A Mathematical Modeling for Location-Routing Problem in Critical Situations with considering to Path Security

The occurrence of natural and unnatural disasters threatens the lives of many people around the world every year. Disaster response consists of some elements such as transferring of healthy people from the affected areas to the camps. The purpose of this study is to provide a mixed-integer linear mathematical programming model for determining the best location of camps and the route of vehicles between affected points and camps. In the transfer operation, fuzzy uncertainties of transportation time, the amount of affected points' demand, the time of service, and the time window are considered. In this research, the optimal amount of arrival time of vehicles to camps is calculated in pessimistic conditions. Then this amount is considered as the time limitation in a model to minimize the expected cost of damage to people and vehicles. The cost has been calculated with regard to the security of each route from the warehouse to the affected points and from the points to the camps. To illustrate the performance of the proposed model, the model is implemented on a random example. The results of this research can be used as a model for planning the response of the possible crisis of the operating defense.