A bi-objective humanitarian logistics model considering equity in the affected zones: application to a recent earthquake in Mexico

Abstract

In this paper, we propose a bi-objective program to model a post-disaster strategical decision problem. We consider the situation after a catastrophic disaster occurred, in which temporary distribution centers must be located. The distribution centers consolidate aid to be delivered to affected people. We assume that affected people go to collect needed aid from temporary located distribution centers. Hence, a predefined mobility radius is considered, that indicates the distance that people are willing to travel to receive aid. Additionally, needed aid required by affected individuals is consolidated in an affected demand zone and equity constraints are included to balance the aid given to those affected zones. One objective of the proposed model is to minimize the time employed by demand zones to collect aid. In humanitarian logistics it is common that the decision maker is associated with either government or non-profit organizations that are in charge of relief. Usually, there is a limited budget to conduct the operations. Hence, the decision maker also aims to minimize the cost of locating temporary distribution centers. Both objectives are simultaneously considered. Hence, to obtain efficient solutions of this bi-objective problem, an exact AUGMECON method is proposed, which is an improved version of the classic $\varepsilon$-constraint method for multi-objective optimization. To overcome with the computational limitations shown by the exact method, a genetic algorithm is also designed and used to approximate the Pareto front. To conduct the computational experience, a case study and additional random instances are considered. The case study is based on an earthquake that recently occurred in Mexico. The results obtained by both implemented methods are compared by using different well-known metrics, such as, the number of solutions, the $k$-distance, the size of the space covered, and a coverage measure. It is shown that, on average, the proposed genetic algorithm outperforms the AUGMECON when comparing the quality of the obtained Pareto fronts. Results offer the possibility for the decision maker to prioritize either time or cost when locating temporary distribution centers in a catastrophic situation.