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 We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the uncertain data, classical robust optimization approaches cannot be applied directly to construct its robust counterpart. We exploit the problem structure to develop exact solution methods and present some computational results. 

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We focus on a three-stage supply chain problem for fast moving consumer goods including a supplier, a manufacturer and customers. There are different orders over identical cycles, to be processed in production site. The problem is to find a joint cyclic schedule of raw material procurement and job scheduling minimized the total cost comprised of raw material ordering cost and holding cost, production cost, holding cost of finished products, tardiness cost and rejection cost. An integrated mixed integer programing model is proposed and optimal solution of some instances are provided by solving the model.

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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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First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory can be modeled and solved by an integer programming model and a metaheuristic approach.

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A new integer program is presented to model an independent resources assignment problem with resource shortages in the context of municipal fire service. When shortage in resources exists, a critical task for fire department's administrator in a city is to assign the available resources to the fire stations such that the effect of the shortage to cover (in providing service, in extinguishing fire and so on) is minimized. To solve the problem, we propose a polynomial time greedy algorithm.

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Here, we first associate a graph to a university course timetabling problem (UCTP) and use the components of this graph and some customary and organizational rules to transform the original large scale problem into some smaller problems. Then, we apply the branch and cut method to obtain the optimal solution of each smaller problem. Our presented approach enables us to apply exact methods to obtain high quality solutions for large scale UCTPs. Finally, we examine the numerical efficiency of the resulting algorithm.