LOCATION/RELOCATION MODEL FOR COMPETING FRANCHISE CHAINS

Abstract

This paper focuses on two competing franchise chains and considers a situation in which each chain alternately determines location of stores they operate. In each period, the decision-making chain determines the location of new stores to be opened and the subset of existing stores to be closed in order to maximize profit. We assume two types of demand for services: point-based demand and flow-based demand. The point-based demand represents a customer that accesses a store directly, while the flow-based demand uses the service by stopping at a store along the preplanned travel path. It is assumed that a point-based customer chooses the closest open store, and a flow-based customer stops at each store along the travel path with equal probability. The objective function for the decision maker is defined as the profit obtained from covered customers for all stores, minus the cost of opening new stores and the cost of maintaining existing stores. We formulate the decision-maker's store location problem as an integer programming problem. Using this formulation, we investigate equilibrium locational patterns resulting from the competition of two franchise chains. Through numerical experiments using problem instances based on actual geographical and population data, we analyze (1) how stores in both chains are distributed in the final pattern, (2) how stores in both chains are opened/closed in each period, and (3) how basic input parameters of the model affect the final store distribution. The results showed that the chain that enters the market earlier than the other has a great advantage in the final profit.