37 lines
2 KiB
TeX
37 lines
2 KiB
TeX
\subsection{Calibration of the Time Series Generation Process}
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\label{params}
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Independent of the concrete forecasting models, the time series generation
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must be calibrated.
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We concentrate our forecasts on the pickup side for two reasons.
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First, the restaurants come in a significantly lower number than the
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customers resulting in more aggregation in the order counts and thus a
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better pattern recognition.
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Second, from an operational point of view, forecasts for the pickups are more
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valuable because of the waiting times due to meal preparation.
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We choose pixel sizes of $0.5~\text{km}^2$, $1~\text{km}^2$, $2~\text{km}^2$,
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and $4~\text{km}^2$, and time steps covering 60, 90, and 120 minute windows
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resulting in $H_{60}=12$, $H_{90}=9$, and $H_{120}=6$ time steps per day
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with the platform operating between 11 a.m. and 11 p.m. and corresponding
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frequencies $k_{60}=7*12=84$, $k_{90}=7*9=63$, and $k_{120}=7*6=42$ for the
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vertical time series.
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Smaller pixels and shorter time steps yield no recognizable patterns, yet would
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have been more beneficial for tactical routing.
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90 and 120 minute time steps are most likely not desirable for routing; however,
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we keep them for comparison and note that a UDP may employ such forecasts
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to activate more couriers at short notice if a (too) high demand is
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forecasted in an hour from now.
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This could, for example, be implemented by paying couriers a premium if they
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show up for work at short notice.
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Discrete lengths of 3, 4, 5, 6, 7, and 8 weeks are chosen as training
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horizons.
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We do so as the structure within the pixels (i.e., number and kind of
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restaurants) is not stable for more than two months in a row in the
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covered horizon.
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That is confirmed by the empirical finding that forecasting accuracy
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improves with longer training horizon but this effect starts to
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level off after about six to seven weeks.
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So, the demand patterns of more than two months ago do not resemble more
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recent ones.
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In total, 100,000s of distinct time series are forecast in the study.
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