Optimal Decision-Making Dealing with Enemy Sabotages Using the Maximum Flow Interdiction Problem in Multi-Period Dynamic Networks in Fuzzy Conditions

Abstract

For a long time, one of the most important problems in wars has been the enemy's operations to destroy facilities and communication networks. The destruction of bridges and roads, air, missile, or artillery attacks, and the countless cyber-attacks in recent years prove that one of the main goals of the enemy in wars is to weaken through the destruction of facilities and equipment. In contrast, the defense forces seek to make the most of their resources and facilities to prevent the enemy from reaching its goal. In this research, a multi-period dynamic interdiction problem in fuzzy conditions is investigated in order to help military decision-makers and commanders to choose an appropriate strategy. In this problem, the defense forces in the role of interdictor try to minimize the maximum flow during the T 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 variables. To solve the proposed model, first, the fuzzy dynamic interdiction problem is transformed into the deterministic dynamic interdiction problem with the help of the concepts of 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 theory
• credibility value
• benders decomposition