Multi-objective robust mathematical modeling of emergency relief in disaster under uncertainty

This paper presents a robust location-allocation planning problem for emergency relief in a disaster situation, which is formulated as a robust optimization model. It is a multi-objective, multi-commodity, multi-vehicle and multi-level logistics model considering injury variety through service prioritizing for more injuries and considering unmet demand of particular item type in various damaged areas, public donation of different relief goods, using capacitated medical centers and emergency centers regarding damage type and capacitated relief distribution centers and disaster management centers. This a non-linear mixed-integer programming model that simultaneously optimizes three objectives; i.e., maximizing service fairness to damaged areas, maximizing fair commodity disaster management, and minimizing the total logistics cost. To solve such a hard problem, an NSGA-II is developed and the Taguchi method is applied to adjust its parameters. The ε-constraint method is used for the evaluation of the proposed algorithm performance. Three comparison metrics, including diversification, spacing and mean ideal distance, are used. The results verify the algorithm’s effectiveness in a reasonable computational time. Eventually, to examine the applicability of the presented model and the proposed algorithm, a case study is analyzed in the area located in the north of Iran, known with historical earthquake records and aggregated active faults.