The Research Of Retail Facility Location Problem Based On The Stackelberg Competition

The facility location problem based on Stackelberg competition is usually consisting of a leader and a follower,in which the two competitors are going to locate new facilities sequentially.This kind of competition mode is very common in the retail market,and it is necessary for the one who enters the market consider the influence of the coming competitor on his location selection firstly.If without such consideration,the short-term advantage of location decision may be turning the superior into the inferior in the long run due to the arrival of competitor,and which may result in a significant reduction of his market share.Therefore,we consider a leader-follower facility location model in a competitive market.The traditional studies generally assume that the leader knows in advance the partial or full information about the follower’s response when he makes decision.This assumption,however,may be invalid or impracticable in practice.In this paper,we consider that the leader needs to locate a predetermined number of new facilities without knowing any information about the follower’s response.Besides,the competitors who need to make location decisions are also likely to have no idea on the demand distribution.Based on these assumptions,the specific research work is as follows:(1)A minimax regret model for leader-follower facility location problem:By separating scenarios on the follower’s response with different number of new facilities,a minimax regret model is proposed for the leader so that his maximum possible loss can be minimized.(2)Model linearization and solution method:Based on the structural characteristics of the minimax regret model,we transform the follower’s nonlinear(fraction)programming model into a linear one.Besides,we propose exact solution method for the minimax regret model.Also,the efficiency of linearization in decreasing the computation time is verified.(3)A expectation model for leader-follower facility location problem:When the demand distribution and the number of follower’s new facilities are both uncertain,we study the leader’s location decision.By calculating the leader’s expectation under each demand distribution,we make location decision for leader to minimize the expectation of leader’s maximum market share loss.Also,a genetic algorithm is proposed to solve the model.Where to locate the facility in a competitive market is a problem faced by many enterprises in reality.The research of this paper can provide decision support to these enterprises.By considering the influencing factors of facility location,we help the enterprises to expand market share and reduce possible loss,which can have practical significance for the enterprises in the market.