Maximum Flow Interdiction Problem in Multi-Period Dynamic Networks in Fuzzy Stochastic Hybrid Conditions

Abstract

Undoubtedly, the best tool to help military decision-makers and commanders choose the appropriate strategy is to formulate models that are as close to the real world as possible. This is possible when these problems are presented in conditions of uncertainty. In this research, a multi-period dynamic interdiction problem in fuzzy stochastic conditions is investigated. In general, interdiction problem, scarce resources are allocated to degrade the enemy, whose behavior is formatted by the network optimization problem. In this problem, the defense forces in the role of interdictor try to minimize the maximum flow during the period so that at each stage the interdictor and the enemy are fully aware of the performance of the other side. Edge capacities in this model are considered as fuzzy stochastic variables. To solve the proposed model, first, the fuzzy stochastic dynamic interdiction problem is transformed into the deterministic dynamic interdiction problem with the help of the concepts of probability measure, credibility measure and chance constraint programming. Then, by creating the crisp two-level problem created by duality, it is transformed into a single-level problem, and then it is solved by using the generalization of Banders decomposition algorithm. Finally, the validity of the problem is evaluated by providing a numerical sample.

Keywords

• network interdiction
• fuzzy random variable
• credibility measure
• probability measure
• benders decomposition