45 lines
2.4 KiB
TeX
45 lines
2.4 KiB
TeX
\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}, VRPs 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 (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 (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.
|