Location and Design of Urban Facilities considering Competitors’ Responses: A Case Study of Putuo District, Shanghai

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.

Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule

When consumers faced with the choice of competitive chain facilities that offer exclusive services, current rules cannot describe these customers’ behaviors very well. So we propose a partially proportional rule to represent this kind of customer behavior. In addition, the exact demands of customers in many real-world environments are often difficult to determine. This is contradicting to the assumption in most studies of the competitive facility location problem. For the competitive facility location problem with the partially proportional rule, we establish a robust optimization model to handle the uncertainty of customers’ demands. We propose two methods to solve the robust model by studying the properties of the counterpart problem. The first method MIP is presented by solving a mixed-integer optimization model of the counterpart problem directly. The second method SAS is given by embedding a sorting subalgorithm into the simulated annealing framework, in which the sorting subalgorithm can easily solve the subproblem. The effects of the budget and the robust control parameter to the location scheme are analyzed in a quasi-real example. The result shows that changes in the robust control parameter can affect the customer demands that were captured by the new entrants, thereby changing the optimal solution for facility location. In addition, there is a threshold of the robust control parameter for any given budget. Only when the robust control parameter is larger than this threshold, the market share captured by the new entering firm increases with the increases of this parameter. Finally, numerical experiments show the superiority of the algorithm SAS in large-scare competitive facility location problems.