We study the location–allocation problem where facilities pass on their costs to customers and these costs have economies of scale; in other words, the costs decrease with the number of customers attracted. This problem is an extension to the p-median problem. The problem arises for subsidized or controlled facilities that operate on a cost-plus basis. The more customers patronize a facility the lower is the cost charged to all customers. Individual customers base their selection of a facility on the total cost – the cost of transportation (proportional to the distance to the facility) and the charges required by the facility. By this assumption, customers do not necessarily use the closest facility because the attractiveness of a facility is determined not only by distance but also by the number of customers patronizing the facility. This gives rise to interesting dynamics. The selection of the ‘best’ facility is determined by actions of other customers. A final stable configuration may not exist, and stable configurations may not necessarily be the best ones for customers. The problem is reviewed for demand distributed on a line, demand distributed over an area, and the discrete case (a finite number of demand points).
