The dial-a-ride problem with electric vehicles and battery + swapping stations}, +author={Masmoudi, Mohamed Amine and Hosny, Manar and Demir, Emrah + and Genikomsakis, Konstantinos N and Cheikhrouhou, Naoufel}, +year={2018}, +journal={Transportation research part E: logistics and transportation review}, +volume={118}, +pages={392--420} +} + +@article{wang2018, +title={Delivering meals for multiple suppliers: Exclusive or sharing + logistics service}, +author={Wang, Zheng}, +year={2018}, +journal={Transportation Research Part E: Logistics and Transportation Review}, +volume={118}, +pages={496--512} +} \ No newline at end of file From e146bbdf786d904182c22d09d8175c65879eb7c9 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 4 Oct 2020 22:24:59 +0200 Subject: [PATCH 06/28] Hide built artifacts --- 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Sun, 4 Oct 2020 23:00:15 +0200 Subject: [PATCH 08/28] Add Literature section --- paper.tex | 9 + tex/2_lit/1_intro.tex | 17 +- tex/2_lit/2_class/1_intro.tex | 13 ++ tex/2_lit/2_class/2_ets.tex | 78 +++++++ tex/2_lit/2_class/3_arima.tex | 69 +++++++ tex/2_lit/2_class/4_stl.tex | 62 ++++++ tex/2_lit/3_ml/1_intro.tex | 15 ++ tex/2_lit/3_ml/2_learning.tex | 53 +++++ tex/2_lit/3_ml/3_cv.tex | 38 ++++ tex/2_lit/3_ml/4_rf.tex | 66 ++++++ tex/2_lit/3_ml/5_svm.tex | 60 ++++++ tex/3_mod/1_intro.tex | 8 +- tex/glossary.tex | 18 ++ tex/preamble.tex | 7 +- tex/references.bib | 368 ++++++++++++++++++++++++++++++++++ 15 files changed, 878 insertions(+), 3 deletions(-) create mode 100644 tex/2_lit/2_class/1_intro.tex create mode 100644 tex/2_lit/2_class/2_ets.tex create mode 100644 tex/2_lit/2_class/3_arima.tex create mode 100644 tex/2_lit/2_class/4_stl.tex create mode 100644 tex/2_lit/3_ml/1_intro.tex create mode 100644 tex/2_lit/3_ml/2_learning.tex create mode 100644 tex/2_lit/3_ml/3_cv.tex create mode 100644 tex/2_lit/3_ml/4_rf.tex create mode 100644 tex/2_lit/3_ml/5_svm.tex diff --git a/paper.tex b/paper.tex index d445c71..04a42f1 100644 --- a/paper.tex +++ b/paper.tex @@ -9,6 +9,15 @@ \input{tex/1_intro} \input{tex/2_lit/1_intro} +\input{tex/2_lit/2_class/1_intro} +\input{tex/2_lit/2_class/2_ets} +\input{tex/2_lit/2_class/3_arima} +\input{tex/2_lit/2_class/4_stl} +\input{tex/2_lit/3_ml/1_intro} +\input{tex/2_lit/3_ml/2_learning} +\input{tex/2_lit/3_ml/3_cv} +\input{tex/2_lit/3_ml/4_rf} +\input{tex/2_lit/3_ml/5_svm} \input{tex/3_mod/1_intro} \input{tex/4_stu/1_intro} \input{tex/5_con/1_intro} diff --git a/tex/2_lit/1_intro.tex b/tex/2_lit/1_intro.tex index e875a28..f28e145 100644 --- a/tex/2_lit/1_intro.tex +++ b/tex/2_lit/1_intro.tex @@ -1,2 +1,17 @@ \section{Literature Review} -\label{lit} \ No newline at end of file +\label{lit} + +In this section, we review the specific forecasting methods that make up our + forecasting system. +We group them into classical statistics and ML models. +The two groups differ mainly in how they represent the input data and how + accuracy is evaluated. + +A time series is a finite and ordered sequence of equally spaced observations. +Thus, time is regarded as discrete and a time step as a short period. +Formally, a time series $Y$ is defined as $Y = \{y_t: t \in I\}$, or $y_t$ for + short, where $I$ is an index set of positive integers. +Besides its length $T = |Y|$, another property is the a priori fixed and + non-negative periodicity $k$ of a seasonal pattern in demand: +$k$ is the number of time steps after which a pattern repeats itself (e.g., + $k=12$ for monthly sales data). diff --git a/tex/2_lit/2_class/1_intro.tex b/tex/2_lit/2_class/1_intro.tex new file mode 100644 index 0000000..e296160 --- /dev/null +++ b/tex/2_lit/2_class/1_intro.tex @@ -0,0 +1,13 @@ +\subsection{Demand Forecasting with Classical Forecasting Methods} +\label{class_methods} + +Forecasting became a formal discipline starting in the 1950s and has its + origins in the broader field of statistics. +\cite{hyndman2018} provide a thorough overview of the concepts and methods + established, and \cite{ord2017} indicate business-related applications + such as demand forecasting. +These "classical" forecasting methods share the characteristic that they are + trained over the entire $Y$ first. +Then, for prediction, the forecaster specifies the number of time steps for + which he wants to generate forecasts. +That is different for ML models. diff --git a/tex/2_lit/2_class/2_ets.tex b/tex/2_lit/2_class/2_ets.tex new file mode 100644 index 0000000..6db9781 --- /dev/null +++ b/tex/2_lit/2_class/2_ets.tex @@ -0,0 +1,78 @@ +\subsubsection{Na\"{i}ve Methods, Moving Averages, and Exponential Smoothing.} +\label{ets} + +Simple forecasting methods are often employed as a benchmark for more + sophisticated ones. +The so-called na\"{i}ve and seasonal na\"{i}ve methods forecast the next time + step in a time series, $y_{T+1}$, with the last observation, $y_T$, + and, if a seasonal pattern is present, with the observation $k$ steps + before, $y_{T+1-k}$. +As variants, both methods can be generalized to include drift terms in the + presence of a trend or changing seasonal amplitude. + +If a time series exhibits no trend, a simple moving average (SMA) is a + generalization of the na\"{i}ve method that is more robust to outliers. +It is defined as follows: $\hat{y}_{T+1} = \frac{1}{h} \sum_{i=T-h}^{T} y_i$ + where $h$ is the horizon over which the average is calculated. +If a time series exhibits a seasonal pattern, setting $h$ to a multiple of the + periodicity $k$ suffices that the forecast is unbiased. + +Starting in the 1950s, another popular family of forecasting methods, + so-called exponential smoothing methods, was introduced by + \cite{brown1959}, \cite{holt1957}, and \cite{winters1960}. +The idea is that forecasts $\hat{y}_{T+1}$ are a weighted average of past + observations where the weights decay over time; in the case of the simple + exponential smoothing (SES) method we obtain: +$ +\hat{y}_{T+1} = \alpha y_T + \alpha (1 - \alpha) y_{T-1} + + \alpha (1 - \alpha)^2 y_{T-2} + + \dots + \alpha (1 - \alpha)^{T-1} y_{1} +$ +where $\alpha$ (with $0 \le \alpha \le 1$) is a smoothing parameter. + +Exponential smoothing methods are often expressed in an alternative component + form that consists of a forecast equation and one or more smoothing + equations for unobservable components. +Below, we present a generalization of SES, the so-called Holt-Winters' + seasonal method, in an additive formulation. +$\ell_t$, $b_t$, and $s_t$ represent the unobservable level, trend, and + seasonal components inherent in $y_t$, and $\beta$ and $\gamma$ complement + $\alpha$ as smoothing parameters: +\begin{align*} +\hat{y}_{t+1} & = \ell_t + b_t + s_{t+1-k} \\ +\ell_t & = \alpha(y_t - s_{t-k}) + (1 - \alpha)(\ell_{t-1} + b_{t-1}) \\ +b_t & = \beta (\ell_{t} - \ell_{t-1}) + (1 - \beta) b_{t-1} \\ +s_t & = \gamma (y_t - \ell_{t-1} - b_{t-1}) + (1-\gamma)s_{t-k} +\end{align*} +With $b_t$, $s_t$, $\beta$, and $\gamma$ removed, this formulation reduces to + SES. +Distinct variations exist: Besides the three components, \cite{gardner1985} + add dampening for the trend, \cite{pegels1969} provides multiplicative + formulations, and \cite{taylor2003} adds dampening to the latter. +The accuracy measure commonly employed is the sum of squared errors between + the observations and their forecasts. + +Originally introduced by \cite{assimakopoulos2000}, \cite{hyndman2003} show + how the Theta method can be regarded as an equivalent to SES with a drift + term. +We mention this method here only because \cite{bell2018} emphasize that it + performs well at Uber. +However, in our empirical study, we find that this is not true in general. + +\cite{hyndman2002} introduce statistical processes, so-called innovations + state-space models, to generalize the methods in this sub-section. +They call this family of models ETS as they capture error, trend, and seasonal + terms. +Linear and additive ETS models have a structure like so: +\begin{align*} +y_t & = \vec{w} \cdot \vec{x}_{t-1} + \epsilon_t \\ +\vec{x_t} & = \mat{F} \vec{x}_{t-1} + \vec{g} \epsilon_t +\end{align*} +$y_t$ denote the observations as before while $\vec{x}_t$ is a state vector of + unobserved components. +$\epsilon_t$ is a white noise series and the matrix $\mat{F}$ and the vectors + $\vec{g}$ and $\vec{w}$ contain a model's coefficients. +Just as the models in the next sub-section, ETS models are commonly fitted + with maximum likelihood and evaluated using information theoretical + criteria against historical data. +We refer to \cite{hyndman2008b} for a thorough summary. diff --git a/tex/2_lit/2_class/3_arima.tex b/tex/2_lit/2_class/3_arima.tex new file mode 100644 index 0000000..d55ffd8 --- /dev/null +++ b/tex/2_lit/2_class/3_arima.tex @@ -0,0 +1,69 @@ +\subsubsection{Autoregressive Integrated Moving Averages.} +\label{arima} + +\cite{box1962}, \cite{box1968}, and more papers by the same authors in the + 1960s introduce a type of model where observations correlate with their + neighbors and refer to them as autoregressive integrated moving average + (ARIMA) models for stationary time series. +For a thorough overview, we refer to \cite{box2015} and \cite{brockwell2016}. + +A time series $y_t$ is stationary if its moments are independent of the + point in time where it is observed. +A typical example is a white noise $\epsilon_t$ series. +Therefore, a trend or seasonality implies non-stationarity. +\cite{kwiatkowski1992} provide a test to check the null hypothesis of + stationary data. +To obtain a stationary time series, one chooses from several techniques: +First, to stabilize a changing variance (i.e., heteroscedasticity), one + applies a Box-Cox transformation (e.g., $log$) as first suggested by + \cite{box1964}. +Second, to factor out a trend (or seasonal) pattern, one computes differences + of consecutive (or of lag $k$) observations or even differences thereof. +Third, it is also common to pre-process $y_t$ with one of the decomposition + methods mentioned in Sub-section \ref{stl} below with an ARIMA model + then trained on an adjusted $y_t$. + +In the autoregressive part, observations are modeled as linear combinations of + its predecessors. +Formally, an $AR(p)$ model is defined with a drift term $c$, coefficients + $\phi_i$ to be estimated (where $i$ is an index with $0 < i \leq p$), and + white noise $\epsilon_t$ like so: +$ +AR(p): \ \ +y_t = c + \phi_1 y_{t-1} + \phi_2 y_{t-2} + \dots + \phi_p y_{t-p} + + \epsilon_t +$. +The moving average part considers observations to be regressing towards a + linear combination of past forecasting errors. +Formally, a $MA(q)$ model is defined with a drift term $c$, coefficients + $\theta_j$ to be estimated, and white noise terms $\epsilon_t$ (where $j$ + is an index with $0 < j \leq q$) as follows: +$ +MA(q): \ \ +y_t = c + \epsilon_t + \theta_1 \epsilon_{t-1} + \theta_2 \epsilon_{t-2} + + \dots + \theta_q \epsilon_{t-q} +$. +Finally, an $ARIMA(p,d,q)$ model unifies both parts and adds differencing + where $d$ is the degree of differences and the $'$ indicates differenced + values: +$ +ARIMA(p,d,q): \ \ +y'_t = c + \phi_1 y'_{t-1} + \dots + \phi_p y'_{t-p} + \theta_1 \epsilon_{t-1} + + \dots + \theta_q \epsilon_{t-q} + \epsilon_{t} +$. + +$ARIMA(p,d,q)$ models are commonly fitted with maximum likelihood estimation. +To find an optimal combination of the parameters $p$, $d$, and $q$, the + literature suggests calculating an information theoretical criterion + (e.g., Akaike's Information Criterion) that evaluates the fit on + historical data. +\cite{hyndman2008a} provide a step-wise heuristic to choose $p$, $d$, and $q$, + that also decides if a Box-Cox transformation is to be applied, and if so, + which one. +To obtain a one-step-ahead forecast, the above equation is reordered such + that $t$ is substituted with $T+1$. +For forecasts further into the future, the actual observations are + subsequently replaced by their forecasts. +Seasonal ARIMA variants exist; however, the high frequency $k$ in the kind of + demand a UDP faces typically renders them impractical as too many + coefficients must be estimated. diff --git a/tex/2_lit/2_class/4_stl.tex b/tex/2_lit/2_class/4_stl.tex new file mode 100644 index 0000000..127123c --- /dev/null +++ b/tex/2_lit/2_class/4_stl.tex @@ -0,0 +1,62 @@ +\subsubsection{Seasonal and Trend Decomposition using Loess.