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Stochastic Optimization Approaches to Fleet Allocation for a Last-Mile Transportation System under Demand Uncertainty

Karmel S. Shehadeh(kas720***at***lehigh.edu)
Hai Wang(haiwang***at***smu.edu.sg)
Peter Zhang(pyzhang***at***cmu.edu)

Abstract: In this paper, we investigate two stochastic optimization approaches for a vehicle fleet sizing and allocation problem for a last-mile (LM) transportation system. Specifically, we consider the perspective of an LM service provider who wants to determine the number of servicing vehicles to allocate to each service region in a particular city. In each service region, passengers demanding LM services arrive in batches, and vehicles deliver passengers to their final destinations, i.e., LM stops. The size of each batch of passengers is random and hard to predict in advance. The quality of fleet-allocation decisions is a function of vehicle fixed cost plus a weighted sum of passenger’s waiting time before boarding a vehicle and in-vehicle riding time. We propose and analyze two stochastic optimization approaches—a two-stage stochastic programming model and a two-stage distributionally robust optimization model—to solve the problem, assuming known and unknown distribution of the demand, respectively. We conduct extensive numerical experiments to compare the two approaches and derive insights into optimal fleet allocation for an LM transportation system under demand uncertainty.

Keywords: Last mile transportation, demand uncertainty, fleet allocation, stochastic programming, distributionally robust optimization, mixed-integer programming

Category 1: Applications -- OR and Management Sciences

Citation: Shehadeh, K.S., Wang, H., and Zhang, P. (2020). Stochastic Optimization Approaches to Fleet Allocation for a Last-Mile Transportation System under Demand Uncertainty. Preprint version available at Optimization Online.

Download: [PDF]

Entry Submitted: 10/29/2020
Entry Accepted: 10/29/2020
Entry Last Modified: 10/29/2020

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