A new approach for locating multiple facilities in a network competitive environment

In this paper, we investigate location problems of one or more facilities in a network in which several competing facilities already exist. Consider some demand points on the network. Each demand point has demand in proportion to the buying power of all customers of the point. It is assumed that customers patronize the nearest facility. If a facility is newly located within the distance from a demand point to its nearest existing facility, customers of the demand point will use the new facility. In this situation, we would like to locate given number of facilities to maximize the buying power to obtain from the existing facilities. In order to solve the problem, the network is divided into a sub-network according to the combination of the demand points and the existing facilities. And we calculate the buying power of the demand points when we locate a new facility on the sub-network. Then we formulate the problem as a maximum covering problem with p facilities. As an example, we use the road network and existing convenience stores of Seto City. This example shows that our method can be used in the city of real size.