Add Conclusion section

tex/5_con/1_intro.tex

@@ -1,2 +1,6 @@
 \section{Conclusion}
-\label{con}
+\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.

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}

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.

tex/5_con/4_further_research.tex

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+\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.