Locating service centers to maximize the competitive share in a closed supply chain

Competitive location deals with the problem of locating facilities to provide the service to the customers where other competing facilities offering the same services. Many competitive location models are presented in the literature. However, the literature on competitive location considering reverse logistic in closed-loop supply chain is rather scarce. Also, there are two main approaches in the related literature; increasing profit, and increasing market share of the service centers. Most of the studies in the literature consider one of these issues as the objective function. But, in this study it is shown that these objectives may have conflict with each other. Therefore, addressing these issues simultaneously is important for a successful design of supply chain. This study addresses a novel bi-objective competitive facility location problem in a closed-loop supply chain in a manner that increasing profit and market share are considered simultaneously. On the other hand, in the real world, the customer may choose facilities that are not necessarily close to them, because of the greater attractiveness of other facilities. Hence, in this study, a new relationship is introduced to determine the attractiveness of each potential center for customers based on the distance and quality of service centers. To solve the proposed model and tackle the computational complexity of the proposed model, two approaches are developed: LP-metric and NSGAII. Furthermore, multiple numerical instances are defined and solved with exact approach of LP-metric through GAMS and the results are evaluated in order to validate the accuracy of the proposed model. The best value of “P” in LP-metric approach is also obtained via analyzing the results. Furthermore, the performance of the NSGAII is analyzed by comparing with exact solution of LP-metric through GAMS. The results indicate that the proposed NSGAII is more appropriate than LP-metric and consequently solving the large size problems through GAMS in a logical time is impossible.