A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold.

Wuyang Yu,Baogui Xin

doi:10.1371/journal.pone.0225693

Abstract

When consumers are faced with the choice of competitive chain facilities that offer exclusive services, current rules do not properly describe the behavior pattern of these consumers. To eliminate the gap between the current rules and this kind of customers behavior pattern, the partially proportional rule with a threshold is proposed in this paper. A leader-follower model for discrete competitive facility location problem is established under the partially proportional rule with a threshold. Combining with the greedy strategy and the 2-opt strategy, a heuristical algorithm (GFA) is designed to solve the follower's problem. By embedding the algorithm (GFA), an improved ranking-based algorithm (IRGA) is proposed to solve the leader-follower model. Numerical tests show that the algorithm proposed in this paper can solve the leader-follower model for discrete competitive facility location problem effectively. The effects of different parameters on the market share captured by the leader firm and the follower firm are analyzed in detail using a quasi-real example. An interesting finding is that in some cases the leader firm does not have a first-mover advantage.

Highlights

In a market environment, competing facilities are those provided similar products or services for customers’ patronage
We first propose a suitable rule to describe the behavior of customers when they faced the choice of competitive chain facilities that offer exclusive services
Based on the above conclusion, we proposed an improved ranking-based greedy algorithm by embedding the algorithm (GFA) as follows: Improved Ranking-Based Greedy Algorithm (IRGA): 1. Input the parameter T, which indicates the number of iterations of the algorithm

Summary

Introduction

In a market environment, competing facilities are those provided similar products or services for customers’ patronage. Following the partially binary rule, the customer first selects the most attractive facility from each firm in the market, splits his demand among those facilities proportionally to its attraction [19]. Some variants of these customer choice rules, mainly of the proportional rule, are proposed in some research works (see [20]–[28]). The remainder of the paper is organized as follows: Section 2 is devoted to present the definition of the partially proportional rule with a threshold and to propose a competitive facility location model with foresight. We first propose a suitable rule to describe the behavior of customers when they faced the choice of competitive chain facilities that offer exclusive services.

Proposed model

Solution method

Numerical example

Performance of the algorithm

A quasi-real example

Conclusion