This paper seeks to present a new multi-objective defensive location problem (MDLP) with the manufacturing cost and considering different capacities for facilities in a network. In the novel MDLP, to prevent the attacker from reaching strategic sites (cores), the defender locates various facilities in the vertices of the network. In this regard, a mixed integer programming is formulated to find the Stackelberg solutions that defender and attacker are the upper and lower-level decision makers, respectively. In this study, the goal of defensive strategy is to maximize the distance between the cores and the attacker, which aims at reaching the closest possible vertices to the cores. On the other hand, since the problem is an NP-hard problem, to find a satisfactory solution, an interactive fuzzy method based on the cuckoo search algorithm has been introduced. The application of the method is illustrated solving two random instances of MDLP.

Keywords: Defensive Location Problem, Stackelberg Equilibrium, Mixed Integer Programming, Cuckoo Search Algorithm.

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