A fast-response mathematical programming approach for delivering disaster relief goods: an earthquake case study

Abstract

This paper tackles a complex logistics challenge of disaster management, encompassing warehouse location, pre-disaster inventory planning, routing, and post-disaster relief supply delivery. We establish an iterative process for optimizing relief distribution to shelters. Adaptable warehouse inventory reallocation responds to fluctuating demands, guided by a two-phase mathematical programming approach. In the first phase, a two-stage stochastic programming (TSSP) model determines optimal warehouse and shelter locations and inventory levels. In the subsequent phase, we introduce a mixed-integer programming (MIP) model to minimize the overall delivery time by making routing decisions. To streamline the process, we introduce a novel enumeration algorithm that trims down route options by considering unavailable links, effectively transforming the MIP model into an assignment-based model. This innovation results in a noticeable 74% reduction in solution time. Further efficiency is achieved by developing a branch-and-cut algorithm for swift MIP resolution. A real-world case study confirms the practicality of our approach.