| Summary: | On the networks existing servers and customers, each node indicates a customer demand and demand rate is estimated for them. The edges of the network indicate connective ways among the nods which is usually shown with the distance of two nods or the time of travelling. In the covering location problems, the objective is locating some of the servers on the network in a way that the customers' demand supported by the maximum covering of the servers and optimized objective criterion. In this research the location model with Probability Structure, which the probability of choosing servers by customer is estimated based on their distance, is developed. In the presented model, supposing there is a competitive market, lost demand is considered, too. And according to the mentioned matter the objective of the model is to minimize the cost of losing demands or to maximize the earned profits of responding to the demands. Then, we propose a genetic algorithm (GA) to solve this model. In addition, we employ design of experiments and response surface methodology to both tune the GA parameters and to evaluate the performance of the proposed method in 45 test problems. The results of the performance analysis show that the efficiency of the proposed GA method is very well.
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