Robust Vehicle Pre-Allocation with Uncertain Covariates

Forthcoming, Production and Operations Management

42 Pages Posted: 13 Jan 2020 Last revised: 8 Mar 2020

See all articles by Zhaowei Hao

Zhaowei Hao

Dongbei University of Finance and Economics

Long He

NUS Business School, National University of Singapore

Zhenyu Hu

National University of Singapore (NUS) - Department of Decision Sciences

Jun Jiang

National University of Singapore (NUS)

Date Written: October 5, 2019

Abstract

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.

Keywords: Vehicle pre-allocation, distributionally robust optimization, covariate information, multivariate regression tree

Suggested Citation

Hao, Zhaowei and He, Long and Hu, Zhenyu and Jiang, Jun, Robust Vehicle Pre-Allocation with Uncertain Covariates (October 5, 2019). Forthcoming, Production and Operations Management, Available at SSRN: https://ssrn.com/abstract=3509026 or http://dx.doi.org/10.2139/ssrn.3509026

Zhaowei Hao (Contact Author)

Dongbei University of Finance and Economics ( email )

China

Long He

NUS Business School, National University of Singapore ( email )

15 Kent Ridge Drive
Mochtar Riady Building, BIZ1 #8-73
Singapore, 119245
Singapore

Zhenyu Hu

National University of Singapore (NUS) - Department of Decision Sciences ( email )

NUS Business School
BIZ 1 Building, #02-01, 1 Business Link
117592
Singapore

Jun Jiang

National University of Singapore (NUS) ( email )

1E Kent Ridge Road
NUHS Tower Block Level 7
Singapore, 119228
Singapore

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