A tri-level covering fortification model for facility protection against disturbance in r-interdiction median problem

Proposing a tri-level model defense facilities location to provide a full coverage.Suggesting defense facilities providing extra protection for service facilities.Developing concept of possible successful defense according to the distance of them.Presenting EX-EX-EX, GA-EX-EX and BBO-EX-EX based on exact and meta-heuristics. The available literature for facility interdiction problems is separately modeled by the two r-interdiction covering and median approaches. In this paper, a tri-level defense facility location model for full coverage in r-interdiction median problem is addressed which considers both modeling approaches, simultaneously. The purpose of this model is to design a proper service system in a way that after a worst case scenario of disturbance, it can utilize its full capacity of providing services. In this regard, we have considered the defense facilities to provide extra protection for service facilities and the purpose is to optimally locate these facilities. The tri-level model is proposed based on leader-follower games as defender-attacker-defender framework. In order to solve the model, three approaches have been used. In the first approach (EX-EX-EX), explicit enumeration method is used for the first and second levels and an exact approach is used for the third level. In the second and third approaches, hybrid methods consisting of genetic algorithm, explicit exact enumeration and exact approach (GA-EX-EX) and biogeography-based algorithm, explicit enumeration method and exact approach (BBO-EX-EX) have been used to tackle the problem in a reasonable time. Finally, the proposed approaches are used to solve 27 random instance problems. Comparing the proposed meta-heuristics and the exact approach and studying the numerical examples solved using these approaches are quite satisfactory.

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