A stochastic bi-objective simulation–optimization model for cascade disaster location-allocation-distribution problems

Cascade disasters can destroy urban infrastructures, kill thousands of people, and permanently displace millions of people. The paramount goal of disaster relief programs is to save lives, reduce financial loss, and accelerate the relief process. This study proposes a bi-level two-echelon mathematical model to minimize pre-disaster costs and maximize post-disaster relief coverage area. The model uses a geographic information system (GIS) to classify the disaster area and determine the optimal number and location of distribution centers while minimizing the relief supplies’ inventory costs. A simulation model is used to estimate the demand for relief supplies. Initially, vulnerable urban infrastructures are identified, and then the interaction among them is investigated for cascade disasters. The aims of this study are threefold: (1) to identify vulnerable urban infrastructures in cascade disasters, (2) to prioritize urban areas based on the severity of cascade disasters using a GIS, and (3) to develop a bi-objective multi-echelon multi-supplies mathematical model for location, allocation, and distribution of relief supplies under uncertainty. The model is solved with an epsilon-constraint method for small and medium-scale problems and the invasive weed optimization algorithm for large-scale problems. A case study is presented to demonstrate the applicability and efficacy of the proposed method. The results confirm the difficulty of relief operations during the night as the cost of night-time relief operations is higher than daytime. In addition, the results show the coverage area increases as the demand surges. Therefore, establishing more distribution centers will increase operating costs and expand coverage are.