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In general, any system may be at risk in a case of losing the critical facilities by natural disasters or terrorist attacks. This paper focuses on identifying the critical facilities and planning to reduce the effect of this event. A three-level model is suggested in the form of a defender-attacker-defender. It is assumed that the facilities are hierarchical and capable of nesting. Also, the attacker budget for the interdiction and defender budget for fortification is limited. At the first level, a defender locates facilities in order to enhance the system capability with the lowest possible cost and full covering customer demand before any interdiction. The worst-case scenario losses are modeled in the second-level. At the third level, a defender is responsible for satisfying the demand of all customers while minimizing the total transportation and outsourcing costs. We use two different approaches to solve this model. In the first approach, the third level of the presented model is coded in Gams software, its second level is solved by an explicit enumeration method, and the first level is solved by tabu search (TS). In the second approach the first level is solved by the bat algorithm (BA). Finally, the conclusion is provided.

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In an uncapacitated facility location problem, the aim is to find the best locations for facilities on a specific network in order to service the existing clients at the maximum total profit or minimum cost. In this paper, we investigate the uncapacitated facility location problem where the profits of the demands and the opening costs of the facilities are uncertain values. We first present the belief degree-constrained, expected value and tail value at risk programming models of the problem under investigation. Then, we apply the concepts of the uncertainty theory to transform these uncertain programs into the corresponding deterministic optimization models. The efficient algorithms
are provided for deriving the optimal solutions the problem under investigation.

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One of the key challenges in supply chain management is the design of the supply chain network, which aims to determine the optimal locations of distribution centers across different regions in order to satisfy customer demand. In the proposed model, customer demand is fulfilled through distribution centers, which receive products from manufacturing plants. This study presents an integer linear programming model that simultaneously addresses supply chain network design and facility location decisions. The objective of the model is to minimize the total costs associated with establishing
distribution centers, transporting products from manufacturing plants to distribution centers, and distributing products from distribution centers to customers. To evaluate the effectiveness of the proposed model, several randomly generated test instances of different sizes were examined. Computational experiments were conducted using a linear programming solver and an iterative local search algorithm to compare their performance in obtaining optimal solutions. The results demonstrate that the iterative local search algorithm outperforms the linear programming solver by achieving optimal solutions with significantly shorter computational time across all tested instances.

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In this paper, we investigate a solution procedure for a fuzzy linear fractional optimization problem in which the input parameters are considered as convex fuzzy numbers. By applying a specific fuzzy ranking method which is based on the α-cut concept, and according to Charnes and Cooper’s approach of variable transformation, the solution of the original fuzzy linear fractional optimization model is transformed to the solution of at most two semi-infinite linear programs that are dis similar among themselves via a sign in a constraint and in the objective function. An appropriate cutting plane algorithm(CPA) of Fang is uti lized to obtain the optimal solution of the semi-infinite linear programs. Further, the application of our provided algorithm in facility location theory is discussed properly. Finally, an illustrative example is given to clarify the developed solution procedure.

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The line location problem, which represents a specific case within the broader class of hyperplane location problems, has attracted considerable research focus location theory. This investigation addresses locating lines from a location science perspective. Given n points situated in the plane, each assigned a positive weight that reflects its relative importance, the median line is defined as the line minimizing the total sum of these weighted distances. Our study is, to our knowledge, the first to examine the inverse median line location problem in the plane under both the Euclidean and rectilinear distance norms. Specifically, when a line L is fixed, the goal is to determine the Minimum-cost modifications to the problem parameters—either the demand point weights or their spatial coordinates—such that L becomes the globally optimal median line. We proceed by developing and analyzing mathematical models that characterize this inverse problem across the two norm settings. We demonstrate that the inverse model, when demand weights are the variables, can be precisely formulated and solved via linear programming. Conversely, for the instance involving necessary modifications to the coordinates, an effective greedy algorithm is proposed for solution approximation. The practical application and performance of this developed methodology are subsequently illustrated through a set of computational experiments.