A Note on a Profit Maximizing Location Model

In this paper we discuss a locational model with a profit-maximizing objective. The model can be illustrated by the followingsituation. There is a set of potential customers in a given region. A firm enters the market and wants to sell a certainproduct to this set of customers. The location and demand of each potential customer are assumed to be known. In orderto maximize its total profit, the firm has to decide:1) where to locate its distribution warehouse to serve the customers;2) the price for its product. Due to existence ofcompetition, each customer holds a reservation price for the product. This reservation price is a decreasing function inthe distance to the warehouse. If the actual price is higher than the reservation price, then the customer will turn to someother supplier and hence is lost from the firm's market. The problem of the firm is to find the best location for its warehouseand the best price for its product at the same time in order to maximize the total profit. We show that this problem can besolved in polynomial time.