Simultaneous solution of location and routing problem in critical times with the help of mathematical modeling

This study processes a basic pre-disaster transportation problem at the management level, where a decision maker decides on different intersection locations considering different possible vehicle routes. Modeling and practical solution methods in the operation of transportation systems ensure that the damage caused by the disaster is minimized. A decision management model is proposed for location selection and distribution operations in relief strategy with conventional fuel consumption estimation. In the mentioned problem, the amount of demand of each node depends on the extent and size of the possible disaster. The possibility of each arch/road being closed or open and heterogeneous vehicle fleets in terms of vehicle size are also observed. This process is expressed as probabilistic multi-objective mixed integer linear programming whose objectives are to minimize the total system cost (i.e. fixed vehicle cost, fuel cost and fixed opening cost) and the total travel time to the destination. According to the studies carried out in this particular field, the proposed decision support model is unique in terms of the features that are simultaneously considered. The application of this process deals with a case study and subsequent numerical analysis of a possible earthquake in Tehran. Throughout the paper, it has been proven that the proposed model has the potential to assist managers in preparing for a natural disaster. A solution approach based on the clustering method is also proposed to solve the larger problems of the problem. The effective application of this heuristic method is demonstrated by presenting it to real-scale problems.