多目标多模式模糊运输问题的最优折衷解

Optimal Compromise Solution for Multiobjective Fuzzy Solid Transportation Problems

在不确定性运输问题研究现状的基础上,建立了目标函数费用系数、可供应量和需求量均为模糊数的多目标多模式运输问题(MOSTP)数学模型。首先根据Zadeh的扩展原理将模糊数多目标多模式运输问题转化为不同截集水平α下的区间数多目标多模式运输问题。然后根据区间数序关系,将区间数MOSTP转化为典型的MOSTP,并将模糊数约束转化为确定性的不等式约束。通过运用模糊折衷规划方法求解,得到了模糊数MOSTP的最优折衷解。文章最后采用具体算例论证了该方法的求解过程。

Based on recent research on uncertain transportation problems, the paper considers a new multi-objective solid transportation problem （MOSTP） mathematical model, where the cost coefficients of the objective functions, the source and destination parameters are expressed as fuzzy numbers. Firstly, based on the extension principle, the fuzzy MOSTP problem is transformed into a series of MOSTP problems with the fuzzy number cut level as its parameter. Then, considering to the actual meanings of parameters and the relations between intervals, this problem is transformed into a classical crisp MOSTP, and the constraints with interval source and destination parameters are converted into deterministic inequality ones. Finally, the equivalent transformed problem is solved by fuzzy compromise programming technique. An illustrative numerical example is provided to demonstrate the proposed approach.