Network Location Problem with Stochastic and Uniformly Distributed Demands

This paper investigates the network location problem for single-server facilities that are subjected to congestion. On each network edge, customers are uniformly distributed, and their requests for service are assumed to be generated according to a Poisson process. A number of facilities are to be selected from a number of candidate sites, and a single server is located at each facility with exponentially distributed service times. Using queueing analysis, we develop a mixed integer mathematical model to minimize the total travel and the average waiting times for customers. For evaluation of the validity of the proposed model, a numerical example is solved and analyzed using GAMS software. In addition, since the proposed problem is NP-hard, two metaheuristic algorithms including a genetic algorithm and a simulated annealing algorithm are developed and applied for large-size problems.