Inthe current competitive market, obtaining a greater share of the market requires consideration of the customers’ preferences and meticulous demands. Thisstudy addresses this issue with a queuing modelthat uses multi-objective set covering constraints. It considers facilities as potential locations with the objective of covering all customers with a minimum number of facilities. Themodel is designed based on the assumption that customers can meet their needs from a singlefacility. It also considers three objective functions, namely minimizing the total number of the assigned server, minimizing the total transportation and facility deploymentcostsand maximizing the quality of service from the customers’ point of view. The main constraintis that every center shouldhave less than b numbers of people in line with a probability of at least α, upon the arrival of a new customer.The feasibility of the approach is demonstrated by several examples which aredesigned and optimized byaproposed hybrid simulated annealing (SA)algorithm to evaluate the model’svalidity. Finally, the study compares the performance of the proposed algorithm with that of variable neighborhood search (VNS)algorithm and concludes that it can arrive at an optimal solution in much less time than the VNS algorithm.