Modeling r-interdiction median problem with fortification in a fuzzy environment

This study intends to formulate the r-interdiction median problem with fortification (RIMF) in a fuzzy environment. In this novel model, all data corresponding to the demand of customers and fortification and interdiction resources are imprecise and vague and to consider the degree of certainty of the solution. Fuzzy model of RIMF also is given as a bi-level programming with two decision maker, i.e., fortifier and interdictor. For solving the problem, the fuzzy RIMF is reformulated as a single level problem by using the Karush-Kuhn-Tucker (KKT) conditions, which is amenable to an exact approach. The single level model can be solved to optimality using CPLEX 12.5.1. Finally, a random instance is generated for illustration. Through this instance, it is demonstrated how the results of novel model can be applied to notify fortifier in disaster recovery planning.