具有弹性约束的模糊运输问题求解

A Method for Solving the Fuzzy Transportation Problem with Elastic Constraint

为了研究信息不完整、不确定条件下的运输问题,建立了目标函数费用系数为三角模糊数,约束条件为弹性约束的模糊运输问题的模型。首先,将约束条件中的弹性约束转化为两个经典的不等式约束,同时,利用结构元加权排序准则,将模糊目标函数转化为传统的目标函数。然后对转化后的目标函数和约束条件进行整合,从而建立与原模型等价的线性规划模型,进而求出其最优解及其满意度。最后通过具体算例,证明了模型求解方法的可行性。

In order to study the transportation problem under the condition of incomplete and imprecise informa- tion, a fuzzy transportation problem is established. Its objective function cost coefficient is represented by trian- gular fuzzy number and its constraint is elastic constraint, first, the elastic constraints are transformed into two classical inequality constraints. At the same time, fuzzy objective functions are transformed into classical objec- tive functions by a weighted ranking criteria with structuring element. And then, the linear programming model equivalent to the original model is established after integrating transformed objective function and constraints, then and we calculate the optimal solution and its satisfaction. At last, a numeric example is presented to illus- trate the applicability of the approach proposed.