Robust Vehicle Allocation with Uncertain Covariates
32 Pages Posted: 7 Jan 2019
Date Written: December 24, 2018
Motivated by a leading taxi operator in Singapore, we consider the idle vehicle allocation problem with uncertain demands and other uncertain covariate information such as weather. In this problem, the operator, upon observing its distribution of idle vehicles, proactively reallocates the idle vehicles to serve future uncertain demands. With perfect information of demand distribution, the problem can be formulated as a stochastic transportation problem. Yet, the non-stationarity and spatial correlation of demands pose significant challenges in estimating its distribution accurately from historical data. We employ a novel distributionally robust optimization approach that utilizes covariate information via multivariate regression tree as well as the moment information of demands. Although information about uncertain covariates provides no value when there is perfect knowledge of demand distribution, we show that it could alleviate the over-conservativeness of the robust solution. The resulting distributionally robust optimization problem can be exactly and tractably solved using linear decision rule technique. We further validate the performance of our solution via extensive numerical simulations, and a case study using trip and vehicle status data from our partner taxi operator, paired with the rainfall data from the Meteorological Service Singapore.
Keywords: Vehicle allocation, distributionally robust optimization, covariate information, multivariate regression tree
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