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

We propose two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet-sizing, routing, and scheduling problem (MFRSP) with time-dependent random demand as well methodologies solving these models. Specifically, given set of MFs, planning horizon, service region, our aim to find the number MFs use (i.e., fleet size) within horizon route time schedule each MF in fleet. The objective is minimize fixed cost establishing plus risk measure (expectation or mean conditional value at risk) operational over all distributions defined by an ambiguity set. In first model, we based on demand’s mean, support, absolute deviation. second that incorporates 1-Wasserstein distance from reference distribution. To solve proposed DRO models, decomposition-based algorithm. addition, derive valid lower bound inequalities efficiently strengthen master decomposition algorithm, thus improving convergence. also families symmetry-breaking constraints improve solvability Finally, present extensive computational experiments comparing performance stochastic programming demonstrating when significant improvements could be gained, insights into MFRSP. Supplemental Material: online appendix available https://doi.org/10.1287/trsc.2022.1153 .