Uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation model for earthquake evacuation planning

Abstract

In this paper, an uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation mixed-integer mathematical programing model is proposed for the response phase of the earthquake. The proposed model includes five echelons as affected areas, distribution centers, hospitals, temporary accommodation centers and temporary care centers. Two objective functions as minimizing the total cost of the location-allocation of facilities and minimizing the amount of the shortage of relief supplies, are considered. The uncertainty is modeled using a scenario-based probability approach. The main decisions made by the proposed model are locating of the temporary care and accommodation centers, allocation of the affected areas to the located centers and hospitals, as well as the allocation of the distribution centers to temporary accommodation centers. Several decisions associated with flow of injured people and commodities between facilities, and decisions associated with number of vehicles between facilities and shortage and inventory level at centers are also made by the proposed model. Several sets of constraints including demand and flow of relief commodities, capacity of centers, transportation of injured people, capacity of transportation vehicles for commodities and injured people, and back up centers are considered in multiple periods of planning in the proposed model. The proposed model is applied in a real case study in Tehran. The model is solved using modified multiple-objective particle swarm optimization (MMOPSO), Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and epsilon constraint method. The performance of the solution procedures is analyzed using multi-objective performance evaluation metrics. The results reveal the superiority of the MMOPSO over the other solution approaches. A preferred solution, from the set of non-dominated solutions generated by MMOPSO, has been selected, analyzed and described. Sensitivity analysis on main parameters of proposed model and the probabilities of the earthquake and failures of the facilities has also been accomplished.