Multi-period stochastic programming for relief delivery considering evolving transportation network and temporary facility relocation/closure

In this study, we address a dynamic network design problem pertaining to the distribution of essential supplies during the post-disaster response phase. We present a two-stage, stochastic multi-period model that minimizes both expected unmet demand and costs associated with operating emergency response facilities and distributing relief supplies, taking into account evolving road conditions as well as the closure and relocation of temporary relief facilities. To address the computational intractability inherent in large-scale mixed-integer linear programming (MILP), we implement an accelerated branch-and-Benders-cut algorithm, facilitating efficient problem solving processes. We validate this approach through extensive numerical analysis and its application to a real-world scenario, demonstrating its superiority over deterministic methods, especially when considering the trade-off between nominal operational costs and out-of-sample reliability. Results show that dynamically adjusting the number of operating facilities and their locations may enhance cost efficiency while decreasing unmet demand during the relief delivery process as the transportation network changes with time. Additionally, we show that utilizing stochastic models for decision-making can substantially hedge against demand uncertainty, both in meeting demand and reducing operational costs. However, the benefits of stochastic solutions diminish as the disruption rate increases.