} +\label{stl} + +A time series $y_t$ may exhibit different types of patterns; to fully capture + each of them, the series must be decomposed. +Then, each component is forecast with a distinct model. +Most commonly, the components are the trend $t_t$, seasonality $s_t$, and + remainder $r_t$. +They are themselves time series, where only $s_t$ exhibits a periodicity $k$. +A decomposition may be additive (i.e., $y_t = s_t + t_t + r_t$) or + multiplicative (i.e., $y_t = s_t * t_t * r_t$); the former assumes that + the effect of the seasonal component is independent of the overall level + of $y_t$ and vice versa. +The seasonal component is centered around $0$ in both cases such that its + removal does not affect the level of $y_t$. +Often, it is sufficient to only seasonally adjust the time series, and model + the trend and remainder together, for example, as $a_t = y_t - s_t$ in the + additive case. + +Early approaches employed moving averages (cf., Sub-section \ref{ets}) to + calculate a trend component, and, after removing that from $y_t$, averaged + all observations of the same seasonal lag to obtain the seasonal + component. +The downsides of this are the subjectivity in choosing the window lengths for + the moving average and the seasonal averaging, the incapability of the + seasonal component to vary its amplitude over time, and the missing + handling of outliers. + +The X11 method developed at the U.S. Census Bureau and described in detail by + \cite{dagum2016} overcomes these disadvantages. +However, due to its background in economics, it is designed primarily for + quarterly or monthly data, and the change in amplitude over time cannot be + controlled. +Variants of this method are the SEATS decomposition by the Bank of Spain and + the newer X13-SEATS-ARIMA method by the U.S. Census Bureau. +Their main advantages stem from the fact that the models calibrate themselves + according to statistical criteria without manual work for a statistician + and that the fitting process is robust to outliers. + +\cite{cleveland1990} introduce a seasonal and trend decomposition using a + repeated locally weighted regression - the so-called Loess procedure - to + smoothen the trend and seasonal components, which can be viewed as a + generalization of the methods above and is denoted by the acronym + \gls{stl}. +In contrast to the X11, X13, and SEATS methods, the STL supports seasonalities + of any lag $k$ that must, however, be determined with additional + statistical tests or set with out-of-band knowledge by the forecaster + (e.g., hourly demand data implies $k = 24 * 7 = 168$ assuming customer + behavior differs on each day of the week). +Moreover, the seasonal component's rate of change, represented by the $ns$ + parameter and explained in detail with Figure \ref{f:stl} in Section + \ref{decomp}, must be set by the forecaster as well, while the trend's + smoothness may be controlled via setting a non-default window size. +Outliers are handled by assignment to the remainder such that they do not + affect the trend and seasonal components. +In particular, the manual input needed to calibrate the STL explains why only + the X11, X13, and SEATS methods are widely used by practitioners. +However, the widespread adoption of concepts like cross-validation (cf., + Sub-section \ref{cv}) in recent years enables the usage of an automated + grid search to optimize the parameters. +The STL's usage within a grid search is facilitated even further by its being + computationally cheaper than the other methods discussed. diff --git a/tex/2_lit/3_ml/1_intro.tex b/tex/2_lit/3_ml/1_intro.tex new file mode 100644 index 0000000..f04f137 --- /dev/null +++ b/tex/2_lit/3_ml/1_intro.tex @@ -0,0 +1,15 @@ +\subsection{Demand Forecasting with Machine Learning Methods} +\label{ml_methods} + +ML methods have been employed in all kinds of prediction tasks in recent + years. +In this section, we restrict ourselves to the models that performed well in + our study: Random Forest (\gls{rf}) and Support Vector Regression + (\gls{svr}). +RFs are in general well-suited for datasets without a priori knowledge about + the patterns, while SVR is known to perform well on time series data, as + shown by \cite{hansen2006} in general and \cite{bao2004} specifically for + intermittent demand. +Gradient Boosting, another popular ML method, was consistently outperformed by + RFs, and artificial neural networks require an amount of data + exceeding what our industry partner has by far. diff --git a/tex/2_lit/3_ml/2_learning.tex b/tex/2_lit/3_ml/2_learning.tex new file mode 100644 index 0000000..86d157a --- /dev/null +++ b/tex/2_lit/3_ml/2_learning.tex @@ -0,0 +1,53 @@ +\subsubsection{Supervised Learning.} +\label{learning} + +A conceptual difference between classical and ML methods is the format + for the model inputs. +In ML models, a time series $Y$ is interpreted as labeled data. +Labels are collected into a vector $\vec{y}$ while the corresponding + predictors are aligned in an $(T - n) \times n$ matrix $\mat{X}$: +$$ +\vec{y} += +\begin{pmatrix} + y_T \\ + y_{T-1} \\ + \dots \\ + y_{n+1} +\end{pmatrix} +~~~~~~~~~~ +\mat{X} += +\begin{bmatrix} + y_{T-1} & y_{T-2} & \dots & y_{T-n} \\ + y_{T-2} & y_{T-3} & \dots & y_{T-(n+1)} \\ + \dots & \dots & \dots & \dots \\ + y_n & y_{n-1} & \dots & y_1 +\end{bmatrix} +$$ +The $m = T - n$ rows are referred to as samples and the $n$ columns as + features. +Each row in $\mat{X}$ is "labeled" by the corresponding entry in $\vec{y}$, + and ML models are trained to fit the rows to their labels. +Conceptually, we model a functional relationship $f$ between $\mat{X}$ and + $\vec{y}$ such that the difference between the predicted + $\vec{\hat{y}} = f(\mat{X})$ and the true $\vec{y}$ are minimized + according to some error measure $L(\vec{\hat{y}}, \vec{y})$, where $L$ + summarizes the goodness of the fit into a scalar value (e.g., the + well-known mean squared error [MSE]; cf., Section \ref{mase}). +$\mat{X}$ and $\vec{y}$ show the ordinal character of time series data: + Not only overlap the entries of $\mat{X}$ and $\vec{y}$, but the rows of + $\mat{X}$ are shifted versions of each other. +That does not hold for ML applications in general (e.g., the classical + example of predicting spam vs. no spam emails, where the features model + properties of individual emails), and most of the common error measures + presented in introductory texts on ML, are only applicable in cases + without such a structure in $\mat{X}$ and $\vec{y}$. +$n$, the number of past time steps required to predict a $y_t$, is an + exogenous model parameter. +For prediction, the forecaster supplies the trained ML model an input + vector in the same format as a row $\vec{x}_i$ in $\mat{X}$. +For example, to predict $y_{T+1}$, the model takes the vector + $(y_T, y_{T-1}, ..., y_{T-n+1})$ as input. +That is in contrast to the classical methods, where we only supply the number + of time steps to be predicted as a scalar integer. diff --git a/tex/2_lit/3_ml/3_cv.tex b/tex/2_lit/3_ml/3_cv.tex new file mode 100644 index 0000000..1d5186b --- /dev/null +++ b/tex/2_lit/3_ml/3_cv.tex @@ -0,0 +1,38 @@ +\subsubsection{Cross-Validation.} +\label{cv} + +Because ML models are trained by minimizing a loss function $L$, the + resulting value of $L$ underestimates the true error we see when + predicting into the actual future by design. +To counter that, one popular and model-agnostic approach is cross-validation + (\gls{cv}), as summarized, for example, by \cite{hastie2013}. +CV is a resampling technique, which ranomdly splits the samples into a + training and a test set. +Trained on the former, an ML model makes forecasts on the latter. +Then, the value of $L$ calculated only on the test set gives a realistic and + unbiased estimate of the true forecasting error, and may be used for one + of two distinct aspects: +First, it assesses the quality of a fit and provides an idea as to how the + model would perform in production when predicting into the actual future. +Second, the errors of models of either different methods or the same method + with different parameters may be compared with each other to select the + best model. +In order to first select the best model and then assess its quality, one must + apply two chained CVs: +The samples are divided into training, validation, and test sets, and all + models are trained on the training set and compared on the validation set. +Then, the winner is retrained on the union of the training and validation + sets and assessed on the test set. + +Regarding the splitting, there are various approaches, and we choose the + so-called $k$-fold CV, where the samples are randomly divided into $k$ + folds of the same size. +Each fold is used as a test set once and the remaining $k-1$ folds become + the corresponding training set. +The resulting $k$ error measures are averaged. +A $k$-fold CV with $k=5$ or $k=10$ is a compromise between the two extreme + cases of having only one split and the so-called leave-one-out CV + where $k = m$: Computation is still relatively fast and each sample is + part of several training sets maximizing the learning from the data. +We adapt the $k$-fold CV to the ordinal stucture in $\mat{X}$ and $\vec{y}$ in + Sub-section \ref{unified_cv}. diff --git a/tex/2_lit/3_ml/4_rf.tex b/tex/2_lit/3_ml/4_rf.tex new file mode 100644 index 0000000..784d2a7 --- /dev/null +++ b/tex/2_lit/3_ml/4_rf.tex @@ -0,0 +1,66 @@ +\subsubsection{Random Forest Regression.} +\label{rf} + +\cite{breiman1984} introduce the classification and regression tree + (\gls{cart}) model that is built around the idea that a single binary + decision tree maps learned combinations of intervals of the feature + columns to a label. +Thus, each sample in the training set is associated with one leaf node that + is reached by following the tree from its root and branching along the + arcs according to some learned splitting rule per intermediate node that + compares the sample's realization for the feature specified by the rule to + the learned decision rule. +While such models are computationally fast and offer a high degree of + interpretability, they tend to overfit strongly to the training set as + the splitting rules are not limited to any functional form (e.g., linear) + in the relationship between the features and the labels. +In the regression case, it is common to maximize the variance reduction $I_V$ + from a parent node $N$ to its two children, $C1$ and $C2$, as the + splitting rule. +\cite{breiman1984} formulate this as follows: +$$ +I_V(N) += +\frac{1}{|S_N|^2} \sum_{i \in S_N} \sum_{j \in S_N} + \frac{1}{2} (y_i - y_j)^2 +- \left( + \frac{1}{|S_{C1}|^2} \sum_{i \in S_{C1}} \sum_{j \in S_{C1}} + \frac{1}{2} (y_i - y_j)^2 + + + \frac{1}{|S_{C2}|^2} \sum_{i \in S_{C2}} \sum_{j \in S_{C2}} + \frac{1}{2} (y_i - y_j)^2 +\right) +$$ +$S_N$, $S_{C1}$, and $S_{C2}$ are the index sets of the samples in $N$, $C1$, + and $C2$. + +\cite{ho1998} and then \cite{breiman2001} generalize this method by combining + many CART models into one forest of trees where every single tree is + a randomized variant of the others. +Randomization is achieved at two steps in the training process: +First, each tree receives a distinct training set resampled with replacement + from the original training set, an idea also called bootstrap + aggregation. +Second, at each node a random subset of the features is used to grow the tree. +Trees can be fitted in parallel speeding up the training significantly. +For prediction at the tree level, the average of all the samples at a + particular leaf node is used. +Then, the individual values are combined into one value by averaging again + across the trees. +Due to the randomization, the trees are decorrelated offsetting the + overfitting. +Another measure to counter overfitting is pruning the tree, either by + specifying the maximum depth of a tree or the minimum number of samples + at leaf nodes. + +The forecaster must tune the structure of the forest. +Parameters include the number of trees in the forest, the size of the random + subset of features, and the pruning criteria. +The parameters are optimized via grid search: We train many models with + parameters chosen from a pre-defined list of values and select the best + one by CV. +RFs are a convenient ML method for any dataset as decision trees do not + make any assumptions about the relationship between features and labels. +\cite{herrera2010} use RFs to predict the hourly demand for water in an urban + context, a similar application as the one in this paper, and find that RFs + work well with time series type of data. diff --git a/tex/2_lit/3_ml/5_svm.tex b/tex/2_lit/3_ml/5_svm.tex new file mode 100644 index 0000000..1c12af5 --- /dev/null +++ b/tex/2_lit/3_ml/5_svm.tex @@ -0,0 +1,60 @@ +\subsubsection{Support Vector Regression.} +\label{svm} + +\cite{vapnik1963} and \cite{vapnik1964} introduce the so-called support vector + machine (\gls{svm}) model, and \cite{vapnik2013} summarizes the research + conducted since then. +In its basic version, SVMs are linear classifiers, modeling a binary + decision, that fit a hyperplane into the feature space of $\mat{X}$ to + maximize the margin around the hyperplane seperating the two groups of + labels. +SVMs were popularized in the 1990s in the context of optical character + recognition, as shown in \cite{scholkopf1998}. + +\cite{drucker1997} and \cite{stitson1999} adapt SVMs to the regression case, + and \cite{smola2004} provide a comprehensive introduction thereof. +\cite{mueller1997} and \cite{mueller1999} focus on SVRs in the context of time + series data and find that they tend to outperform classical methods. +\cite{chen2006a} and \cite{chen2006b} apply SVRs to predict the hourly demand + for water in cities, an application similar to the UDP case. + +In the SVR case, a linear function + $\hat{y}_i = f(\vec{x}_i) = \langle\vec{w},\vec{x}_i\rangle + b$ + is fitted so that the actual labels $y_i$ have a deviation of at most + $\epsilon$ from their predictions $\hat{y}_i$ (cf., the constraints + below). +SVRs are commonly formulated as quadratic optimization problems as follows: +$$ +\text{minimize } +\frac{1}{2} \norm{\vec{w}}^2 + C \sum_{i=1}^m (\xi_i + \xi_i^*) +\quad \text{subject to } +\begin{cases} +y_i - \langle \vec{w}, \vec{x}_i \rangle - b \leq \epsilon + \xi_i +\text{,} \\ +\langle \vec{w}, \vec{x}_i \rangle + b - y_i \leq \epsilon + \xi_i^* +\end{cases} +$$ +$\vec{w}$ are the fitted weights in the row space of $\mat{X}$, $b$ is a bias + term in the column space of $\mat{X}$, and $\langle\cdot,\cdot\rangle$ + denotes the dot product. +By minimizing the norm of $\vec{w}$, the fitted function is flat and not prone + to overfitting strongly. +To allow individual samples outside the otherwise hard $\epsilon$ bounds, + non-negative slack variables $\xi_i$ and $\xi_i^*$ are included. +A non-negative parameter $C$ regulates how many samples may violate the + $\epsilon$ bounds and by how much. +To model non-linear relationships, one could use a mapping $\Phi(\cdot)$ for + the $\vec{x}_i$ from the row space of $\mat{X}$ to some higher + dimensional space; however, as the optimization problem only depends on + the dot product $\langle\cdot,\cdot\rangle$ and not the actual entries of + $\vec{x}_i$, it suffices to use a kernel function $k$ such that + $k(\vec{x}_i,\vec{x}_j) = \langle\Phi(\vec{x}_i),\Phi(\vec{x}_j)\rangle$. +Such kernels must fulfill certain mathematical properties, and, besides + polynomial kernels, radial basis functions with + $k(\vec{x}_i,\vec{x}_j) = exp(\gamma \norm{\vec{x}_i - \vec{x}_j}^2)$ are + a popular candidate where $\gamma$ is a parameter controlling for how the + distances between any two samples influence the final model. +SVRs work well with sparse data in high dimensional spaces, such as + intermittent demand data, as they minimize the risk of misclassification + or predicting a significantly far off value by maximizing the error + margin, as also noted by \cite{bao2004}. diff --git a/tex/3_mod/1_intro.tex b/tex/3_mod/1_intro.tex index bf72f24..fdc9207 100644 --- a/tex/3_mod/1_intro.tex +++ b/tex/3_mod/1_intro.tex @@ -1,2 +1,8 @@ \section{Model Formulation} -\label{mod} \ No newline at end of file +\label{mod} + +% temporary placeholders +\label{decomp} +\label{f:stl} +\label{mase} +\label{unified_cv} \ No newline at end of file diff --git a/tex/glossary.tex b/tex/glossary.tex index b34e1b9..6c685f7 100644 --- a/tex/glossary.tex +++ b/tex/glossary.tex @@ -1,7 +1,25 @@ % Abbreviations for technical terms. +\newglossaryentry{cart}{ + name=CART, description={Classification and Regression Trees} +} +\newglossaryentry{cv}{ + name=CV, description={Cross Validation} +} \newglossaryentry{ml}{ name=ML, description={Machine Learning} } +\newglossaryentry{rf}{ + name=RF, description={Random Forest} +} +\newglossaryentry{stl}{ + name=STL, description={Seasonal and Trend Decomposition using Loess} +} +\newglossaryentry{svm}{ + name=SVM, description={Support Vector Machine} +} +\newglossaryentry{svr}{ + name=SVR, description={Support Vector Regression} +} \newglossaryentry{udp}{ name=UDP, description={Urban Delivery Platform} } diff --git a/tex/preamble.tex b/tex/preamble.tex index bc34c42..85ddd10 100644 --- a/tex/preamble.tex +++ b/tex/preamble.tex @@ -6,4 +6,9 @@ % Make opening quotes look different than closing quotes. \usepackage[english=american]{csquotes} -\MakeOuterQuote{"} \ No newline at end of file +\MakeOuterQuote{"} + +% Define helper commands. +\usepackage{bm} +\newcommand{\mat}[1]{\bm{#1}} +\newcommand{\norm}[1]{\left\lVert#1\right\rVert} \ No newline at end of file diff --git a/tex/references.bib b/tex/references.bib index be2c815..9d330ff 100644 --- a/tex/references.bib +++ b/tex/references.bib @@ -7,6 +7,25 @@ volume={129}, pages={263--286} } +@article{assimakopoulos2000, +title={The theta model: a decomposition approach to forecasting}, +author={Assimakopoulos, Vassilis and Nikolopoulos, Konstantinos}, +year={2000}, +journal={International Journal of Forecasting}, +volume={16}, +number={4}, +pages={521--530} +} + +@inproceedings{bao2004, +title={Forecasting intermittent demand by SVMs regression}, +author={Bao, Yukun and Wang, Wen and Zhang, Jinlong}, +year={2004}, +booktitle={2004 IEEE International Conference on Systems, Man and Cybernetics}, +volume={1}, +pages={461--466} +} + @misc{bell2018, title = {Forecasting at Uber: An Introduction}, author={Bell, Franziska and Smyl, Slawek}, @@ -15,6 +34,119 @@ howpublished = {\url{https://eng.uber.com/forecasting-introduction/}}, note = {Accessed: 2020-10-01} } +@article{box1962, +title={Some statistical Aspects of adaptive Optimization and Control}, +author={Box, George and Jenkins, Gwilym}, +year={1962}, +journal={Journal of the Royal Statistical Society. Series B (Methodological)}, +volume={24}, +number={2}, +pages={297--343} +} + +@article{box1964, +title={An Analysis of Transformations}, +author={Box, George and Cox, David}, +year={1964}, +journal={Journal of the Royal Statistical Society. Series B (Methodological)}, +volume={26}, +number={2}, +pages={211--252} +} + +@article{box1968, +title={Some recent Advances in Forecasting and Control}, +author={Box, George and Jenkins, Gwilym}, +year={1968}, +journal={Journal of the Royal Statistical Society. + Series C (Applied Statistics)}, +volume={17}, +number={2}, +pages={91--109} +} + +@book{box2015, +title={Time Series Analysis: Forecasting and Control}, +author={Box, George and Jenkins, Gwilym and Reinsel, Gregory and Ljung, Greta}, +series={Wiley Series in Probability and Statistics}, +year={2015}, +publisher={Wiley} +} + +@book{breiman1984, +title={Classification and Regression Trees}, +author={Breiman, Leo and Friedman, Jerome and Olshen, R.A. + and Stone, Charles}, +year={1984}, +publisher={Wadsworth} +} + +@article{breiman2001, +title={Random Forests}, +author={Breiman, Leo}, +year={2001}, +journal={Machine Learning}, +volume={45}, +number={1}, +pages={5--32} +} + +@book{brockwell2016, +title={Introduction to Time Series and Forecasting}, +author={Brockwell, Peter and Davis, Richard}, +series={Springer Texts in Statistics}, +year={2016}, +publisher={Springer} +} + +@book{brown1959, +title={Statistical Forecasting for Inventory Control}, +author={Brown, Robert}, +year={1959}, +publisher={McGraw/Hill} +} + +@article{chen2006a, +title={Hourly Water Demand Forecast Model based on Bayesian Least Squares + Support Vector Machine}, +author={Chen, Lei and Zhang, Tu-qiao}, +year={2006}, +journal={Journal of Tianjin University}, +volume={39}, +number={9}, +pages={1037--1042} +} + +@article{chen2006b, +title={Hourly Water Demand Forecast Model based on Least Squares Support + Vector Machine}, +author={Chen, Lei and Zhang, Tu-qiao}, +year={2006}, +journal={Journal of Harbin Institute of Technology}, +volume={38}, +number={9}, +pages={1528--1530} +} + +@article{cleveland1990, +title={STL: A Seasonal-Trend Decomposition Procedure Based on Loess}, +author={Cleveland, Robert and Cleveland, Williiam and McRae, Jean + and Terpenning, Irma}, +year={1990}, +journal={Journal of Official Statistics}, +volume={6}, +number={1}, +pages={3--73} +} + +@book{dagum2016, +title={Seasonal Adjustment Methods and Real Time Trend-Cycle Estimation}, +author={Dagum, Estela and Bianconcini, Silvia}, +series={Statistics for Social and Behavioral Sciences}, +year={2016}, +publisher={Springer} +} + @article{de2006, title={25 Years of Time Series Forecasting}, author={De Gooijer, Jan and Hyndman, Rob}, @@ -25,6 +157,16 @@ number={3}, pages={443--473} } +@inproceedings{drucker1997, +title={Support Vector Regression Machines}, +author={Drucker, Harris and Burges, Christopher and Kaufman, Linda + and Smola, Alex and Vapnik, Vladimir}, +year={1997}, +booktitle={Advances in Neural Information Processing Systems}, +pages={155--161}, +organization={Springer} +} + @article{ehmke2018, title={Optimizing for total costs in vehicle routing in urban areas}, author={Ehmke, Jan Fabian and Campbell, Ann M and Thomas, Barrett W}, @@ -34,6 +176,45 @@ volume={116}, pages={242--265} } +@article{gardner1985, +title={Forecasting Trends in Time Series}, +author={Gardner, Everette and McKenzie, Ed}, +year={1985}, +journal={Management Science}, +volume={31}, +number={10}, +pages={1237--1246} +} + +@article{hansen2006, +title={Some Evidence on Forecasting Time-Series with Support Vector Machines}, +author={Hansen, James and McDonald, James and Nelson, Ray}, +year={2006}, +journal={Journal of the Operational Research Society}, +volume={57}, +number={9}, +pages={1053--1063} +} + +@book{hastie2013, +title={The Elements of Statistical Learning: Data Mining, Inference, + and Prediction}, +author={Hastie, Trevor and Tibshirani, Robert and Friedman, Jerome}, +year={2013}, +publisher={Springer} +} + +@article{herrera2010, +title={Predictive Models for Forecasting Hourly Urban Water Demand}, +author={Herrera, Manuel and Torgo, Lu{\'\i}s and Izquierdo, Joaqu{\'\i}n + and P{\'e}rez-Garc{\'\i}a, Rafael}, +year={2010}, +journal={Journal of Hydrology}, +volume={387}, +number={1-2}, +pages={141--150} +} + @misc{hirschberg2016, title = {McKinsey: The changing market for food delivery}, author={Hirschberg, Carsten and Rajko, Alexander and Schumacher, Thomas @@ -44,6 +225,25 @@ howpublished = "\url{https://www.mckinsey.com/industries/high-tech/ note = {Accessed: 2020-10-01} } +@article{ho1998, +title={The Random Subspace Method for Constructing Decision Forests}, +author={Ho, Tin Kam}, +year={1998}, +journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, +volume={20}, +number={8}, +pages={832--844} +} + +@article{holt1957, +title={Forecasting Seasonals and Trends by Exponentially Weighted Moving + Averages}, +author={Holt, Charles}, +year={1957}, +journal={ONR Memorandum}, +volume={52} +} + @article{hou2018, title={Ride-matching and routing optimisation: Models and a large neighbourhood search heuristic}, @@ -54,6 +254,62 @@ volume={118}, pages={143--162} } +@article{hyndman2002, +title={A State Space Framework for Automatic Forecasting using Exponential + Smoothing Methods}, +author={Hyndman, Rob and Koehler, Anne and Snyder, Ralph and Grose, Simone}, +year={2002}, +journal={International Journal of Forecasting}, +volume={18}, +number={3}, +pages={439--454} +} + +@article{hyndman2003, +title={Unmasking the Theta method}, +author={Hyndman, Rob and Billah, Baki}, +year={2003}, +journal={International Journal of Forecasting}, +volume={19}, +number={2}, +pages={287--290} +} + +@article{hyndman2008a, +title={Automatic Time Series Forecasting: The forecast package for R}, +author={Hyndman, Rob and Khandakar, Yeasmin}, +year={2008}, +journal={Journal of Statistical Software}, +volume={26}, +number={3} +} + +@book{hyndman2008b, +title={Forecasting with Exponential Smoothing: the State Space Approach}, +author={Hyndman, Rob and Koehler, Anne and Ord, Keith and Snyder, Ralph}, +year={2008}, +publisher={Springer} +} + +@book{hyndman2018, +title={Forecasting: Principles and Practice}, +author={Hyndman, Rob and Athanasopoulos, George}, +year={2018}, +publisher={OTexts} +} + +@article{kwiatkowski1992, +title={Testing the null hypothesis of stationarity against the alternative of a + unit root: How sure are we that economic time series have a unit root?}, +author={Kwiatkowski, Denis and Phillips, Peter and Schmidt, Peter + and Shin, Yongcheol}, +year={1992}, +journal={Journal of Econometrics}, +volume={54}, +number={1-3}, +pages={159--178} +} + @misc{laptev2017, title = {Engineering Extreme Event Forecasting at Uber with Recurrent Neural Networks}, @@ -74,6 +330,108 @@ volume={118}, pages={392--420} } +@inproceedings{mueller1997, +title={Predicting Time Series with Support Vector Machines}, +author={M{\"u}ller, Klaus-Robert and Smola, Alexander and R{\"a}tsch, Gunnar + and Sch{\"o}lkopf, Bernhard and Kohlmorgen, Jens and Vapnik, Vladimir}, +year={1997}, +booktitle={International Conference on Artificial Neural Networks}, +pages={999--1004}, +organization={Springer} +} + +@article{mueller1999, +title={Using Support Vector Machines for Time Series Prediction}, +author={M{\"u}ller, Klaus-Robert and Smola, Alexander and R{\"a}tsch, Gunnar + and Sch{\"o}lkopf, Bernhard and Kohlmorgen, Jens and Vapnik, Vladimir}, +year={1999}, +journal={Advances in Kernel Methods — Support Vector Learning}, +pages={243--254}, +publisher={MIT, Cambridge, MA, USA} +} + +@book{ord2017, +title={Principles of Business Forecasting}, +author={Ord, Keith and Fildes, Robert and Kourentzes, Nikos}, +year={2017}, +publisher={WESSEX Press} +} + +@article{pegels1969, +title={Exponential Forecasting: Some new variations}, +author={Pegels, C.}, +year={1969}, +journal={Management Science}, +volume={15}, +number={5}, +pages={311--315} +} + +@incollection{scholkopf1998, +title={Fast Approximation of Support Vector Kernel Expansions, and an + Interpretation of Clustering as Approximation in Feature Spaces}, +author={Sch{\"o}lkopf, Bernhard and Knirsch, Phil and Smola, Alex + and Burges, Chris}, +year={1998}, +booktitle={Mustererkennung 1998}, +publisher={Springer}, +pages={125--132} +} + +@article{smola2004, +title={A Tutorial on Support Vector Regression}, +author={Smola, Alex and Sch{\"o}lkopf, Bernhard}, +year={2004}, +journal={Statistics and Computing}, +volume={14}, +number={3}, +pages={199--222} +} + +@article{stitson1999, +title={Support Vector Regression with ANOVA Decomposition Kernels}, +author={Stitson, Mark and Gammerman, Alex and Vapnik, Vladimir + and Vovk, Volodya and Watkins, Chris and Weston, Jason}, +year={1999}, +journal={Advances in Kernel Methods — Support Vector Learning}, +pages={285--292}, +publisher={MIT, Cambridge, MA, USA} +} + +@article{taylor2003, +title={Exponential Smoothing with a Damped Multiplicative Trend}, +author={Taylor, James}, +year={2003}, +journal={International Journal of Forecasting}, +volume={19}, +number={4}, +pages={715--725} +} + +@article{vapnik1963, +title={Pattern Recognition using Generalized Portrait Method}, +author={Vapnik, Vladimir and Lerner, A}, +year={1963}, +journal={Automation and Remote Control}, +volume={24}, +pages={774--780}, +} + +@article{vapnik1964, +title={A Note on one Class of Perceptrons}, +author={Vapnik, Vladimir and Chervonenkis, A}, +year={1964}, +journal={Automation and Remote Control}, +volume={25} +} + +@book{vapnik2013, +title={The Nature of Statistical Learning Theory}, +author={Vapnik, Vladimir}, +year={2013}, +publisher={Springer} +} + @article{wang2018, title={Delivering meals for multiple suppliers: Exclusive or sharing logistics service}, @@ -82,4 +440,14 @@ year={2018}, journal={Transportation Research Part E: Logistics and Transportation Review}, volume={118}, pages={496--512} +} + +@article{winters1960, +title={Forecasting Sales by Exponentially Weighted Moving Averages}, +author={Winters, Peter}, +year={1960}, +journal={Management Science}, +volume={6}, +number={3}, +pages={324--342} } \ No newline at end of file From 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0000000..1712c9e --- /dev/null +++ b/static/slashbox.sty @@ -0,0 +1,77 @@ +% slashbox.sty by Koichi Yasuoka, May 27, 1993 +% minor modification by Toru Sato, May 31, 1993 +\typeout{slashbox style by K.Yasuoka, May 1993.