Abstract
This paper investigates a competitive location problem with reliability. The reliability is the probability of out of service facilities for customers who cannot be served because of natural causes or human reasons. In this case, for each customer, there are several levels of allocations. If a facility fails to serve a customer, the customer will be served by the facility at the next allocation level. The two firms determine their optimal location, respectively. The problem is modeled based on a Stackelberg game, in which the leader's and follower's facility locations are determined respectively. The follower chooses the location of his choice according to the leader choice. The object of each competitor is maximizing the profit. Demographic parameters are considered as effective factors in choosing the location for leaders and followers, which means that the candidate location with more positive demographic factors is a better choice for facility establishment. The behavior of customers in choosing any of the facilities is affected by the quality and distance parameters which are considered in the model. According to gravity huff model, when the distance between costumers and candidate location is shorter and the quality factor is higher, the candidate location is a better choice for establishment. To solve the small part of the problem, the full space searching method is used, in which all possible points in space of answer are investigated. The answers are compared and Pareto optimal solutions are obtained which are shown in figures. As the problem is NP-hard, NSGA-II meta-heuristics algorithm is used to solve the medium and large size of the problem. Representation of answer and crossover and mutation operator for algorithms also specified for the problem. Ultimately, the numerical problems are randomly generated and Pareto optimal solutions are identified for each problem which is shown in figures. The answers obtained from both methods for small size problem are also compared.
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