A Lexicographic Approach to Postdisaster Relief Logistics Planning Considering Fill Rates and Costs under Uncertainty

Predicting the occurrences of earthquakes is difficult, but because they often bring huge catastrophes, it is necessary to launch relief logistics campaigns soon after they occur. This paper proposes a stochastic optimization model for post-disaster relief logistics to guide the strategic planning with respect to the locations of temporary facilities, the mobilization levels of relief supplies, and the deployment of transportation assets with uncertainty on demands. In addition, delivery plans for relief supplies and evacuation plans for critical population have been developed for each scenario. Two objectives are featured in the proposed model: maximizing the expected minimal fill rate of affected areas, where the mismatching distribution among correlated relief demands is penalized, and minimizing the expected total cost. An approximate lexicographic approach is here used to transform the bi-objective stochastic programming model into a sequence of single objective stochastic programming models, and scenario-decomposition-based heuristic algorithms are furthermore developed to solve these transformed models. The feasibility of the proposed bi-objective stochastic model has been demonstrated empirically, and the effectiveness of the developed solution algorithms has also been evaluated and compared to that of commercial mixed-integer optimization software.