Network optimization models with fairness concern for disaster relief operations

Humanitarian logistics activities, which aim to alleviate the suffering of the population after a sudden and calamitous event, confront us with a large number of interrelated and challenging network optimization problems. This study focuses on the preparedness and response stages of the disaster life-cycle. Humanitarian network design decisions are of critical importance since they set the frame for all further post-disaster operations. Having an adequate number of strategically located storage and distribution centers for supplies is the key that enables effectiveness, efficiency and fairness when responding to a disaster. The preparedness model proposed in this study aims to find a robust relief network design that ensures the right mix of relief items can be supplied at the right time, and satisfies the demand for all given disaster scenarios. We propose a logic-based Benders decomposition approach to solve this problem to optimality. The numerical studies demonstrate that it is possible to obtain optimal or very good solutions to instances with realistic sizes for this NP-hard problem. After disaster occurrence, it is critical to have a relief distribution plan that is efficient and effective while being equitable among the beneficiaries. For this purpose, a rich vehicle routing model along with alternative linear objective functions is presented in the second stage of the study. These objectives provide a balance between timely and fair response plans. Two heuristic methods are presented for the response stage problem. Although solution quality is comparable to the solver in smaller sized problem instances, the heuristic methods provide robust solution methods since they are able to find solutions for larger cases where the solver fails. The assumptions and the parameters used in the models are justified by authorities of humanitarian organizations. The benefit of using these two complementary models consecutively to achieve a better response is also demonstrated.