广义模糊指派问题的解法

Solution to the Generalized Fuzzy Assignment Problem

对于指派问题,工作未完成之前,其效率矩阵中的元素应该是不确定的。但是决策者为了得到具有指导性的决策,有必要对效率矩阵中的元素进行统计或粗略估计。由此产生了更加贴近于现实生活中的不确定环境中的指派问题。针对现实生活中的模糊指派问题,讨论了模糊指派问题出现的三种可能情况,分别建立了它们的数学模型。将求解传统指派问题的匈牙利算法和伏格尔法进行了推广,讨论了模糊指派问题的求解方法,并结合算例进行了说明。

For the assignment problem, before the work is completed, its elements in efficiency matrix should be uncertain. The statistics or rough estimation for efficiency matrix elements is necessary for decision-makers to obtain guidance of decision-making. This has resulted in the assignment problem in the uncertain environment, which is closer to the reality of life. This paper investigated a practical fuzzy assignment problem, and discussed three types of fuzzy assignment problems, constructed their mathematical models. The methods for fuzzy assignment problem are developed, which are classical Hungary algorithm and Vogel method. This paper discussed the method for solving fuzzy assignment problem. Finally, an example is given to illustrate the methods.