Robust optimization of emergency resource location and coupling allocation considering multiple uncertainties

Emergency resource location decision is strategic due to its high cost and long-lasting implications. There exist multiple potential uncertainties in disaster events that could lead to the current optimal location decision becoming suboptimal in the future, so it is crucial to consider possible emergency resource allocation as recourse decisions. This paper addresses the emergency resource location and allocation issue under uncertain demand, uncertain transportation cost, and disruption risk and proposes a two-stage robust framework. Especially, we categorize emergency resources into personnel and materials and consider their coupling relationship. The two-stage robust framework is reformulated utilizing duality, Karush-Kuhn-Tucker condition, and linearization methods. In addition, we develop an improved column-and-constraint generation algorithm to solve the proposed models. The experiments illustrate that the developed two-stage framework surpasses the established single-stage robust framework, and the presented improved column-and-constraint generation algorithm exhibits superior performance in comparison to the benders-dual cutting plane algorithm. Furthermore, the results reveal that increased fixed costs of opening supply points and uncertainty levels lead to higher total costs and computational time for the proposed seven models considering combinations of different uncertainties, with disruption risk significantly impacting model performance. To enhance resilience, it is recommended that emergency logistics decision-makers prioritize investments in transportation infrastructure and storage capacities at key supply points while adjusting uncertain budget parameters and disturbance ratios to optimize location and resource allocation, ensuring timely delivery of essential resources to disaster-affected areas.