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In view of the problem of competitive facility location in urban planning, the response of competitors to the new facility is considered. We use Huff's probability model to describe the market share of all facilities which depends on its service quality and its distance from customers. To maximize the market share of facilities, a two-stage method (quality decision stage and location decision stage) is adopted, which takes into account the responses of competitors. In the stage of quality decision, the competitive decision-making process is simulated as a game process and solved by Nash equilibrium. The solution of the quality decision process can be expressed as a function of the new facility's location which can be obtained by polynomial approximation. In the location decision stage, we apply the interval analysis based on branch and bound algorithm to determine the optimal location of new facility. Then, we use the randomly generated numerical experiment to verify the effectiveness of the model and algorithm. Finally, we apply this model and algorithm to the location of a new shopping mall in Putuo district, Shanghai. [ABSTRACT FROM AUTHOR]

In view of the problem of competitive facility location in urban planning, the response of competitors to the new facility is considered. We use Huff's probability model to describe the market share of all facilities which depends on its service quality and its distance from customers. To maximize the market share of facilities, a two-stage method (quality decision stage and location decision stage) is adopted, which takes into account the responses of competitors. In the stage of quality decision, the competitive decision-making process is simulated as a game process and solved by Nash equilibrium. The solution of the quality decision process can be expressed as a function of the new facility's location which can be obtained by polynomial approximation. In the location decision stage, we apply the interval analysis based on branch and bound algorithm to determine the optimal location of new facility. Then, we use the randomly generated numerical experiment to verify the effectiveness of the model and algorithm. Finally, we apply this model and algorithm to the location of a new shopping mall in Putuo district, Shanghai. [ABSTRACT FROM AUTHOR]