Treffer: A stochastic leader-follower model in competitive facility location.

AbstractThe competitive facilities location problem is to find the locations of one or more new facilities among existing competing facilities that maximize the captured market share by the new facilities. In the leader-follower models, the leader locates his facility first and anticipates a competing follower to locate his facility optimally, knowing the location selected by the leader. The leader’s objective is to maximize his captured market share following the follower’s action. In this paper we consider the case that the leader is not sure whether there will be a follower or not. We investigate and test the minimax regret and the expected value rules. Algorithms for locating the competing facilities anywhere in the plane, which are more difficult to solve, were designed. The follower’s problem and the leader’s problem when there is no follower are solved to optimality within a given relative accuracy by available algorithms. For solving the leader’s problem when a follower will react knowing the leader’s move, a special heuristic algorithm that can be applied to other location problems is constructed. The leader’s location problem with the objective of minimax regret or expected value decision rules, and 20,000 demand points, were solved in less than 4 min of computer time. [ABSTRACT FROM AUTHOR]

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