Distributionally Robust Optimization Approaches for a Stochastic Mobile Facility Fleet Sizing, Routing, and Scheduling Problem
针对需求随机且随时间变化的移动设施车队规模、路径与调度问题，提出了两种分布鲁棒优化模型，并设计了分解算法和有效不等式来求解，通过实验对比展示了性能优势。
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 time 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 when significant performance improvements could be gained, and derive insights into the MFRSP. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1153 .