Reliable location-allocation model for congested systems under disruptions using accelerated Benders decomposition

This paper aims to propose a reliable location-allocation model where facilities are subject to the risk of disruptions. Since service facilities are expected to satisfy random and heavy demands, we model the congested situations in the system within a queuing framework which handles two sources of uncertainty associated with demand and service. To insure the service quality, a minimum limit reflected in the customers’ expected waiting time is considered in the model. We also consider the geographical accessibility of the service network in terms of the proximity of a facility to the potential demands. The model determines the optimal number and locations of facilities and the corresponding customer assignments in such a way as to minimize the fixed installation cost as well as expected traveling, serving and penalty costs. To obtain exact solution of the proposed model, a Benders decomposition algorithm enhanced by two efficient accelerating methods including valid inequalities and knapsack inequalities is proposed. Numerical results illustrate the applicability of the proposed model as well as the effectiveness of the designed solution procedure.