Discrete location assignment problem with congestion

Given a set of sites, this paper deals with the selection of sites for installing facilities and the assignment of customers to them. The customers have random demands for service and form finite source queues at the installed facilities. The objective is to minimize the expected total cost per unit of time consisting of travel cost, waiting cost for service, and fixed cost for installing and maintaining the facilities. A heuristic algorithm is developed. Computational results supporting the efficiency and accuracy of the heuristic are included. Under specific conditions, the problem is reduced to a linear integer programming problem and is solved by a branch and bound algorithm.