A New Competitive Facility Location Model Based On Discrete Choice Theory

Competitive facility location theory is an important branch of location science,its main goal is to investigate how to maximize a company's market share by optimizing the position or attribute of its new facility,considering the existing facilities,or possible facilities of its competitors.In the beginning of this theory,only the new facilities' location will be treated as variables,like the earliest Hotelling research on linear Two-Oligarch market.In nearest research,the key attributes of new facility will also be regard as variables,which is named as competitive facility location and design problem.Current customers' choice behavior is more diversified and personalized,the price or position is not the only factor that will attract customers.It's very important for company to analyze customers' choice behavior from a more precise way,by optimizing the attributes of its facilities,such parking space,service level and etc.,to make sure the company can obtain sustainable profit.Competitive facility location theory is a tool for such problems,it consists of two parts: first part is to analyze the customers' choice behavior,the possibility to choose its own facilities and the possibility to choose competitors;the second part is to maximize the possibility by optimizing the position or attributes of new facility.The Huff model is the most widely used in the first part.In this article,we analyze the Huff model with multinomial Logit model,and prove the similar deviation in Huff model caused by “Independence of irrelevant alternatives” when predict customers' behavior.In discrete theory,nested Logit model is an improved method of multinomial Logit model,which can avoid such deviation on predication.Therefore,we propose combine nested Logit model with competitive facility location theory,and construct a new model.To solve the model proposed in this article,we choose several meta-heuristic algorithms,including gravitational search algorithm,PSO-gravitational search algorithm and chaoticgravitational search algorithm.Considering the randomness along with meta-heuristic algorithms,we design a numerical experiment and indicators,including average CPU time,average relative error,maximum relative error and number of optimal solutions.We can choose the best algorithm based on the performance of these candidates in every one-hundred running.The experiment shows the introduced chaotic operators doesn't improve the performance of GSA,and PSO-GSA has the best performance,which is also a reliable solution for new constructed model.