}% +\newbox\@slashboxa +\newbox\@slashboxb +\newbox\@slashboxc +\newcount\@slashboxwd +\newcount\@slashboxht +\newdimen\@slashsepl +\newdimen\@slashsepr +\def\slashbox{% + \def\@slashboxpicture##1{% + \put(0,0){\line(##1,1){\@slashboxwd}}% + \put(0,\@slashboxht){\makebox(0,0)[tl]{\box\@slashboxa}}% + \put(\@slashboxwd,0){\makebox(0,0)[br]{\box\@slashboxb}}% + }% + \@slashbox +}% +\def\backslashbox{% + \def\@slashboxpicture##1{% + \put(0,\@slashboxht){\line(##1,-1){\@slashboxwd}}% + \put(0,0){\makebox(0,0)[bl]{\box\@slashboxa}}% + \put(\@slashboxwd,\@slashboxht){\makebox(0,0)[tr]{\box\@slashboxb}}% + }% + \@slashbox +}% +\def\@slashbox{\@ifnextchar [{\@@slashbox}{\@@slashbox[0pt]}} +\def\@@slashbox[#1]{\@ifnextchar [{\@@@slashbox[#1]}{\@@@slashbox[#1][c]}} +\def\@@@slashbox[#1][#2]#3#4{% +% #1: width, #2: suppression of \tabcolsep on `l', `r', or `lr' side +% #3: left item, #4: right item + \@slashsepl=\tabcolsep + \@slashsepr=\tabcolsep + \@tfor\@tempa :=#2\do{\expandafter\let + \csname @slashsep\@tempa\endcsname=\z@}% + \setbox\@slashboxa=\hbox{\strut\hskip\tabcolsep\shortstack[l]{#3}}% + \setbox\@slashboxb=\hbox{\shortstack[r]{#4}\hskip\tabcolsep\strut}% + \setbox\@slashboxa=\hbox{\raise\dp\@slashboxa\box\@slashboxa}% + \setbox\@slashboxb=\hbox{\raise\dp\@slashboxb\box\@slashboxb}% + \setbox\@slashboxc=\hbox{% + \@tempdima=\wd\@slashboxa + \advance\@tempdima by \wd\@slashboxb + \advance\@tempdima by \@slashsepl + \advance\@tempdima by \@slashsepr + \@tempdimb=#1\relax% + \ifdim\@tempdimb>\@tempdima \@tempdima=\@tempdimb\fi% + \@tempdimb=\ht\@slashboxa + \advance\@tempdimb by \dp\@slashboxa + \advance\@tempdimb by \ht\@slashboxb + \advance\@tempdimb by \dp\@slashboxb + \@tempcnta=\@tempdima + \@tempcntb=\@tempdimb + \advance\@tempcnta 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From: Alexander Hess Date: Mon, 5 Oct 2020 01:02:28 +0200 Subject: [PATCH 14/28] Add Conclusion section --- paper.tex | 3 + tex/5_con/1_intro.tex | 6 +- tex/5_con/2_generalizability.tex | 23 ++++++ tex/5_con/3_implications.tex | 58 ++++++++++++++ tex/5_con/4_further_research.tex | 45 +++++++++++ tex/glossary.tex | 6 ++ tex/references.bib | 132 +++++++++++++++++++++++++++++++ 7 files changed, 272 insertions(+), 1 deletion(-) create mode 100644 tex/5_con/2_generalizability.tex create mode 100644 tex/5_con/3_implications.tex create mode 100644 tex/5_con/4_further_research.tex diff --git a/paper.tex b/paper.tex index 0cded62..333f2f1 100644 --- a/paper.tex +++ b/paper.tex @@ -37,6 +37,9 @@ \input{tex/4_stu/6_fams} \input{tex/4_stu/7_pixels_intervals} \input{tex/5_con/1_intro} +\input{tex/5_con/2_generalizability} +\input{tex/5_con/3_implications} +\input{tex/5_con/4_further_research} \newpage \input{tex/glossary} diff --git a/tex/5_con/1_intro.tex b/tex/5_con/1_intro.tex index 42126bd..9188f96 100644 --- a/tex/5_con/1_intro.tex +++ b/tex/5_con/1_intro.tex @@ -1,2 +1,6 @@ \section{Conclusion} -\label{con} \ No newline at end of file +\label{con} + +We conclude this paper by elaborating on how the findings are transferable + to similar settings, providing some implications for a UDP's + managers, and discussing further research opportunities. diff --git a/tex/5_con/2_generalizability.tex b/tex/5_con/2_generalizability.tex new file mode 100644 index 0000000..5275fc0 --- /dev/null +++ b/tex/5_con/2_generalizability.tex @@ -0,0 +1,23 @@ +\subsection{Generalizability of the Methology and Findings} +\label{generalizability} + +Whereas forecasting applications are always data-specific, the following + aspects generalize to UDPs with ad-hoc transportation services: +\begin{itemize} +\item \textbf{Double Seasonality}: +The double seasonality causes a periodicity $k$ too large to be modeled by + classical models, and we adapt the STL method in the \textit{fnaive} model + such that it "flexibly" fits a seasonal pattern changing in a non-trivial + way over time. +\item \textbf{Order Sparsity}: +The intermittent time series resulting from gridification require simple + methods like \textit{hsma} or \textit{trivial} that are not as susceptible + to noise as more sophisticated ones. +\item \textbf{Unified CV}: +A CV unified around a whole day allows evaluating classical statistical and ML + methods on the same scale. +It is agnostic of both the type of the time series and retraining. +\item \textbf{Error Measure}: +Analogous to \cite{hyndman2006}, we emphasize the importance of choosing a + consistent error measure, and argue for increased use of MASE. +\end{itemize} diff --git a/tex/5_con/3_implications.tex b/tex/5_con/3_implications.tex new file mode 100644 index 0000000..6fe91a4 --- /dev/null +++ b/tex/5_con/3_implications.tex @@ -0,0 +1,58 @@ +\subsection{Managerial Implications} +\label{implications} + +Even though zeitgeist claims that having more data is always better, our study + shows this is not the case here: +First, under certain circumstances, accuracy may go up with shorter training + horizons. +Second, none of the external data sources improves the accuracies. +Somewhat surprisingly, despite ML-based methods` popularity in both business + and academia in recent years, we must conclude that classical forecasting + methods suffice to reach the best accuracy in our study. +There is one case where ML-based methods are competitive in our case study: + In a high demand pixel, if only about four to six weeks of past data is + available, the \textit{vrfr} model outperformed the classical ones. +So, we recommend trying out ML-based methods in such scenarios. +In addition, with the \textit{hsma} and \textit{hets} models being the overall + winners, incorporating real-time data is not beneficial, in particular, + with more than six weeks of training material available. +Lastly, with just \textit{hets}, that exhibits an accuracy comparable to + \textit{hsma} for low and medium demand, our industry partner can likely + schedule its shifts on an hourly basis one week in advance. + +This study gives rise to the following managerial implications. +First, UDPs can implement readily available forecasting algorithms with limited + effort. +This, however, requires purposeful data collection and preparation by those + companies, which, according to our study, is at least equally important as + the selection of the forecasting algorithm, as becomes clear from + investigating the impact of the length of the training horizon. +Second, the benefits of moving from manual forecasting to automated forecasting + include being able to pursue a predictive routing strategy and + demand-adjusted shift scheduling. +At the time the case study data was collected, our industry partner did not + conduct any forecasting; the only forecasting-related activities were the + shift managers scheduling the shifts one week in advance manually in + spreadsheets. +Thus, selecting the right forecasting algorithm according to the framework + proposed in this study becomes a prerequisite to the much needed + operational improvements UDPs need to achieve in their quest for + profitability. +In general, many UDPs launched in recent years are venture capital backed + start-up companies that almost by definition do not have a strong + grounding in operational excellence, and publications such as the ones by + Uber are the exception rather than the rule. +Our paper shows that forecasting the next couple of hours can already be + implemented within the first year of a UDP's operations. +Even if such forecasts could not be exploited by predictive routing (e.g., due + to prolonged waiting times at restaurants), they would help monitoring the + operations for exceptional events. +Additionally, the shift planning may be automated saving as much as one shift + manager per city. +We emphasize that for the most part, our proposed forecasting system + is calibrated automatically and no manual work by a data scientist is required. +The only two parameters where assumptions need to be made are the pixel size + and the time step. +While they can only be optimized by the data scientist over time, the results in our + empirical study suggest that a pixel size of $1~\text{km}^2$ and a time step of + one hour are ideal. \ No newline at end of file diff --git a/tex/5_con/4_further_research.tex b/tex/5_con/4_further_research.tex new file mode 100644 index 0000000..be2a006 --- /dev/null +++ b/tex/5_con/4_further_research.tex @@ -0,0 +1,45 @@ +\subsection{Further Research} +\label{further_research} + +Sub-sections \ref{overall_results} and \ref{fams} present the models' average + performance. +We did not research what is the best model in a given pixel on a given day. +To answer this, a study finding an optimal number of outer validation days is + neccessary. +With the varying effect of the training horizon, this model selection is a + two-dimensional grid search that is prone to overfitting due to the high + noise in low count data. +Except heuristics relating the ADD to the training horizon, we cannot say + anything about that based on our study. +\cite{lemke2010} and \cite{wang2009} show how, for example, a time series' + characteristics may be used to select models. +Thus, we suggest conducting more detailed analyses on how to incorporate model + selection into our proposed forecasting system. + +Future research should also integrate our forecasting system into a predictive + routing application and evaluate its business impact. +This embeds our research into the vast literature on the VRP. +Initially introduced by \cite{dantzig1959}, \gls{vrp}s are concerned with + finding optimal routes serving customers. +We refer to \cite{toth2014} for a comprehensive overview. +The two variants relevant for the UDP case are the dynamic VRP and + the pickup and delivery problem (\gls{pdp}). +A VRP is dynamic if the data to solve a problem only becomes available + as the operations are underway. +\cite{thomas2010}, \cite{pillac2013}, and \cite{psaraftis2016} describe how + technological advances, in particular, mobile technologies, have led to a + renewed interest in research on dynamic VRPs, and + \cite{berbeglia2010} provide a general overview. +\cite{ichoua2006} and \cite{ferrucci2013} provide solution methods for + simulation studies where they assume stochastic customer demand based on + historical distributions. +In both studies, dummy demand nodes are inserted into the VRP instance. +Forecasts by our system extend this idea naturally as dummy nodes could be + derived from point forecasts as well. +The concrete case of a meal delivering UDP is contained in a recent + literature stream started by \cite{ulmer2017} and extended by + \cite{reyes2018} and \cite{yildiz2018}: They coin the term meal delivery + routing problem (\gls{mdrp}). +The MDRP is a special case of the dynamic PDP where the defining + characteristic is that once a vehicle is scheduled, a modification of the + route is inadmissible. diff --git a/tex/glossary.tex b/tex/glossary.tex index ea86d45..63cb402 100644 --- a/tex/glossary.tex +++ b/tex/glossary.tex @@ -11,9 +11,15 @@ \newglossaryentry{mase}{ name=MASE, description={Mean Absolute Scaled Error} } +\newglossaryentry{mdrp}{ + name=MDRP, description={Meal Delivery Routing Proplem} +} \newglossaryentry{ml}{ name=ML, description={Machine Learning} } +\newglossaryentry{pdp}{ + name=PDP, description={Pickup and Delivery Problem} +} \newglossaryentry{rf}{ name=RF, description={Random Forest} } diff --git a/tex/references.bib b/tex/references.bib index 05fd42b..8926f3f 100644 --- a/tex/references.bib +++ b/tex/references.bib @@ -44,6 +44,18 @@ howpublished = {\url{https://eng.uber.com/forecasting-introduction/}}, note = {Accessed: 2020-10-01} } +@article{berbeglia2010, +title={Dynamic Pickup and Delivery Problems}, +author={Berbeglia, Gerardo and Cordeau, Jean-Fran{\c{c}}ois + and Laporte, Gilbert}, +year={2010}, +journal={European Journal of Operational Research}, +volume={202}, +number={1}, +pages={8--15}, +publisher={Elsevier} +} + @article{box1962, title={Some statistical Aspects of adaptive Optimization and Control}, author={Box, George and Jenkins, Gwilym}, @@ -167,6 +179,17 @@ year={2016}, publisher={Springer} } +@article{dantzig1959, +title={The truck dispatching problem}, +author={Dantzig, George and Ramser, John}, +year={1959}, +journal={Management science}, +volume={6}, +number={1}, +pages={80--91}, +publisher={Informs} +} + @article{de2006, title={25 Years of Time Series Forecasting}, author={De Gooijer, Jan and Hyndman, Rob}, @@ -196,6 +219,18 @@ volume={116}, pages={242--265} } +@article{ferrucci2013, +title={A pro-active real-time Control Approach for Dynamic Vehicle Routing + Problems dealing with the Delivery of urgent Goods}, +author={Ferrucci, Francesco and Bock, Stefan and Gendreau, Michel}, +year={2013}, +journal={European Journal of Operational Research}, +volume={225}, +number={1}, +pages={130--141}, +publisher={Elsevier} +} + @article{gardner1985, title={Forecasting Trends in Time Series}, author={Gardner, Everette and McKenzie, Ed}, @@ -329,6 +364,18 @@ year={2018}, publisher={OTexts} } +@article{ichoua2006, +title={Exploiting Knowledge about Future Demands for Real-time Vehicle + Dispatching}, +author={Ichoua, Soumia and Gendreau, Michel and Potvin, Jean-Yves}, +year={2006}, +journal={Transportation Science}, +volume={40}, +number={2}, +pages={211--225}, +publisher={INFORMS} +} + @article{kim2016, title={A new Metric of Absolute Percentage Error for Intermittent Demand Forecasts}, @@ -362,6 +409,17 @@ howpublished = {\url{https://eng.uber.com/neural-networks/}}, note = {Accessed: 2020-10-01} } +@article{lemke2010, +title={Meta-Learning for Time Series Forecasting and Forecast Combination}, +author={Lemke, Christiane and Gabrys, Bogdan}, +year={2010}, +journal={Neurocomputing}, +volume={73}, +number={10-12}, +pages={2006--2016}, +publisher={Elsevier} +} + @article{ma2018, title={Using the Gradient Boosting Decision Tree to Improve the Delineation of Hourly Rain Areas during the Summer from Advanced Himawari Imager Data}, @@ -430,6 +488,18 @@ number={5}, pages={311--315} } +@article{pillac2013, +title={A Review of Dynamic Vehicle Routing Problems}, +author={Pillac, Victor and Gendreau, Michel and Gu{\'e}ret, Christelle + and Medaglia, Andr{\'e}s L}, +year={2013}, +journal={European Journal of Operational Research}, +volume={225}, +number={1}, +pages={1--11}, +publisher={Elsevier} +} + @article{prestwich2014, title={Mean-based Error Measures for Intermittent Demand Forecasting}, author={Prestwich, Steven and Rossi, Roberto and Tarim, Armagan @@ -442,6 +512,25 @@ pages={6782--6791}, publisher={Taylor \& Francis} } +@article{psaraftis2016, +title={Dynamic Vehicle Routing Problems: Three Decades and Counting}, +author={Psaraftis, Harilaos and Wen, Min and Kontovas, Christos}, +year={2016}, +journal={Networks}, +volume={67}, +number={1}, +pages={3--31}, +publisher={Wiley Online Library} +} + +@article{reyes2018, +title={The Meal Delivery Routing Problem}, +author={Reyes, Damian and Erera, Alan and Savelsbergh, Martin + and Sahasrabudhe, Sagar and O’Neil, Ryan}, + year={2018}, +journal={Optimization Online} +} + @incollection{scholkopf1998, title={Fast Approximation of Support Vector Kernel Expansions, and an Interpretation of Clustering as Approximation in Feature Spaces}, @@ -501,6 +590,30 @@ number={4}, pages={715--725} } +@article{thomas2010, +title={Dynamic vehicle routing}, +author={Thomas, Barrett W}, +year={2010}, +journal={Wiley Encyclopedia of Operations Research and Management Science}, +publisher={Wiley Online Library} +} + +@book{toth2014, +title={Vehicle Routing: Problems, Methods, and Applications}, +author={Toth, Paolo and Vigo, Daniele}, +year={2014}, +publisher={SIAM} +} + +@techreport{ulmer2017, +title={The Restaurant Meal Delivery Problem: Dynamic Pick-up and Delivery with + Deadlines and Random Ready Times}, +author={Ulmer, Marlin and Thomas, Barrett and Campbell, Ann Melissa + and Woyak, Nicholas}, +year={2017}, +institution={Technical Report} +} + @article{vapnik1963, title={Pattern Recognition using Generalized Portrait Method}, author={Vapnik, Vladimir and Lerner, A}, @@ -525,6 +638,18 @@ year={2013}, publisher={Springer} } +@article{wang2009, +title={Rule