Locations of congested facilities with interruptible immobile servers

This research addresses the problem of locating facilities with immobile servers. The possibility of occurrence of congestion in the facilities and the risk of interruption in the servers are considered as the sources of uncertainty. As the stochastic process of interruption in servers stops the process of providing service, the customers leave the facility once the interruption occurs, while no customer enters the facility until the server is fixed. The proposed model specifies the number and the optimal locations of the facilities so that the profit obtained by serving customers is maximized on the one hand. On the other hand, the cost of the system, including those corresponding to the customers' travel and waiting time and locating the facilities, is minimized. Furthermore, two meta-heuristic algorithms, i.e., a genetic algorithm and an ant lion algorithm, are proposed to solve the complicated optimization problem. The results of running the proposed algorithms on standard test problems suggest their efficiency as compared to the results obtained by solving the mathematical model. Moreover, the ant lion algorithm exhibits a higher quality and convergence rate than the genetic algorithm.