Multi-period facility location and capacity planning under $\infty$-Wasserstein joint chance constraints in humanitarian logistics

TL;DR

This paper presents a data-driven, multi-period facility location and capacity planning model for post-disaster humanitarian logistics, ensuring high probability of on-time relief delivery using $ abla$-Wasserstein joint chance constraints.

Contribution

It introduces a novel multi-period FLCP model under $ abla$-Wasserstein joint chance constraints and develops an efficient solution algorithm with practical case study validation.

Findings

Outperforms existing models in cost and service quality.

Algorithm converges faster than CPLEX with better optimality gap.

Effective in hurricane disaster scenarios.

Abstract

The key of the post-disaster humanitarian logistics (PD-HL) is to build a good facility location and capacity planning (FLCP) model for delivering relief supplies to affected areas in time. To fully exploit the historical PD data, this paper adopts the data-driven distributionally robust (DR) approach and proposes a novel multi-period FLCP model under the $\infty$-Wasserstein joint chance constraints (MFLCP-W). Specifically, we sequentially decide locations from a candidate set to build facilities with supply capacities, which are expanded if more economical, and use a finite number of historical demand samples in chance constraints to ensure a high probability of on-time delivery. To solve the MFLCP-W model, we equivalently reformulate it as a mixed integer second-order cone program and then solve it by designing an effective outer approximation algorithm with two tailored valid cuts. Finally, a case study under hurricane threats shows that MFLCP-W outperforms its counterparts in the terms of the cost and service quality, and that our algorithm converges significantly faster than the commercial solver CPLEX 12.8 with a better optimality gap.