Induction for Forecasting Method Selection: + Meta-learning the Characteristics of Univariate Time Series}, +author={Wang, Xiaozhe and Smith-Miles, Kate and Hyndman, Rob}, +year={2009}, +journal={Neurocomputing}, +volume={72}, +number={10-12}, +pages={2581--2594}, +publisher={Elsevier} +} + @article{wang2018, title={Delivering meals for multiple suppliers: Exclusive or sharing logistics service}, @@ -555,4 +680,11 @@ journal={Management Science}, volume={6}, number={3}, pages={324--342} +} + +@article{yildiz2018, +title={Provably High-Quality Solutions for the Meal Delivery Routing Problem}, +author={Yildiz, Baris and Savelsbergh, Martin}, + year={2018}, +journal={Optimization Online} } \ No newline at end of file From 4784f76ec87779c2ef3a76c8509b9f0c302bc1ca Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Mon, 5 Oct 2020 01:03:06 +0200 Subject: [PATCH 15/28] Adjust placement of tables --- tex/4_stu/4_overall.tex | 14 +++++++------- tex/4_stu/6_fams.tex | 26 +++++++++++++------------- 2 files changed, 20 insertions(+), 20 deletions(-) diff --git a/tex/4_stu/4_overall.tex b/tex/4_stu/4_overall.tex index dff9559..4d11718 100644 --- a/tex/4_stu/4_overall.tex +++ b/tex/4_stu/4_overall.tex @@ -44,13 +44,6 @@ As the non-seasonal \textit{hses} reaches a similar accuracy as its So, in the absence of seasonality, models that only model a trend part are the least susceptible to the noise. -For medium demand (i.e., $10 < \text{ADD} < 25$) and training horizons up to - six weeks, the best-performing models are the same as for low demand. -For longer horizons, \textit{hets} provides the highest accuracy. -Thus, to fit a seasonal pattern, longer training horizons are needed. -While \textit{vsvr} enters the top three, \textit{hets} has the edge as they - neither require parameter tuning nor real-time data. - \begin{center} \captionof{table}{Top-3 models by training weeks and average demand ($1~\text{km}^2$ pixel size, 60-minute time steps)} @@ -206,6 +199,13 @@ While \textit{vsvr} enters the top three, \textit{hets} has the edge as they \end{tabular} \end{center} +For medium demand (i.e., $10 < \text{ADD} < 25$) and training horizons up to + six weeks, the best-performing models are the same as for low demand. +For longer horizons, \textit{hets} provides the highest accuracy. +Thus, to fit a seasonal pattern, longer training horizons are needed. +While \textit{vsvr} enters the top three, \textit{hets} has the edge as they + neither require parameter tuning nor real-time data. + In summary, except for high demand, simple models trained on horizontal time series work best. By contrast, high demand (i.e., $25 < \text{ADD} < \infty$) and less than diff --git a/tex/4_stu/6_fams.tex b/tex/4_stu/6_fams.tex index 8fdd17d..c398824 100644 --- a/tex/4_stu/6_fams.tex +++ b/tex/4_stu/6_fams.tex @@ -1,19 +1,6 @@ \subsection{Results by Model Families} \label{fams} -Besides the overall results, we provide an in-depth comparison of models - within a family. -Instead of reporting the MASE per model, we rank the models holding the - training horizon fixed to make comparison easier. -Table \ref{t:hori} presents the models trained on horizontal time series. -In addition to \textit{naive}, we include \textit{fnaive} and \textit{pnaive} - already here as more competitive benchmarks. -The tables in this section report two rankings simultaneously: -The first number is the rank resulting from lumping the low and medium - clusters together, which yields almost the same rankings when analyzed - individually. -The ranks from only high demand pixels are in parentheses if they differ. - \begin{center} \captionof{table}{Ranking of benchmark and horizontal models ($1~\text{km}^2$ pixel size, 60-minute time steps): @@ -47,6 +34,19 @@ The ranks from only high demand pixels are in parentheses if they differ. \end{center} \ +Besides the overall results, we provide an in-depth comparison of models + within a family. +Instead of reporting the MASE per model, we rank the models holding the + training horizon fixed to make comparison easier. +Table \ref{t:hori} presents the models trained on horizontal time series. +In addition to \textit{naive}, we include \textit{fnaive} and \textit{pnaive} + already here as more competitive benchmarks. +The tables in this section report two rankings simultaneously: +The first number is the rank resulting from lumping the low and medium + clusters together, which yields almost the same rankings when analyzed + individually. +The ranks from only high demand pixels are in parentheses if they differ. + A first insight is that \textit{fnaive} is the best benchmark in all scenarios: Decomposing flexibly by tuning the $ns$ parameter is worth the computational From 76343f1f682e2bb76918d3b2c2f0ecd8a099dd46 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Mon, 5 Oct 2020 01:05:03 +0200 Subject: [PATCH 16/28] Update rendered PDF version --- paper.pdf | Bin 782217 -> 788998 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/paper.pdf b/paper.pdf index 132288a27fc443d727509fc74b58412ca0b38f02..7d6ed23197971cef731209e5e50e2e7ea745d697 100644 GIT binary patch delta 125287 zcmV)FK)=6<-!F!gFpwpa(ibVQPLTx=Zn|`XRT3r90)T%2M#N`qm!WJ26O#c37MEdm z1SzvX26+L0wtJD09Y)ug5hvZsdu{!m+?r<_zT;U=<&y5vt9f3S*BzPhm{?T*mE_P0K%lV2!i<%FnKU zl_lulf~=lQ7<;Re0H2sCNRExe4=Mmz#)*LO)VssG%E=?swt7}*E;3*N3O1Gwy@Ld4 zjlf-wDvG;2PvF_^)LI=wYwR6QN8c;SoKB=gURIIeAOsC?U|v}rnn?(4b~74m1r2EF z%^8({A|E7NVJZ7ZnUg2!Ymt<66COhyFR?+u!huSxVd)aJ0L-^09{dz)F+hpf+{d+- z91Nx&eHhlfeF-{#TOsUBaGqS40YnJ{Xe9a(WeR)K3+eWfM7fGRni9bM`uI;p9Bd|Z 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z$f(lgetqHne~Pp(ej(sG(q*~TH#lT^^;=K4m8*o8E>C)cES8eQ_HcADtv-{>e=1I5Dn8FE{z*&4*NYXS&X-M? z^RBHpge$ISDz<9Hl$G-vb9aa=qnTZdNF|l#J zJ@Yon7U@me8A2_3dpY3QbAdqfKZ1{g{FecG3KN(A=?e{)HUFE<3NKS>dSxIo zH8%<`S0Gz4ATuB_T?#K!Z*O!UGBq?HFd$M2FG+4@Zy+)?H6Sn`QVK6gL?Bx{H#jym zIWs~xL`5|-GchnQGch4P6Q^Ol59obZ8(qGBTIZ?FT7;C6irDk6{?bpDVBb^Zft+-bx=T ziqf|VeMyp}NJT_MzCY$f8?)u4=Hq~9bHbJr4wx~AvN0ax#EcU&A6w12%`%Q0V3V$^ zli#lEe(vXfpZ9t0+Zbb}6O0K#7#NdmW|XfZYKc`u6VXVN6KjZiq6V&MnRcvWfjLA1 zOvEUE7Nwm_1TaZ=7z-^CfywkrSxz(%Rm5sy8B?^^!Q}tZwm1=ksi@JmYTA%UgsFe4 zSPN}3kp$B=rfu_x6qxSIvS~yrO#gk^3?d!o*d`TNL9Apflb8>4YOeCKi7c4m3(8v$ zbG2Cu3yB3V7gMy*Oq)yOAn2+w2=?7p-eO{Z5rWQbT%k^WT%_P}w)Du{B}BU7@v*h<)eN3#6i za5?PYEm_@Z73|q}`feL7TOh1~y`l#Vbvbpg*GFa98(}@{jco0xq~!~S4X_VpPsLV$ z2^(R@XWvZ+T1zy+KL4)R23oaGGwhorZCg*Yzq{la2o8=oi9Q>a!#rk@$S!3C5YcllPX30=`N`< x#NVHk;%InwiSHoTAifLniHw Date: Fri, 9 Oct 2020 14:48:10 +0200 Subject: [PATCH 17/28] Streamline text --- tex/5_con/3_implications.tex | 13 ++++++++----- 1 file changed, 8 insertions(+), 5 deletions(-) diff --git a/tex/5_con/3_implications.tex b/tex/5_con/3_implications.tex index 6fe91a4..ce9c194 100644 --- a/tex/5_con/3_implications.tex +++ b/tex/5_con/3_implications.tex @@ -10,8 +10,9 @@ Somewhat surprisingly, despite ML-based methods` popularity in both business and academia in recent years, we must conclude that classical forecasting methods suffice to reach the best accuracy in our study. There is one case where ML-based methods are competitive in our case study: - In a high demand pixel, if only about four to six weeks of past data is - available, the \textit{vrfr} model outperformed the classical ones. + In a high demand pixel (defined as more than 25 orders per day on average), + if only about four to six weeks of past data is available, + the \textit{vrfr} model outperformed the classical ones. So, we recommend trying out ML-based methods in such scenarios. In addition, with the \textit{hsma} and \textit{hets} models being the overall winners, incorporating real-time data is not beneficial, in particular, @@ -53,6 +54,8 @@ We emphasize that for the most part, our proposed forecasting system is calibrated automatically and no manual work by a data scientist is required. The only two parameters where assumptions need to be made are the pixel size and the time step. -While they can only be optimized by the data scientist over time, the results in our - empirical study suggest that a pixel size of $1~\text{km}^2$ and a time step of - one hour are ideal. \ No newline at end of file +The results in our empirical study suggest + that a pixel size of $1~\text{km}^2$ and a time step of one hour are ideal, + which results in the optimal trade-off + between signal strength and spatial-temporal resolution. +Future research may explore adaptive grid-sizing depending on, for instance, demand density. \ No newline at end of file From a440752c4e4f7bd40d906d5d8ae30f060ddbe4ba Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Fri, 9 Oct 2020 14:48:29 +0200 Subject: [PATCH 18/28] Rephrase abstract - streamline first half - add "on a grid" - add note on predictive routing applications - mention managerial findings and winning forecasting method in second half --- tex/meta.tex | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/tex/meta.tex b/tex/meta.tex index d944b33..8296540 100644 --- a/tex/meta.tex +++ b/tex/meta.tex @@ -23,18 +23,18 @@ Emails: \begin{abstract} Meal delivery platforms like Uber Eats shape the landscape in cities around the world. -This paper addresses forecasting demand into the short-term future. +This paper addresses forecasting demand on a grid into the short-term future, + enabling, for example, predictive routing applications. We propose an approach incorporating - both classical forecasting - and machine learning methods. -Model evaluation and selection is adapted to demand typical for such a platform - (i.e., intermittent with a double-seasonal pattern). -The results of an empirical study with a European meal delivery service show - that machine learning models become competitive - once the average daily demand passes a threshold. -As a main contribution, the paper explains - how a forecasting system must be set up - to enable predictive routing. + both classical forecasting and machine learning methods + and adapt model evaluation and selection to typical demand: + intermittent with a double-seasonal pattern. +An empirical study shows that + an exponential smoothing based method trained on past demand data alone + achieves optimal accuracy, + if at least two months are on record. +With only a shorter demand history, + machine learning methods and real-time data may improve prediction. \end{abstract} 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znNPvZrF}tkfdl@(RxG*LLEn)P$$=dD@XV@K-e#n1TpaMsnxwj{r0k@u|BNaQ4zB-< ztfVZYD)7uQ_T~=%G`9b%iIeIINV0QraIvw9h=_}`OLFi^uySxqvhnb8v$1fAvGR(r z36cK)hv*~yKMQ-@>>U5I!wIBHlCxD5!3{gIivu2hDJkiGuabMn_nt{zY>Kk3z$w>k zNu4dPM=cu+3yr8nC1Z@29xN9X4bpBh_(*B7>7PDGl63Kn^2z zURxYFs2M*P@W#1tfCg-X1B8=ES47AzLsF>dzd*-4q9Ygft&4a6%DDFKls0A_2f0WU5=1;W&RCpK8&l|Ax>%vq;Z=*Du9fOW7_>&|#Gc&y4QjN8 zDmB^i*CAC)mH?xmBm7%my-!H%Agd1|T_cv^meA(>1-gjE8WHSGaz&o^nyHtYgdzb) zF9Cp_7u-ILyI%nI7pOj=TRO)NvsKa*z|^yA(8Vr0tb0_hXswJdc3<`NT*QeZB=0H! zdVR#LDBUscivFP2?^rn_wDk=*t2fxeM0Y^eeU+jjWVB0RkphqU#GGtS@p+f5LWZ8* zj`Ra2QY>9oLRv3^0gJ-P;%6CDb)5o{8WenLVkK3^@&amv2PIpm3nL7mk1PT7jM yzph8t7HLc5+U}VtpJ3;S0h+E(@)m From cff8e480be088886b20b0c4e5353d89bcf9b7bd1 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Wed, 14 Oct 2020 11:46:44 +0200 Subject: [PATCH 20/28] Rephrase abstract --- tex/meta.tex | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/tex/meta.tex b/tex/meta.tex index 8296540..b5d0aa0 100644 --- a/tex/meta.tex +++ b/tex/meta.tex @@ -33,8 +33,9 @@ An empirical study shows that an exponential smoothing based method trained on past demand data alone achieves optimal accuracy, if at least two months are on record. -With only a shorter demand history, - machine learning methods and real-time data may improve prediction. +With a more limited demand history, + machine learning is shown + to yield more accurate prediction results than classical methods. \end{abstract} \begin{keyword} From e356af7c778eaef9a0710dbb7d048c293c61676f Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Wed, 14 Oct 2020 11:46:53 +0200 Subject: [PATCH 21/28] Update rendered PDF version --- paper.pdf | Bin 791062 -> 791333 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/paper.pdf b/paper.pdf index ebca2c7a28ec6dd400533d2c4b1014968245ef85..6eeca4486f967b872e002af1379c0eee49816fee 100644 GIT binary patch delta 26001 zcmV(Rv9C!h0Cx(B9t7`=OEEHtl 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z#cAc^M}S4US^hg_pz)x5EFQl~jRQ6!HcVZe9M#>X3(MI1SSTNPJJ3d*?eoTFi4AVw z(zE0B0%CVjXiUL&J7PClcS@z$qiwf{PkrAjY&A_2^8ePlQ&F)|F_6I=+{o0_5=xTD F{|`C+A Date: Sun, 25 Oct 2020 17:41:16 +0100 Subject: [PATCH 22/28] Mention corresponding author --- tex/meta.tex | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/tex/meta.tex b/tex/meta.tex index b5d0aa0..941fc1f 100644 --- a/tex/meta.tex +++ b/tex/meta.tex @@ -3,7 +3,7 @@ \journal{Transportation Research Part E} \title{Real-time Demand Forecasting for an Urban Delivery Platform} -\author[WHU]{Alexander Hess\fnref{emails}} +\author[WHU]{Alexander Hess\fnref{emails}\fnref{corresponding}} \author[WHU]{Stefan Spinler\fnref{emails}} \author[MIT]{Matthias Winkenbach\fnref{emails}} \address[WHU]{ @@ -21,6 +21,11 @@ Emails: mwinkenb@mit.edu } +\fntext[corresponding]{ +The corresponding author is Alexander Hess. +Use the provided email. +} + \begin{abstract} Meal delivery platforms like Uber Eats shape the landscape in cities around the world. This paper addresses forecasting demand on a grid into the short-term future, From 7797cad0582c061c6054c83763ab32a12102e6d3 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 25 Oct 2020 17:48:25 +0100 Subject: [PATCH 23/28] Use Author (Year) citation style --- paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper.tex b/paper.tex index 333f2f1..2e5a040 100644 --- a/paper.tex +++ b/paper.tex @@ -1,4 +1,4 @@ -\documentclass[preprint,review,12pt]{static/elsarticle} +\documentclass[preprint,review,12pt,authoryear]{static/elsarticle} \input{tex/preamble} From f8321bf8354b296bb26d069db2f74a0a18bfd2d7 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 25 Oct 2020 18:25:53 +0100 Subject: [PATCH 24/28] Remove dots in sub-sub-sections --- tex/2_lit/2_class/2_ets.tex | 2 +- tex/2_lit/2_class/3_arima.tex | 2 +- tex/2_lit/2_class/4_stl.tex | 2 +- tex/2_lit/3_ml/2_learning.tex | 2 +- tex/2_lit/3_ml/3_cv.tex | 2 +- tex/2_lit/3_ml/4_rf.tex | 2 +- tex/2_lit/3_ml/5_svm.tex | 2 +- tex/3_mod/7_models/2_hori.tex | 2 +- tex/3_mod/7_models/3_vert.tex | 2 +- tex/3_mod/7_models/4_rt.tex | 2 +- tex/3_mod/7_models/5_ml.tex | 2 +- 11 files changed, 11 insertions(+), 11 deletions(-) diff --git a/tex/2_lit/2_class/2_ets.tex b/tex/2_lit/2_class/2_ets.tex index 6db9781..53537da 100644 --- a/tex/2_lit/2_class/2_ets.tex +++ b/tex/2_lit/2_class/2_ets.tex @@ -1,4 +1,4 @@ -\subsubsection{Na\"{i}ve Methods, Moving Averages, and Exponential Smoothing.