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\section{Introduction}
\label{intro}
\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.

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% 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

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% Use the document width more effectively.
\usepackage[margin=2.5cm]{geometry}
\usepackage[acronym]{glossaries}
\makeglossaries
\makeglossaries
% Make opening quotes look different than closing quotes.
\usepackage[english=american]{csquotes}
\MakeOuterQuote{"}

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@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}
}