We study a mobile facility (MF) routing and scheduling problem in which probability distributions of the time-dependent demand for MF services is unknown. To address distributional ambiguity, we propose and analyze two distributionally robust MF routing and scheduling (DMFRS) models that seek to minimize the fixed cost of establishing the MF fleet and maximum expected transportation and unmet demand costs over all possible demand distributions residing within an ambiguity set. In the first model, we use a moment-based ambiguity set. In the second model, we use an ambiguity set that incorporates all distributions within a 1-Wasserstein distance from a reference distribution. To solve DMFRS models, we propose a decomposition-based algorithm and derive lower bound and two–families of symmetry breaking inequalities to strengthen the master problem and speed up convergence. Finally, we present extensive computational experiments comparing the operational and computational performance of the proposed distributionally robust models and a stochastic programming model and drive insights into DMFRS.
Shehadeh, K.S. Distributionally Robust Optimization Approaches for a Stochastic Mobile Facility Routing and Scheduling Problem. Preprint version available at Optimization Online. 2020.