} +\subsubsection{Na\"{i}ve Methods, Moving Averages, and Exponential Smoothing} \label{ets} Simple forecasting methods are often employed as a benchmark for more diff --git a/tex/2_lit/2_class/3_arima.tex b/tex/2_lit/2_class/3_arima.tex index d55ffd8..3432b7e 100644 --- a/tex/2_lit/2_class/3_arima.tex +++ b/tex/2_lit/2_class/3_arima.tex @@ -1,4 +1,4 @@ -\subsubsection{Autoregressive Integrated Moving Averages.} +\subsubsection{Autoregressive Integrated Moving Averages} \label{arima} \cite{box1962}, \cite{box1968}, and more papers by the same authors in the diff --git a/tex/2_lit/2_class/4_stl.tex b/tex/2_lit/2_class/4_stl.tex index 127123c..39c987a 100644 --- a/tex/2_lit/2_class/4_stl.tex +++ b/tex/2_lit/2_class/4_stl.tex @@ -1,4 +1,4 @@ -\subsubsection{Seasonal and Trend Decomposition using Loess.} +\subsubsection{Seasonal and Trend Decomposition using Loess} \label{stl} A time series $y_t$ may exhibit different types of patterns; to fully capture diff --git a/tex/2_lit/3_ml/2_learning.tex b/tex/2_lit/3_ml/2_learning.tex index 86d157a..5e7c2bc 100644 --- a/tex/2_lit/3_ml/2_learning.tex +++ b/tex/2_lit/3_ml/2_learning.tex @@ -1,4 +1,4 @@ -\subsubsection{Supervised Learning.} +\subsubsection{Supervised Learning} \label{learning} A conceptual difference between classical and ML methods is the format diff --git a/tex/2_lit/3_ml/3_cv.tex b/tex/2_lit/3_ml/3_cv.tex index 1d5186b..abfdebc 100644 --- a/tex/2_lit/3_ml/3_cv.tex +++ b/tex/2_lit/3_ml/3_cv.tex @@ -1,4 +1,4 @@ -\subsubsection{Cross-Validation.} +\subsubsection{Cross-Validation} \label{cv} Because ML models are trained by minimizing a loss function $L$, the diff --git a/tex/2_lit/3_ml/4_rf.tex b/tex/2_lit/3_ml/4_rf.tex index 784d2a7..eeb7161 100644 --- a/tex/2_lit/3_ml/4_rf.tex +++ b/tex/2_lit/3_ml/4_rf.tex @@ -1,4 +1,4 @@ -\subsubsection{Random Forest Regression.} +\subsubsection{Random Forest Regression} \label{rf} \cite{breiman1984} introduce the classification and regression tree diff --git a/tex/2_lit/3_ml/5_svm.tex b/tex/2_lit/3_ml/5_svm.tex index 1c12af5..528fe9e 100644 --- a/tex/2_lit/3_ml/5_svm.tex +++ b/tex/2_lit/3_ml/5_svm.tex @@ -1,4 +1,4 @@ -\subsubsection{Support Vector Regression.} +\subsubsection{Support Vector Regression} \label{svm} \cite{vapnik1963} and \cite{vapnik1964} introduce the so-called support vector diff --git a/tex/3_mod/7_models/2_hori.tex b/tex/3_mod/7_models/2_hori.tex index 5d5959a..21cc627 100644 --- a/tex/3_mod/7_models/2_hori.tex +++ b/tex/3_mod/7_models/2_hori.tex @@ -1,4 +1,4 @@ -\subsubsection{Horizontal and Whole-day-ahead Forecasts.} +\subsubsection{Horizontal and Whole-day-ahead Forecasts} \label{hori} The upper-left in Figure \ref{f:inputs} illustrates the simplest way to diff --git a/tex/3_mod/7_models/3_vert.tex b/tex/3_mod/7_models/3_vert.tex index 5459b81..43aaaf1 100644 --- a/tex/3_mod/7_models/3_vert.tex +++ b/tex/3_mod/7_models/3_vert.tex @@ -1,4 +1,4 @@ -\subsubsection{Vertical and Whole-day-ahead Forecasts without Retraining.} +\subsubsection{Vertical and Whole-day-ahead Forecasts without Retraining} \label{vert} The upper-right in Figure \ref{f:inputs} shows an alternative way to diff --git a/tex/3_mod/7_models/4_rt.tex b/tex/3_mod/7_models/4_rt.tex index 75122cc..6fa038d 100644 --- a/tex/3_mod/7_models/4_rt.tex +++ b/tex/3_mod/7_models/4_rt.tex @@ -1,4 +1,4 @@ -\subsubsection{Vertical and Real-time Forecasts with Retraining.} +\subsubsection{Vertical and Real-time Forecasts with Retraining} \label{rt} The lower-left in Figure \ref{f:inputs} shows how models trained on vertical diff --git a/tex/3_mod/7_models/5_ml.tex b/tex/3_mod/7_models/5_ml.tex index 26f22a6..7ca00c4 100644 --- a/tex/3_mod/7_models/5_ml.tex +++ b/tex/3_mod/7_models/5_ml.tex @@ -1,4 +1,4 @@ -\subsubsection{Vertical and Real-time Forecasts without Retraining.} +\subsubsection{Vertical and Real-time Forecasts without Retraining} \label{ml_models} The lower-right in Figure \ref{f:inputs} shows how ML models take From ec7b18822a0854a83e691770cb7994b53327d023 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 25 Oct 2020 18:43:47 +0100 Subject: [PATCH 25/28] Move glossary into an appendix --- paper.tex | 5 ++--- tex/1_intro.tex | 9 +++++---- tex/{ => apx}/glossary.tex | 5 ++++- 3 files changed, 11 insertions(+), 8 deletions(-) rename tex/{ => apx}/glossary.tex (98%) diff --git a/paper.tex b/paper.tex index 2e5a040..4659df3 100644 --- a/paper.tex +++ b/paper.tex @@ -42,9 +42,6 @@ \input{tex/5_con/4_further_research} \newpage -\input{tex/glossary} -\newpage - \appendix \newpage \input{tex/apx/tabular_ml_models} @@ -55,6 +52,8 @@ \newpage \input{tex/apx/peak_results} \newpage +\input{tex/apx/glossary} +\newpage \bibliographystyle{static/elsarticle-harv} \bibliography{tex/references} diff --git a/tex/1_intro.tex b/tex/1_intro.tex index 87d0171..c35cf91 100644 --- a/tex/1_intro.tex +++ b/tex/1_intro.tex @@ -11,8 +11,9 @@ A common feature of these platforms is that they do not operate kitchens but related processes in simple smartphone apps, and managing the delivery via a fleet of either employees or crowd-sourced sub-contractors. -Various kind of urban delivery platforms (UDP) have received attention in - recent scholarly publications. +Various kinds of urban delivery platforms + (\gls{udp}; \ref{glossary} provides a glossary with all abbreviations) + have received attention in recent scholarly publications. \cite{hou2018} look into heuristics to simultaneously optimize courier scheduling and routing in general, while \cite{masmoudi2018} do so for the popular dial-a-ride problem and \cite{wang2018} investigate @@ -63,8 +64,8 @@ Moreover, many of the established forecasting methods can only handle a single and often low seasonality (i.e., repeated regular pattern), if at all. In this paper, we develop a rigorous methodology as to how to build and - evaluate a robust forecasting system for an urban delivery platform - (\gls{udp}) that offers ad-hoc point-to-point transportation of any kind. + evaluate a robust forecasting system for an UDP + that offers ad-hoc point-to-point transportation of any kind. We implement such a system with a broad set of commonly used forecasting methods. We not only apply established (i.e., "classical") time series methods but also diff --git a/tex/glossary.tex b/tex/apx/glossary.tex similarity index 98% rename from tex/glossary.tex rename to tex/apx/glossary.tex index 63cb402..77eb8b3 100644 --- a/tex/glossary.tex +++ b/tex/apx/glossary.tex @@ -1,3 +1,6 @@ +\section{Glossary} +\label{glossary} + % Abbreviations for technical terms. \newglossaryentry{add}{ name=ADD, description={Average Daily Demand} @@ -138,4 +141,4 @@ trained on vertical time series} } -\printglossaries \ No newline at end of file +\printglossary[title=] \ No newline at end of file From 3706dd44b727c9abacb09bfb64b4662fa6dc4ec5 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 25 Oct 2020 19:18:54 +0100 Subject: [PATCH 26/28] Amend literature --- tex/3_mod/3_grid.tex | 8 +++++--- tex/references.bib | 42 ++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 47 insertions(+), 3 deletions(-) diff --git a/tex/3_mod/3_grid.tex b/tex/3_mod/3_grid.tex index baa0828..222b1ec 100644 --- a/tex/3_mod/3_grid.tex +++ b/tex/3_mod/3_grid.tex @@ -9,9 +9,11 @@ Figure \ref{f:grid} shows how the orders' delivery locations are each covering the entire service area within a city. This gridification step is also applied to the pickup locations separately. The lower-left corner is chosen at random. -\cite{winkenbach2015} apply the same gridification idea and slice an urban - area to model a location-routing problem, and \cite{singleton2017} portray - it as a standard method in the field of urban analytics. +Applications of this gridification idea to model location-routing problems + can be viewed, for example, in \cite{winkenbach2015}, \cite{bergmann2020}, + \cite{janjevic2019}, \cite{snoeck2020}, and \cite{janjevic2020} + while \cite{singleton2017} portray it as a standard method in the field of + urban analytics. With increasing pixel sizes, the time series exhibit more order aggregation with a possibly stronger demand pattern. On the other hand, the larger the pixels, the less valuable become the diff --git a/tex/references.bib b/tex/references.bib index 8926f3f..3dca6ea 100644 --- a/tex/references.bib +++ b/tex/references.bib @@ -56,6 +56,17 @@ pages={8--15}, publisher={Elsevier} } +@article{bergmann2020, +title={Integrating first-mile pickup and last-mile delivery + on shared vehicle routes for efficient urban e-commerce distribution}, +author={Bergmann, Felix M and Wagner, Stephan M and Winkenbach, Matthias}, +year={2020}, +journal={Transportation Research Part B: Methodological}, +volume={131}, +pages={26--62}, +publisher={Elsevier} +} + @article{box1962, title={Some statistical Aspects of adaptive Optimization and Control}, author={Box, George and Jenkins, Gwilym}, @@ -376,6 +387,26 @@ pages={211--225}, publisher={INFORMS} } +@article{janjevic2019, +title={Integrating collection-and-delivery points + in the strategic design of urban last-mile e-commerce distribution networks}, +author={Janjevic, Milena and Winkenbach, Matthias and Merch{\'a}n, Daniel}, +year={2019}, +journal={Transportation Research Part E: Logistics and Transportation Review}, +volume={131}, +pages={37--67}, +publisher={Elsevier} +} + +@article{janjevic2020, +title={Designing Multi-tier, Multi-service-level, and Multi-modal + Last-Mile Distribution Networks for Omni-Channel Operations}, +author={Janjevic, Milena and Merchan, Daniel and Winkenbach, Matthias}, +year={2020}, +journal={European Journal of Operational Research}, +publisher={Elsevier} +} + @article{kim2016, title={A new Metric of Absolute Percentage Error for Intermittent Demand Forecasts}, @@ -559,6 +590,17 @@ number={3}, pages={199--222} } +@article{snoeck2020, +title={The value of physical distribution flexibility + in serving dense and uncertain urban markets}, +author={Snoeck, Andr{\'e} and Winkenbach, Matthias}, +year={2020}, +journal={Transportation Research Part A: Policy and Practice}, +volume={136}, +pages={151--177}, +publisher={Elsevier} +} + @article{stitson1999, title={Support Vector Regression with ANOVA Decomposition Kernels}, author={Stitson, Mark and Gammerman, Alex and Vapnik, Vladimir From ea0f5edc628d9e97e08bd96fd437720b8caa7c46 Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 25 Oct 2020 19:31:17 +0100 Subject: [PATCH 27/28] Update rendered version - move tables to avoid half blank pages --- paper.pdf | Bin 791333 -> 795190 bytes tex/4_stu/4_overall.tex | 62 +++++++++++++++++++++------------------- 2 files changed, 32 insertions(+), 30 deletions(-) diff --git a/paper.pdf b/paper.pdf index 6eeca4486f967b872e002af1379c0eee49816fee..4bdce7d835acbcb952ada2255ef8a1f08ae1ac0f 100644 GIT binary patch delta 149236 zcmV)LK)JuArZBd|FpwhyH8ePr@fRq6l^4m5+cxy>uh3BfMv6pjR8E;`CQVxml4d;3 zA;^K2Xp4xplGHfv*Y}Z+s_jH6TKFK6Z{MHqwwo7k(#lK9h$MODZTB86qmrgx8COwK zR^GPpKKUOw>q0Gh9)xL3{MWo^LxblxL0S2u zDSR$Z`0~DE8YueU^Y+&lZ%FPXNmS)IG1?R)iVNz6DT&fWo7;|m1^L{_06uTIQb?M` zUKv$ooEXXy^iNAKi_+B5u^X}`0*+}?dEo`-4RU_ed~ekzrT;jIp#zbtg5spO7L@!@ 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zop){3P*3|*`*4YcsTW?icKGRkO1yotSL6oMmUg>yp`jj9!+s|A~EhcA;g$0lc5lBlT>NCeoY7EqndH*qgBib#|1m3t b+A@Be-k`}X!)s(>YG!7{rK;-c@5TiH>z#%* From f010a69af21301379d5c2345494ab43dacbe5a8b Mon Sep 17 00:00:00 2001 From: Alexander Hess Date: Sun, 4 Oct 2020 23:58:46 +0200 Subject: [PATCH 12/28] Add Study section --- paper.tex | 11 +- tex/4_stu/1_intro.tex | 5 +- tex/4_stu/2_data.tex | 23 +++ tex/4_stu/3_params.tex | 37 +++++ tex/4_stu/4_overall.tex | 238 +++++++++++++++++++++++++++++++ tex/4_stu/5_training.tex | 31 ++++ tex/4_stu/6_fams.tex | 162 +++++++++++++++++++++ tex/4_stu/7_pixels_intervals.tex | 27 ++++ tex/apx/peak_results.tex | 13 +- tex/glossary.tex | 3 + tex/preamble.tex | 6 +- 11 files changed, 544 insertions(+), 12 deletions(-) create mode 100644 tex/4_stu/2_data.tex create mode 100644 tex/4_stu/3_params.tex create mode 100644 tex/4_stu/4_overall.tex create mode 100644 tex/4_stu/5_training.tex create mode 100644 tex/4_stu/6_fams.tex create mode 100644 tex/4_stu/7_pixels_intervals.tex diff --git a/paper.tex b/paper.tex index 78c1cd5..0cded62 100644 --- a/paper.tex +++ b/paper.tex @@ -30,8 +30,13 @@ \input{tex/3_mod/7_models/4_rt} \input{tex/3_mod/7_models/5_ml} \input{tex/4_stu/1_intro} +\input{tex/4_stu/2_data} +\input{tex/4_stu/3_params} +\input{tex/4_stu/4_overall} +\input{tex/4_stu/5_training} +\input{tex/4_stu/6_fams} +\input{tex/4_stu/7_pixels_intervals} \input{tex/5_con/1_intro} - \newpage \input{tex/glossary} @@ -43,6 +48,10 @@ \newpage \input{tex/apx/enhanced_feats} \newpage +\input{tex/apx/case_study} +\newpage +\input{tex/apx/peak_results} +\newpage \bibliographystyle{static/elsarticle-harv} \bibliography{tex/references} diff --git a/tex/4_stu/1_intro.tex b/tex/4_stu/1_intro.tex index 29411c5..f57ddb1 100644 --- a/tex/4_stu/1_intro.tex +++ b/tex/4_stu/1_intro.tex @@ -1,5 +1,6 @@ \section{Empirical Study: A Meal Delivery Platform in Europe} \label{stu} -% temporary placeholder -\label{params} \ No newline at end of file +In the following, we first give a brief overview of the case study dataset + and the parameters we applied to calibrate the time series generation. +Then, we discuss the overall results. diff --git a/tex/4_stu/2_data.tex b/tex/4_stu/2_data.tex new file mode 100644 index 0000000..53e075e --- /dev/null +++ b/tex/4_stu/2_data.tex @@ -0,0 +1,23 @@ +\subsection{Case Study Dataset} +\label{data} + +The studied dataset consists of a meal delivery platform's entire + transactional data covering the French market from launch in February of + 2016 to January of 2017. +The platform operated in five cities throughout this period and received a + total of 686,385 orders. +The forecasting models were developed based on the data from Lyon and Paris in + the period from August through December; this ensures comparability across + cities and avoids irregularities in demand assumed for a new service + within the first operating weeks. +The data exhibit a steady-state as the UDP's service area remained + unchanged, and the numbers of orders and of couriers grew in lock-step and + organically. +This does not mean that no new restaurants were openend: If that happened, the + new restaurant did not attract new customers, but demand was shifted from + other member restaurants. +Results are similar in both cities, and we only report them for Paris for + greater conciseness. +Lastly, the platform recorded all incoming orders, and lost demand does not + exist. +See \ref{dataset} for details on the raw data. diff --git a/tex/4_stu/3_params.tex b/tex/4_stu/3_params.tex new file mode 100644 index 0000000..329075a --- /dev/null +++ b/tex/4_stu/3_params.tex @@ -0,0 +1,37 @@ +\subsection{Calibration of the Time Series Generation Process} +\label{params} + +Independent of the concrete forecasting models, the time series generation + must be calibrated. +We concentrate our forecasts on the pickup side for two reasons. +First, the restaurants come in a significantly lower number than the + customers resulting in more aggregation in the order counts and thus a + better pattern recognition. +Second, from an operational point of view, forecasts for the pickups are more + valuable because of the waiting times due to meal preparation. +We choose pixel sizes of $0.5~\text{km}^2$, $1~\text{km}^2$, $2~\text{km}^2$, + and $4~\text{km}^2$, and time steps covering 60, 90, and 120 minute windows + resulting in $H_{60}=12$, $H_{90}=9$, and $H_{120}=6$ time steps per day + with the platform operating between 11 a.m. and 11 p.m. and corresponding + frequencies $k_{60}=7*12=84$, $k_{90}=7*9=63$, and $k_{120}=7*6=42$ for the + vertical time series. +Smaller pixels and shorter time steps yield no recognizable patterns, yet would + have been more beneficial for tactical routing. +90 and 120 minute time steps are most likely not desirable for routing; however, + we keep them for comparison and note that a UDP may employ such forecasts + to activate more couriers at short notice if a (too) high demand is + forecasted in an hour from now. +This could, for example, be implemented by paying couriers a premium if they + show up for work at short notice. +Discrete lengths of 3, 4, 5, 6, 7, and 8 weeks are chosen as training + horizons. +We do so as the structure within the pixels (i.e., number and kind of + restaurants) is not stable for more than two months in a row in the + covered horizon. +That is confirmed by the empirical finding that forecasting accuracy + improves with longer training horizon but this effect starts to + level off after about six to seven weeks. +So, the demand patterns of more than two months ago do not resemble more + recent ones. + +In total, 100,000s of distinct time series are forecast in the study. diff --git a/tex/4_stu/4_overall.tex b/tex/4_stu/4_overall.tex new file mode 100644 index 0000000..dff9559 --- /dev/null +++ b/tex/4_stu/4_overall.tex @@ -0,0 +1,238 @@ +\subsection{Overall Results} +\label{overall_results} + +Table \ref{t:results} summarizes the overall best-performing models grouped by + training horizon and a pixel's average daily demand (\gls{add}) for a + pixel size of $1~\text{km}^2$ and 60-minute time steps. +Each combination of pixel and test day counts as one case, and the total + number of cases is denoted as $n$. +Clustering the individual results revealed that a pixel's ADD over the + training horizon is the primary indicator of similarity and three to four + clusters suffice to obtain cohesive clusters: +We labeled them "no", "low", "medium", and "high" demand pixels with + increasing ADD, and present the average MASE per cluster. +The $n$ do not vary significantly across the training horizons, which confirms + that the platform did not grow area-wise and is indeed in a steady-state. +We use this table to answer \textbf{Q1} regarding the overall best methods + under different ADDs. +All result tables in the main text report MASEs calculated with all time + steps of a day. +In contrast, \ref{peak_results} shows the same tables with MASEs calculated + with time steps within peak times only (i.e., lunch from 12 pm to 2 pm and + dinner from 6 pm to 8 pm). +The differences lie mainly in the decimals of the individual MASE + averages while the ranks of the forecasting methods do not change except + in rare cases. +That shows that the presented accuracies are driven by the forecasting methods' + accuracies at peak times. +Intuitively, they all correctly predict zero demand for non-peak times. + +Unsurprisingly, the best model for pixels without demand (i.e., + $0 < \text{ADD} < 2.5$) is \textit{trivial}. +Whereas \textit{hsma} also adapts well, its performance is worse. +None of the more sophisticated models reaches a similar accuracy. +The intuition behind is that \textit{trivial} is the least distorted by the + relatively large proportion of noise given the low-count nature of the + time series. + +For low demand (i.e., $2.5 < \text{ADD} < 10$), there is also a clear + best-performing model, namely \textit{hsma}. +As the non-seasonal \textit{hses} reaches a similar accuracy as its + potentially seasonal generalization, the \textit{hets}, we conclude that + the seasonal pattern from weekdays is not yet strong enough to be + recognized in low demand pixels. +So, in the absence of seasonality, models that only model a trend part are + the least susceptible to the noise. + +For medium demand (i.e., $10 < \text{ADD} < 25$) and training horizons up to + six weeks, the best-performing models are the same as for low demand. +For longer horizons, \textit{hets} provides the highest accuracy. +Thus, to fit a seasonal pattern, longer training horizons are needed. +While \textit{vsvr} enters the top three, \textit{hets} has the edge as they + neither require parameter tuning nor real-time data. + +\begin{center} +\captionof{table}{Top-3 models by training weeks and average demand + ($1~\text{km}^2$ pixel size, 60-minute time steps)} +\label{t:results} +\begin{tabular}{|c|c|*{12}{c|}} + +\hline +\multirow{3}{*}{\rotatebox{90}{\thead{Training}}} + & \multirow{3}{*}{\rotatebox{90}{\thead{Rank}}} + & \multicolumn{3}{c|}{\thead{No Demand}} + & \multicolumn{3}{c|}{\thead{Low Demand}} + & \multicolumn{3}{c|}{\thead{Medium Demand}} + & \multicolumn{3}{c|}{\thead{High Demand}} \\ +~ & ~ + & \multicolumn{3}{c|}{(0 - 2.5)} + & \multicolumn{3}{c|}{(2.5 - 10)} + & \multicolumn{3}{c|}{(10 - 25)} + & \multicolumn{3}{c|}{(25 - $\infty$)} \\ +\cline{3-14} +~ & ~ + & Method & MASE & $n$ + & Method & MASE & $n$ + & Method & MASE & $n$ + & Method & MASE & $n$ \\ + +\hline \hline +\multirow{3}{*}{3} & 1 + & \textbf{\textit{trivial}} + & 0.785 & \multirow{3}{*}{\rotatebox{90}{4586}} + & \textbf{\textit{hsma}} + & 0.819 & \multirow{3}{*}{\rotatebox{90}{2975}} + & \textbf{\textit{hsma}} + & 0.839 & \multirow{3}{*}{\rotatebox{90}{2743}} + & \textbf{\textit{rtarima}} + & 0.872 & \multirow{3}{*}{\rotatebox{90}{2018}} \\ +~ & 2 + & \textit{hsma} & 0.809 & ~ + & \textit{hses} & 0.844 & ~ + & \textit{hses} & 0.858 & ~ + & \textit{rtses} & 0.873 & ~ \\ +~ & 3 + & \textit{pnaive} & 0.958 & ~ + & \textit{hets} & 0.846 & ~ + & \textit{hets} & 0.859 & ~ + & \textit{rtets} & 0.877 & ~ \\ + +\hline +\multirow{3}{*}{4} & 1 + & \textbf{\textit{trivial}} + & 0.770 & \multirow{3}{*}{\rotatebox{90}{4532}} + & \textbf{\textit{hsma}} + & 0.825 & \multirow{3}{*}{\rotatebox{90}{3033}} + & \textbf{\textit{hsma}} + & 0.837 & \multirow{3}{*}{\rotatebox{90}{2687}} + & \textbf{\textit{vrfr}} + & 0.855 & \multirow{3}{*}{\rotatebox{90}{2016}} \\ +~ & 2 + & \textit{hsma} & 0.788 & ~ + & \textit{hses} & 0.848 & ~ + & \textit{hses} & 0.850 & ~ + & \textbf{\textit{rtarima}} & 0.855 & ~ \\ +~ & 3 + & \textit{pnaive} & 0.917 & ~ + & \textit{hets} & 0.851 & ~ + & \textit{hets} & 0.854 & ~ + & \textit{rtses} & 0.860 & ~ \\ + +\hline +\multirow{3}{*}{5} & 1 + & \textbf{\textit{trivial}} + & 0.780 & \multirow{3}{*}{\rotatebox{90}{4527}} + & \textbf{\textit{hsma}} + & 0.841 & \multirow{3}{*}{\rotatebox{90}{3055}} + & \textbf{\textit{hsma}} + & 0.837 & \multirow{3}{*}{\rotatebox{90}{2662}} + & \textbf{\textit{vrfr}} + & 0.850 & \multirow{3}{*}{\rotatebox{90}{2019}} \\ +~ & 2 + & \textit{hsma} & 0.803 & ~ + & \textit{hses} & 0.859 & ~ + & \textit{hets} & 0.845 & ~ + & \textbf{\textit{rtarima}} & 0.852 & ~ \\ +~ & 3 + & \textit{pnaive} & 0.889 & ~ + & \textit{hets} & 0.861 & ~ + & \textit{hses} & 0.845 & ~ + & \textit{vsvr} & 0.854 & ~ \\ + +\hline +\multirow{3}{*}{6} & 1 + & \textbf{\textit{trivial}} + & 0.741 & \multirow{3}{*}{\rotatebox{90}{4470}} + & \textbf{\textit{hsma}} + & 0.847 & \multirow{3}{*}{\rotatebox{90}{3086}} + & \textbf{\textit{hsma}} + & 0.840 & \multirow{3}{*}{\rotatebox{90}{2625}} + & \textbf{\textit{vrfr}} + & 0.842 & \multirow{3}{*}{\rotatebox{90}{2025}} \\ +~ & 2 + & \textit{hsma} & 0.766 & ~ + & \textit{hses} & 0.863 & ~ + & \textit{hets} & 0.842 & ~ + & \textbf{\textit{hets}} & 0.847 & ~ \\ +~ & 3 + & \textit{pnaive} & 0.837 & ~ + & \textit{hets} & 0.865 & ~ + & \textit{hses} & 0.848 & ~ + & \textit{vsvr} & 0.848 & ~ \\ + +\hline +\multirow{3}{*}{7} & 1 + & \textbf{\textit{trivial}} + & 0.730 & \multirow{3}{*}{\rotatebox{90}{4454}} + & \textbf{\textit{hsma}} + & 0.858 & \multirow{3}{*}{\rotatebox{90}{3132}} + & \textbf{\textit{hets}} + & 0.845 & \multirow{3}{*}{\rotatebox{90}{2597}} + & \textbf{\textit{hets}} + & 0.840 & \multirow{3}{*}{\rotatebox{90}{2007}} \\ +~ & 2 + & \textit{hsma} & 0.754 & ~ + & \textit{hses} & 0.871 & ~ + & \textit{hsma} & 0.847 & ~ + & \textbf{\textit{vrfr}} & 0.845 & ~ \\ +~ & 3 + & \textit{pnaive} & 0.813 & ~ + & \textit{hets} & 0.872 & ~ + & \textbf{\textit{vsvr}} & 0.850 & ~ + & \textit{vsvr} & 0.847 & ~ \\ + +\hline +\multirow{3}{*}{8} & 1 + & \textbf{\textit{trivial}} + & 0.735 & \multirow{3}{*}{\rotatebox{90}{4402}} + & \textbf{\textit{hsma}} + & 0.867 & \multirow{3}{*}{\rotatebox{90}{3159}} + & \textbf{\textit{hets}} + & 0.846 & \multirow{3}{*}{\rotatebox{90}{2575}} + & \textbf{\textit{hets}} + & 0.836 & \multirow{3}{*}{\rotatebox{90}{2002}} \\ +~ & 2 + & \textit{hsma} & 0.758 & ~ + & \textit{hets} & 0.877 & ~ + & \textbf{\textit{vsvr}} & 0.850 & ~ + & \textbf{\textit{vrfr}} & 0.842 & ~ \\ +~ & 3 + & \textit{pnaive} & 0.811 & ~ + & \textit{hses} & 0.880 & ~ + & \textit{hsma} & 0.851 & ~ + & \textit{vsvr} & 0.849 & ~ \\ + +\hline +\end{tabular} +\end{center} + +In summary, except for high demand, simple models trained on horizontal time + series work best. +By contrast, high demand (i.e., $25 < \text{ADD} < \infty$) and less than + six training weeks is the only situation where classical models trained on + vertical time series work well. +Then, \textit{rtarima} outperforms their siblings from Sub-sections + \ref{vert} and \ref{rt}. +We conjecture that intra-day auto-correlations as caused, for example, by + weather, are the reason for that. +Intuitively, a certain amount of demand (i.e., a high enough signal-to-noise + ratio) is required such that models with auto-correlations can see them + through all the noise. +That idea is supported by \textit{vrfr} reaching a similar accuracy under + high demand as their tree-structure allows them to fit auto-correlations. +As both \textit{rtarima} and \textit{vrfr} incorporate recent demand, + real-time information can indeed improve accuracy. +However, once models are trained on longer horizons, \textit{hets} is more + accurate than \textit{vrfr}. +Thus, to answer \textbf{Q4}, we conclude that real-time information only + improves accuracy if three or four weeks of training material are + available. + +In addition to looking at the results in tables covering the entire one-year + horizon, we also created sub-analyses on the distinct seasons spring, + summer (incl. the long holiday season in France), and fall. +Yet, none of the results portrayed in this and the subsequent sections change + is significant ways. +We conjecture that there could be differences if the overall demand of the UDP + increased to a scale beyond the one this case study covers and leave that + up to a follow-up study with a bigger UDP. diff --git a/tex/4_stu/5_training.tex b/tex/4_stu/5_training.tex new file mode 100644 index 0000000..ea5320d --- /dev/null +++ b/tex/4_stu/5_training.tex @@ -0,0 +1,31 @@ +\subsection{Impact of the Training Horizon} +\label{training} + +Whereas it is reasonable to assume that forecasts become more accurate as the + training horizon expands, our study reveals some interesting findings. +First, without demand, \textit{trivial} indeed performs better with more + training material, but improved pattern recognition cannot be the cause + here. +Instead, we argue that the reason for this is that the longer there has been + no steady demand, the higher the chance that this will not change soon. +Further, if we focus on shorter training horizons, the sample will necessarily + contain cases where a pixel is initiated after a popular-to-be restaurant + joined the platform: +Demand grows fast making \textit{trivial} less accurate, and the pixel moves + to another cluster soon. + +Second, with low demand, the best-performing \textit{hsma} becomes less + accurate with more training material. +While one could argue that this is due to \textit{hsma} not fitting a trend, + the less accurate \textit{hses} and \textit{hets} do fit a trend. +Instead, we argue that any low-demand time series naturally exhibits a high + noise-to-signal ratio, and \textit{hsma} is the least susceptible to + noise. +Then, to counter the missing trend term, the training horizon must be shorter. + +With medium demand, a similar argument can be made; however, the + signal already becomes more apparent favoring \textit{hets} with more + training data. + +Lastly, with high demand, the signal becomes so clear that more sophisticated + models can exploit longer training horizons. diff --git a/tex/4_stu/6_fams.tex b/tex/4_stu/6_fams.tex new file mode 100644 index 0000000..8fdd17d --- /dev/null +++ b/tex/4_stu/6_fams.tex @@ -0,0 +1,162 @@ +\subsection{Results by Model Families} +\label{fams} + +Besides the overall results, we provide an in-depth comparison of models + within a family. +Instead of reporting the MASE per model, we rank the models holding the + training horizon fixed to make comparison easier. +Table \ref{t:hori} presents the models trained on horizontal time series. +In addition to \textit{naive}, we include \textit{fnaive} and \textit{pnaive} + already here as more competitive benchmarks. +The tables