Linear formulation for extensions of the leader-follower competitive location problem

Abstract

The leader-follower problem is a sequential decision problem where, in a market initially without service centers, a firm, the leader, opens its centers and another competing firm, the follower, will enter later the market opening its centers. The leader chooses the locations taking into account that the follower will enter the market opening its centers and capturing part of the market share. The objective of each competing firm is to maximize its market share. We consider that the clients will behave making a binary choice using the distance as basis for her/his choice criterion. We extend the basic model by considering a threshold in the client choice rule and opening costs depending on the location. We get formulations of the problem extensions as linear programs from the basic linear model.