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On Maximum Discounted Effort Reward Search Problem

In this paper, we formulate a new search model for detecting two related targets that randomly located in a finite set of different cells or randomly moved through those cells. We assume that the search effort at each fixed number of time intervals is a random variable with a normal distribution. Rather than minimizing the expected effort of detecting two related targets, the proposed mathematical model allows us to include the search effort as a function with fuzzy parameter (discounted parameter). Another feature of this paper is considering a fuzzy extension of a stochastic optimization problem, which is interesting. We present an algorithm that gives the optimal distribution of an effort which makes the discounted effort reward of finding the targets is maximum. Two numerical examples are illustrated to show the effectiveness of this model by setting some parameters to represent some situations, such as detecting the enemy ships, fighters and the landmines in the war.