designing a multi-objective three-stage location-routing model for humanitarian logistic planning under uncertainty

Natural and technological disasters threaten human life all around the world significantly and impose many damages and losses on them. the current study introduces a multi-objective three-stage location-routing problem in designing an efficient and timely distribution plan in the response phase of a possible earthquake. this problem considers uncertainty in parameters such as demands, access to routes, time and cost of travels, and the number of available vehicles. accordingly, a three-stage stochastic programming approach is applied to deal with the uncertainties. the objective functions of the proposed problem include minimizing the unsatisfied demands, minimizing the arriving times, and minimizing the relief operations costs. a modified algorithm of the improved version of the augmented ε-constraint method, which finds pareto-optimal solutions in less computational time, is presented to solve the proposed multi-objective mixed-integer linear programming model. to validate the model and evaluate the performance of the methods several test problems are generated and solved by them. the computational results show the satisfactory performance of the proposed methods and the effectiveness of the proposed model for the delivery of relief commodities in the affected areas.