一个带产品定价约束的竞争选址双层规划模型及其求解算法

以大型连锁卖场的选址为研究背景,提出了一个在竞争环境下使获利最大的竞争选址定价双层规划模型,其中上层模型做出选址决策,下层模型确定产品的纳什均衡价格.将设施效用引入到模型中,用指数效用函数来刻画顾客的购物行为偏好,首次证明了不合作状态下双方价格均衡解的存在性和唯一性,并给出了求解最优设施点设置方案和价格均衡解的算法思想及数值算例.

A Bi-level Programming Model for Competitive Location under a Pricing Constraint

In this paper, a bi-level programming model is developed to investigate facility location strategies and product pricing strategies for the best profit under a competitive environment. The upper-level model focuses on the location decision, while the lower-level model is used to investigate the Nash equilibrium prices. Facility utility is introduced into the bi-level programming model and an exponent function is taken to depict the patronizing preference of customers. In the lower-level model, the existence and uniqueness of Nash equilibrium prices are proved firstly when companies are non-cooperative. Besides, an algorithm is presented to solve the model and an example is used to show how to find the Nash equilibrium prices and the optimal location solution.