The Competitive Location Problem Based On Customer Choice Behavior

Facility location is one of the firm’s significant strategic actions.And the location of commercial facility has a direct influence on the firm’s profit.With the competition of market is aggravating gradually and the consumer’s demand is more and more diversified and personalized,taking the competition and customer choice behavior into account make the facility location approach the practical situation and realize a more precise location.So we consider the competitive location problem based on the customer choice behavior and we design the corresponding algorithm to solve this problem.Finally we get the management highlights and provide guidance for the firm’s location strategy.Firstly,we formulate the maximal covering model based on the follower and the preoccupy the market model based on the leader on the basis of customer choice behavior.The multinomial logit model is used to represent the customer choice behavior according to the characteristics of facility and the customer’s preference.The environment of the above problems consists of the determined position of demand points and demands.The decision makers enter the market in succession and hope to maximize the market share that they capture.Every customer in demand points patronizes different decision marker facility which is located closest to him and could serve him with a certain probability.First of all,we stand the follower’s point of view,the follower locates her facilities to maximize the market share when the market has already existed facilities which provide the same products or services and formulate a single level 0-1 programming.Then we stand the leader’s point of view,the leader locates his facilities in order to maximize the market share with the knowledge that the followers’ response to his location strategy and the customer choice behavior,and formulates the Stackelberg game which is the non-linear bi-level programming.Secondly,we design a nested hybrid genetic algorithm based on the non-linear bi-level programming that we mentioned above.The non-linear bi-level programming is very hard and the instances that are involved in this paper are large-scale,so the heuristic algorithm could get satisfactory solutions at a relatively short period of time.This paper we use genetic algorithm to solve the models.Because the model that we reformulate is bi-level so we use the nested genetic algorithm.And at the same time in order to overcome the deficiency of genetic algorithm and improve the efficiency of our algorithm,we add the elitist strategy and probabilistic Tabu search into the nested genetic algorithm and improve the algorithm.Finally,we use the nested hybrid genetic algorithm that we mentioned above to experiment.We explore the sequence of entering market,the radius of facility and the number of facilities how to affect the decision makers’ market share.The numerical experiences show that the leader who first enters the market has first mover advantage and the leader’s market share is ahead of the follower’s market share.With the increase of the number of facilities that to be built,both of decision makers’ market share increase gradually and tend to be stable finally.The radius of facility also has influence on the market share.Above conclusions have guiding function and provide corresponding references for decision of location strategy.