### Multiple-server facility location problem with stochastic demands along the network edges

#### Abstract

This paper investigates the network location problem for multiple-server facilities,which are subject to congestion. A number of facilities are to be selected among several candidate locations in order to satisfy customers’ demands. For each network edge, the corresponding customers are uniformly distributed along the edge, and their demands are generated according to the Poisson process. Furthermore, the number of servers in each established facility is considered as a decision variable, and the service time for each server follows an exponential distribution. Using queuing system analysis, a mathematical model is developed to minimize the customers’ aggregate expected traveling times and the aggregate expected waiting times. Since network location problems are NPhard, three metaheuristic algorithms including genetic algorithm, memetic algorithm, and simulated annealing are then investigated and developed to solve the proposed problem. The results of implementing the algorithms on some test problems demonstrate that the proposed memetic

algorithm outperforms theother two algorithms in terms of objective values.

#### Keywords

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