Abstract: To solve the optimal pricing problems of the pollution charges, a price control problem based on Grey theory is presented, and its model and theorem are given. Under the assumption condition of the constraint region of the proposed model nonempty and compactness, it is shown that the optimal solution of the drifting price control problem can be reached on the extreme points of the constraint region. To solve the drifting price control problem based on Grey theory, a search algorithm based on duality theory is developed, and the model of price control problem is converted to some nonlinear programming models on uncertain parameters, when consider the gray parameters as a new decision variables, Finally, an example is adopted to verify the effectiveness of the proposed algorithm.

Key words: operations research, bilevel programming, price control problem, a search algorithm

摘要： 针对排污收费的最优定价问题,提出了基于灰色理论的价格控制问题,并给出了该问题的模型及相关的定理。在约束域为非空紧集的条件下,证明了漂移型价格控制问题的最优解一定可以在约束域的极点达到。针对漂移型价格控制问题,采用价格控制问题的搜索算法的求解技术,把灰参数看做一个新的决策变量,将该问题转化为多个含参数的非线性规划问题。最后,通过一算例验证了模型及求解方法的有效性。

关键词: 运筹学, 二层规划, 价格控制问题, 搜索算法