in this section report two rankings simultaneously: +The first number is the rank resulting from lumping the low and medium + clusters together, which yields almost the same rankings when analyzed + individually. +The ranks from only high demand pixels are in parentheses if they differ. + +\begin{center} +\captionof{table}{Ranking of benchmark and horizontal models + ($1~\text{km}^2$ pixel size, 60-minute time steps): + the table shows the ranks for cases with $2.5 < ADD < 25$ + (and $25 < ADD < \infty$ in parentheses if they differ)} +\label{t:hori} +\begin{tabular}{|c|ccc|cccccccc|} +\hline +\multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}} + & \multicolumn{3}{c|}{\thead{Benchmarks}} + & \multicolumn{8}{c|}{\thead{Horizontal (whole-day-ahead)}} \\ +\cline{2-12} +~ & \textit{naive} & \textit{fnaive} & \textit{paive} + & \textit{harima} & \textit{hcroston} & \textit{hets} & \textit{hholt} + & \textit{hhwinters} & \textit{hses} & \textit{hsma} & \textit{htheta} \\ +\hline \hline +3 & 11 & 7 (2) & 8 (5) & 5 (7) & 4 & 3 + & 9 (10) & 10 (9) & 2 (6) & 1 & 6 (8) \\ +4 & 11 & 7 (2) & 8 (3) & 5 (6) & 4 (5) & 3 (1) + & 9 (10) & 10 (9) & 2 (7) & 1 (4) & 6 (8) \\ +5 & 11 & 7 (2) & 8 (4) & 5 (3) & 4 (9) & 3 (1) + & 9 (10) & 10 (5) & 2 (8) & 1 (6) & 6 (7) \\ +6 & 11 & 8 (5) & 9 (6) & 5 (4) & 4 (7) & 2 (1) + & 10 & 7 (2) & 3 (8) & 1 (9) & 6 (3) \\ +7 & 11 & 8 (5) & 10 (6) & 5 (4) & 4 (7) & 2 (1) + & 9 (10) & 7 (2) & 3 (8) & 1 (9) & 6 (3) \\ +8 & 11 & 9 (5) & 10 (6) & 5 (4) & 4 (7) & 2 (1) + & 8 (10) & 7 (2) & 3 (8) & 1 (9) & 6 (3) \\ +\hline +\end{tabular} +\end{center} +\ + +A first insight is that \textit{fnaive} is the best benchmark in all + scenarios: +Decomposing flexibly by tuning the $ns$ parameter is worth the computational + cost. +Further, if one is limited in the number of non-na\"{i}ve methods, + \textit{hets} is the best compromise and works well across all demand + levels. +It is also the best model independent of the training horizon for high demand. +With low or medium demand, \textit{hsma} is the clear overall winner; yet, + with high demand, models with a seasonal fit (i.e., \textit{harima}, + \textit{hets}, and \textit{hhwinters}) are more accurate, in particular, + for longer training horizons. +This is due to demand patterns in the weekdays becoming stronger with higher + overall demand. + +\begin{center} +\captionof{table}{Ranking of classical models on vertical time series + ($1~\text{km}^2$ pixel size, 60-minute time steps): + the table shows the ranks for cases with $2.5 < ADD < 25$ + (and $25 < ADD < \infty$ in parentheses if they differ)} +\label{t:vert} +\begin{tabular}{|c|cc|ccccc|ccccc|} +\hline +\multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}} + & \multicolumn{2}{c|}{\thead{Benchmarks}} + & \multicolumn{5}{c|}{\thead{Vertical (whole-day-ahead)}} + & \multicolumn{5}{c|}{\thead{Vertical (real-time)}} \\ +\cline{2-13} +~ & \textit{hets} & \textit{hsma} & \textit{varima} & \textit{vets} + & \textit{vholt} & \textit{vses} & \textit{vtheta} & \textit{rtarima} + & \textit{rtets} & \textit{rtholt} & \textit{rtses} & \textit{rttheta} \\ +\hline \hline +3 & 2 (10) & 1 (7) & 6 (4) & 8 (6) & 10 (9) + & 7 (5) & 11 (12) & 4 (1) & 5 (3) & 9 (8) & 3 (2) & 12 (11) \\ +4 & 2 (8) & 1 (10) & 6 (4) & 8 (6) & 10 (9) + & 7 (5) & 12 (11) & 3 (1) & 5 (3) & 9 (7) & 4 (2) & 11 (12) \\ +5 & 2 (3) & 1 (10) & 7 (5) & 8 (7) & 10 (9) + & 6 & 11 & 4 (1) & 5 (4) & 9 (8) & 3 (2) & 12 \\ +6 & 2 (1) & 1 (10) & 6 (5) & 8 (7) & 10 (9) + & 7 (6) & 11 (12) & 3 (2) & 5 (4) & 9 (8) & 4 (3) & 12 (11) \\ +7 & 2 (1) & 1 (10) & 8 (5) & 7 & 10 (9) + & 6 & 11 (12) & 5 (2) & 4 & 9 (8) & 3 & 12 (11) \\ +8 & 2 (1) & 1 (9) & 8 (5) & 7 (6) & 10 (8) + & 6 & 12 (10) & 5 (2) & 4 & 9 (7) & 3 & 11 \\ +\hline +\end{tabular} +\end{center} +\ + +Table \ref{t:vert} extends the previous analysis to classical models trained + on vertical time series. +Now, the winners from before, \textit{hets} and \textit{hsma}, serve as + benchmarks. +Whereas for low and medium demand, no improvements can be obtained, + \textit{rtarima} and \textit{rtses} are the most accurate with high demand + and short training horizons. +For six or more training weeks, \textit{hets} is still optimal. +Independent of retraining and the demand level, the models' relative + performances are consistent: +The \textit{*arima} and \textit{*ses} models are best, followed by + \textit{*ets}, \textit{*holt}, and \textit{*theta}. +Thus, models that can deal with auto-correlations and short-term forecasting + errors, as expressed by moving averages, and that cannot be distracted by + trend terms are optimal for vertical series. + +Finally, Table \ref{t:ml} compares the two ML-based models against the + best-performing classical models and answers \textbf{Q2}: +With low and medium demand, no improvements can be obtained again; however, + with high demand, \textit{vrfr} has the edge over \textit{rtarima} for + training horizons up to six weeks. +We conjecture that \textit{vrfr} fits auto-correlations better than + \textit{varima} and is not distracted by short-term noise as + \textit{rtarima} may be due to the retraining. +With seven or eight training weeks, \textit{hets} remains the overall winner. +Interestingly, \textit{vsvr} is more accurate than \textit{vrfr} for low and + medium demand. +We assume that \textit{vrfr} performs well only with strong auto-correlations, + which are not present with low and medium demand. + +\begin{center} +\captionof{table}{Ranking of ML models on vertical time series + ($1~\text{km}^2$ pixel size, 60-minute time steps): + the table shows the ranks for cases with $2.5 < ADD < 25$ + (and $25 < ADD < \infty$ in parentheses if they differ)} +\label{t:ml} +\begin{tabular}{|c|cccc|cc|} +\hline +\multirow{2}{*}{\rotatebox{90}{\thead{\scriptsize{Training}}}} + & \multicolumn{4}{c|}{\thead{Benchmarks}} + & \multicolumn{2}{c|}{\thead{ML}} \\ +\cline{2-7} +~ & \textit{fnaive} & \textit{hets} & \textit{hsma} + & \textit{rtarima} & \textit{vrfr} & \textit{vsvr} \\ +\hline \hline +3 & 6 & 2 (5) & 1 (4) & 3 (1) & 5 (2) & 4 (3) \\ +4 & 6 (5) & 2 (4) & 1 (6) & 3 (2) & 5 (1) & 4 (3) \\ +5 & 6 (5) & 2 (4) & 1 (6) & 4 (2) & 5 (1) & 3 \\ +6 & 6 (5) & 2 & 1 (6) & 4 & 5 (1) & 3 \\ +7 & 6 (5) & 2 (1) & 1 (6) & 4 & 5 (2) & 3 \\ +8 & 6 (5) & 2 (1) & 1 (6) & 4 & 5 (2) & 3 \\ +\hline +\end{tabular} +\end{center} +\ + +Analogously, we created tables like Table \ref{t:hori} to \ref{t:ml} for the + forecasts with time steps of 90 and 120 minutes and find that the relative + rankings do not change significantly. +The same holds true for the rankings with changing pixel sizes. +For conciseness reasons, we do not include these additional tables in this + article. +In summary, the relative performances exhibited by certain model families + are shown to be rather stable in this case study. diff --git a/tex/4_stu/7_pixels_intervals.tex b/tex/4_stu/7_pixels_intervals.tex new file mode 100644 index 0000000..8f60041 --- /dev/null +++ b/tex/4_stu/7_pixels_intervals.tex @@ -0,0 +1,27 @@ +\subsection{Effects of the Pixel Size and Time Step Length} +\label{pixels_intervals} + +As elaborated in Sub-section \ref{grid}, more order aggregation leads to a + higher overall demand level and an improved pattern recognition in the + generated time series. +Consequently, individual cases tend to move to the right in tables equivalent + to Table \ref{t:results}. +With the same $ADD$ clusters, forecasts for pixel sizes of $2~\text{km}^2$ and + $4~\text{km}^2$ or time intervals of 90 and 120 minutes or combinations + thereof yield results similar to the best models as revealed in Tables + \ref{t:results}, \ref{t:hori}, \ref{t:vert}, and \ref{t:ml} for high + demand. +By contrast, forecasts for $0.5~\text{km}^2$ pixels have most of the cases + (i.e., $n$) in the no or low demand clusters. +In that case, the pixels are too small, and pattern recognition becomes + harder. +While it is true, that \textit{trivial} exhibits the overall lowest MASE + for no demand cases, these forecasts become effectively worthless for + operations. +In the extreme, with even smaller pixels we would be forecasting $0$ orders + in all pixels for all time steps. +In summary, the best model and its accuracy are determined primarily by the + $ADD$, and the pixel size and interval length are merely parameters to + control that. +The forecaster's goal is to create a grid with small enough pixels without + losing a recognizable pattern. diff --git a/tex/apx/peak_results.tex b/tex/apx/peak_results.tex index 58b4dd8..65e5bb6 100644 --- a/tex/apx/peak_results.tex +++ b/tex/apx/peak_results.tex @@ -1,14 +1,11 @@ \section{Forecasting Accuracies during Peak Times} \label{peak_results} -This appendix shows all result tables from the main text with the MASE - averages calculated from time steps within peak times. -Peaks are the times of the day where the typical customer has a lunch or - dinner meal and defined to be either from 12 pm to 2 pm or from 6 pm to - 8 pm. -While the exact decimals of the MASEs differ from the ones in the main - text, the relative ranks of the forecasting methods are the same except in - rare cases. +This appendix shows all tables from the main text + with the MASE averages calculated from time steps within peak times + that are defined to be from 12 pm to 2 pm (=lunch) or from 6 pm to 8 pm (=dinner). +While the exact decimals of the MASEs differ, + the relative ranks of the forecasting methods are the same except in rare cases. \begin{center} \captionof{table}{Top-3 models by training weeks and average demand diff --git a/tex/glossary.tex b/tex/glossary.tex index 2c270f3..ea86d45 100644 --- a/tex/glossary.tex +++ b/tex/glossary.tex @@ -1,4 +1,7 @@ % Abbreviations for technical terms. +\newglossaryentry{add}{ + name=ADD, description={Average Daily Demand} +} \newglossaryentry{cart}{ name=CART, description={Classification and Regression Trees} } diff --git a/tex/preamble.tex b/tex/preamble.tex index 0a2dffc..207afd3 100644 --- a/tex/preamble.tex +++ b/tex/preamble.tex @@ -10,6 +10,9 @@ % Enable diagonal lines in tables. \usepackage{static/slashbox} +% Enable multiple lines in a table row +\usepackage{multirow} + % Make opening quotes look different than closing quotes. \usepackage[english=american]{csquotes} \MakeOuterQuote{"} @@ -17,4 +20,5 @@ % Define helper commands. \usepackage{bm} \newcommand{\mat}[1]{\bm{#1}} 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zpIhxcnkMoj(^7VnF;cuD2^kvhZ4$isN+O!2eH4WvPJ zm8ymxxJnzcO4Lp*6>oyI8s5n9?#Nq?K}y4&)i(95(JvY0o{#cb5|^;Z3wf9N9!P0t z3eBcKiS~`gx;L5)01d8?;qi0bEime(dYNdecfz=es1)Yv)06Xy!}u)K_zF|cM|Yyz zZ>?5iz@6*46$Pk>sa;ZwrrygnhLaiZA3sNqK>H@^Rh9N zN!8uAe>jv$w(`+qG(KeT7@jYNXJo8qwyu7h}fT~^@=#7p`HP&n2bYUY;II4t!Dg5HihOwn^>? zAxf|51;+$%@)*D|saboQ6LbFaL~9Z2u@JKnv;13Ab#!zk=Hw)1CRT-Gl5wzbBV-(MO={h|G(wmDRA=U4wkM~ z#H`FL$x8pM*A!Fj_FyVM25)hu%z2ieCcLp-YV47G5XISrrC~!3T!o>f$=OB3k;zfG zMc6@D8*Q1hrbm^&z2AEvZb^Cu%RR9hPoj~$^j2aErK2Dc19LGY zbW32EY%O&XNj{1vbDScKP1%_ANo&^eBfw?_SLtDue(^_0sbFEMU@8?+`rgumk*=+S zld!yhOXg}5)fh&|*)0-pmTDwl+11n8+yah;m6MH&6OMvHLP-+te*og& Date: Sun, 4 Oct 2020 23:39:20 +0200 Subject: [PATCH 10/28] Add Model section --- paper.tex | 14 ++ static/cross_validation_gray.png | Bin 0 -> 4557 bytes static/gridification_for_paris_gray.png | Bin 0 -> 267324 bytes static/model_inputs_gray.png | Bin 0 -> 86114 bytes static/slashbox.sty | 77 +++++++ static/stl_gray.png | Bin 0 -> 106662 bytes tex/3_mod/1_intro.tex | 8 +- tex/3_mod/2_overall.tex | 28 +++ tex/3_mod/3_grid.tex | 95 +++++++++ tex/3_mod/4_cv.tex | 86 ++++++++ tex/3_mod/5_mase.tex | 87 ++++++++ tex/3_mod/6_decomp.tex | 76 +++++++ tex/3_mod/7_models/1_intro.tex | 20 ++ tex/3_mod/7_models/2_hori.tex | 42 ++++ tex/3_mod/7_models/3_vert.tex | 39 ++++ tex/3_mod/7_models/4_rt.tex | 22 ++ tex/3_mod/7_models/5_ml.tex | 54 +++++ tex/4_stu/1_intro.tex | 5 +- tex/apx/case_study.tex | 54 +++++ tex/apx/enhanced_feats.tex | 121 +++++++++++ tex/apx/peak_results.tex | 261 ++++++++++++++++++++++++ tex/apx/tabular_ml_models.tex | 58 ++++++ tex/glossary.tex | 102 +++++++++ tex/preamble.tex | 6 + tex/references.bib | 105 ++++++++++ 25 files changed, 1354 insertions(+), 6 deletions(-) create mode 100644 static/cross_validation_gray.png create mode 100644 static/gridification_for_paris_gray.png create mode 100644 static/model_inputs_gray.png create mode 100644 static/slashbox.sty create mode 100644 static/stl_gray.png create mode 100644 tex/3_mod/2_overall.tex create mode 100644 tex/3_mod/3_grid.tex create mode 100644 tex/3_mod/4_cv.tex create mode 100644 tex/3_mod/5_mase.tex create mode 100644 tex/3_mod/6_decomp.tex create mode 100644 tex/3_mod/7_models/1_intro.tex create mode 100644 tex/3_mod/7_models/2_hori.tex create mode 100644 tex/3_mod/7_models/3_vert.tex create mode 100644 tex/3_mod/7_models/4_rt.tex create mode 100644 tex/3_mod/7_models/5_ml.tex create mode 100644 tex/apx/case_study.tex create mode 100644 tex/apx/enhanced_feats.tex create mode 100644 tex/apx/peak_results.tex create mode 100644 tex/apx/tabular_ml_models.tex diff --git a/paper.tex b/paper.tex index 04a42f1..78c1cd5 100644 --- a/paper.tex +++ b/paper.tex @@ -19,6 +19,16 @@ \input{tex/2_lit/3_ml/4_rf} \input{tex/2_lit/3_ml/5_svm} \input{tex/3_mod/1_intro} +\input{tex/3_mod/2_overall} +\input{tex/3_mod/3_grid} +\input{tex/3_mod/4_cv} +\input{tex/3_mod/5_mase} +\input{tex/3_mod/6_decomp} +\input{tex/3_mod/7_models/1_intro} +\input{tex/3_mod/7_models/2_hori} +\input{tex/3_mod/7_models/3_vert} +\input{tex/3_mod/7_models/4_rt} +\input{tex/3_mod/7_models/5_ml} \input{tex/4_stu/1_intro} \input{tex/5_con/1_intro} @@ -29,6 +39,10 @@ \appendix \newpage +\input{tex/apx/tabular_ml_models} +\newpage +\input{tex/apx/enhanced_feats} +\newpage \bibliographystyle{static/elsarticle-harv} \bibliography{tex/references} diff --git a/static/cross_validation_gray.png b/static/cross_validation_gray.png new file mode 100644 index 0000000000000000000000000000000000000000..7deee2190a229b984e2df2629e7a59beb564fb86 GIT binary patch literal 4557 zcmb7|c|278+sB8fi7*pxmDD&HVp7tSvQJL-eVNKKk#)#E5fV*qX0m0=PRMR7$r7PN zQc`3o*|%V2ExN5T}2wYqH1aig7#l^VzGz1PIq?} z${S_-r^xxNV10fAuEliSB5k8XwdbNlZ=BJIir~v$(-TuRfL>b z{EclgKx)Am@4|OES7q!PPFOd0eOmY7Kn;wX^s*Z@PmY~!VmZrzC{yodg~=lrI3ED@ zsrWX@d;_dnRNQd;?Li7&+|*jiGa}XS!OA&WYG!+rTX`Ul1o01K*B<6!S$fZbyJmU}X3nXs>N> z!1T!$lk?+(c_kp!ZE637If>Eg&JWPfj zMy7kJz1NJ;7#%9iqjJk25*;m#0}gts7e2T*?p3~R6<5;0_tfWw 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