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.the objective is to find a search strategy that minimizes the expected cost until the target will be found. In other search problems, Ahlswede and Wegener (1987) and Stone (1975) found a search strategy that maximizes the total probability of successful search. Assaf and Zamir (1987), Assaf and Sharlin (1994) and Sharlin (1987) investigated the discrete search problems when there are more than one stationary hidden targets. Song and Teneketizs (2004) determined the optimal search strategies with multiple sensors that maximize the total probability of successful search where the target is hidden in one of the finite set of different cells. On the other hand, Assaf and Sharlin (1994) investigated a discrete approach when the target moves randomly in a finite set of different cells.The optimal search problem is a decision making process that involves two dynamic partakers: the searcher who owns a sensor and the targets that are searched. In our case, the target movement does not depend on the searcher (i.e., we do not have an evading target). Many authors aimed to find the optimal search path of the searcher, represented by the cells, it visits over the known time periods that minimizes the no detection probability and the search effort. This search problem can be modeled in a continuous way as in Mathews (2008), Gan and Sukkarieh (2010) and Sarmiento et al. (2009) or in a discrete form as in Eagle and Yee (1990) and Yang et al. (2002), depending on the searching region representation, the sensor type and the searcher possible actions. Recently, Hong et al. (2009a, 2009b proposed an approximation algorithm for the optimal search path. This algorithm optimizes an approximate instead of exact path detection probability computed using the conditional probabilities that take an account of the search history of a fixed length window of known periods. Then, finding the maximum detection probability search path can be formulated as a shortest-path problem on an acyclic layered network whose number of layers is the order of search duration. More recently, ...

a b s t r a c tThis paper investigates a search problem for a brownian target motion on one of n-intersected real lines in which any information of the target position is not available to the searchers all the time. We have n-searchers start searching for the target from the origin that is the intersection point of these lines. Each of the searchers moves continuously along his line in both directions of the starting point. The purpose of this paper is to formulate a search model and find the condition under which the expected value of the first meeting time between one of the searchers and the target is finite. Also, we show the existence of the optimal search plan which minimizes the expected value of the first meeting time and find it.

This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.

In this paper, we consider a system of K‐independent Markovian queues such that each one of them has a Poisson arrival process and exponential service time. We assume that every server has some characteristics such as the speed of the service performance or the service cost. To find an appropriate queue, which meets customer needs for the service performance, we present a new approach that gives a suitable decision to choose an appropriate queue from our system. This allows the customer to deal with minimum cost and faster server under steady state. We solve an interesting discrete stochastic optimization problem where the paid cost by the customer is bounded by a Gaussian distribution. Using these hypotheses, we perform a simulation study by generating the paid cost random values and choosing the minimum value between them. This minimum cost gives the highest service rate, which is used to obtain the optimum values of the system effectiveness measures.