Distributionally Robust Optimization Approaches for a Stochastic Mobile Facility Fleet Sizing, Routing, and Scheduling Problem

TL;DR

This paper develops two distributionally robust optimization models for mobile facility fleet planning under uncertain demand, incorporating risk measures and ambiguity sets, with algorithms and computational experiments demonstrating improved performance over stochastic models.

Contribution

Introduces novel DRO models for fleet sizing, routing, and scheduling with new ambiguity sets and solution algorithms, advancing robust operational planning under demand uncertainty.

Findings

DRO models outperform stochastic programming in certain scenarios

Decomposition algorithm with symmetry-breaking enhances computational efficiency

Operational insights into fleet management under demand ambiguity

Abstract

We propose two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet sizing, routing, and scheduling problem (MFRSP) with time-dependent and random demand, as well as methodologies for solving these models. Specifically, given a set of MFs, a planning horizon, and a service region, our models aim to find the number of MFs to use (i.e., fleet size) within the planning horizon and a route and schedule for each MF in the fleet. The objective is to minimize the fixed cost of establishing the MF fleet plus a risk measure (expectation or mean conditional value-at-risk) of the operational cost over all demand distributions defined by an ambiguity set. In the first model, we use an ambiguity set based on the demand's mean, support, and mean absolute deviation. In the second model, we use an ambiguity set that incorporates all distributions within a 1-Wasserstein distance from a reference distribution. To solve the proposed DRO models, we propose a decomposition-based algorithm. In addition, we derive valid lower bound inequalities that efficiently strengthen the master problem in the decomposition algorithm, thus improving convergence. We also derive two families of symmetry-breaking constraints that improve the solvability of the proposed models. Finally, we present extensive computational experiments comparing the operational and computational performance of the proposed models and a stochastic programming model, demonstrating where significant performance improvements could be gained and derive insights into the MFRSP.