This research addresses the location problem of congested facilities, assuming service interruptions and customer withdrawals. Service interruptions can occur as a result of events such as machine failures, power outages, and communication system disconnections. As long as no interruption occurs, each facility functions as a M/M/1 queuing system. Upon an interruption, the server stops working, and customers receiving service or waiting in line leave the queue before being served. Moreover, customers who visit the facility during the repair avoid entering the facility. The problem is first formulated as a mixed-integer nonlinear programming (MINLP) model, for which two piecewise mixed-integer linear programming (MILP) relaxations, an exact solution algorithm (the branch and bound algorithm), and a metaheuristic algorithm (the antlion algorithm), are then presented for solution. Numerical experiments indicate the efficiency of the branch and bound algorithm. The antlion algorithm also exhibits the proper convergence speed to obtain near-optimal solutions.
