The emergency location-routing problem with facilities sharing and evacuation

This paper addresses an emergency location-routing problem encompassing facility sharing and evacuation within an emergency response system. We develop an integrated network combining an emergency response center, two disaster site types, and two emergency facility types. A differentiated time window distinguishes the rescue time sensitivity of the two disaster site types, while a time-dependent psychological cost function assesses the psychological impact on victims. The Bureau of Public Roads (BPR) road resistance function is adapted to evaluate post-disaster traffic capacity. The problem is formulated as a mixed integer programming model to minimize the facility opening, emergency vehicle travel, and victims’ time-dependent psychological costs. We investigate the model’s analytical properties and construct several valid inequalities. Seven problem-specific route generation heuristics are proposed to warm start the set partitioning model, yielding high-quality emergency vehicle routes. Numerical experiments on small- and medium-scale instances validate the performance of the proposed method. The three strategies for comparison, evaluated using cases from Xi’an, China, demonstrate that our method achieves a reasonable balance between fairness and efficiency.