Allocation of demand when cost is demand-dependent

This paper extends the location-allocation model with continuously distributed demands by making the cost charged to users by a facility a function of the total number of users patronizing the facility. Users select their facility based on facility charges and transportation costs. We explore equilibria where each customer selects the least expensive facility (cost and transportation). One special case where facilities and customers are located on a finite line segment is discussed in a previous paper. In this paper we analyze the problem of multiple facilities and a convex region of demand. Algorithms to solve it are devised and computational experiments reported. The case of two facilities serving customers uniformly distributed on a square is solved in detail.