Objective: The aim of this paper is to choose the optimal coverage for threatened targets with various security resources which are limited and minimizing the costs of transporting these forces from different locations to the targets.

Methodology: In this paper, a method is presented to determine the defender’s optimal strategy when multiple types of security forces can be employed to cover the targets in a security game. It is assumed that different types of defense forces are sent from different locations to the targets, and the cost of sending each type of force from each location is different. Thus, using lexicographic programming, a method has been proposed to optimally allocate the required forces from different locations to these targets with the lowest possible cost.

Findings and Originality: This paper demonstrates that it is not possible to devise a polynomial-time algorithm to solve the security game problem involving multiple types of defenders. Consequently, using game theory, a model is proposed to optimize the defender's payoff under defensive resource constraints while accounting for the attacker's response. In the final section, a model is introduced to minimize the defender's cost in deploying various types of forces.