Robust Vehicle Pre-Allocation with Uncertain Covariates

Motivated by a leading taxi operator in Singapore, we consider the idle vehicle pre-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 allocates 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 can utilize covariate information as well as the moment information of demand to construct a scenario-wise ambiguity set. We further illustrate how the key parameters required by the new ambiguity set, such as the scenarios and their probabilities, can be estimated via multivariate regression tree. 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.