^{1}Department of Industrial Engineering, Faculty of Technology and Engineering, University of Qom, Qom, Iran

^{2}Department of Industrial Engineering, University of Kashan, Kashan, Iran

Abstract

This paper addresses a situation in which a firm is willing to locate several new multi-server facilities in a geographical area to provide a service to his customers within the M/M/m/K queue system. As a new assumption, it is also considered that there is already operating competitors in such system. This paper is going to find the location of facilities in a way that the market share of entering firm is maximized. For this purpose, simultaneous minimization of total cost and maximum idle time in each facility is considered as two objective functions in the model. The total cost consists of two parts: (1) the fixed cost for opening a new facility, and (2) the operational costs regarding to the customers, which depends on travel time to the facility and the waiting time at the facility. In addition, in order to make the problem more adapted to real-world situations, two new constraints on budget and number of the servers in each facility are added to the model. Eventually, to tackle the suggested problem, a non-dominated sorting genetic algorithm (NSGA-II) and a non-dominated ranked genetic algorithm (NRGA) are utilized. Finally, the performance of algorithms are investigated via analyzing a set of test problems.

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