summary:We consider the following bottleneck transportation problem with both random and fuzzy factors. There exist $m$ supply points with flexible supply quantity and $n$ demand points with flexible demand quantity. For each supply-demand point pair, the transportation time is an independent positive random variable according to a normal distribution. Satisfaction degrees about the supply and demand quantity are attached to each supply and each demand point, respectively. They are denoted by membership functions of corresponding fuzzy sets. Under the above setting, we seek a transportation pattern minimizing the transportation time target subject to a chance constraint and maximizing the minimal satisfaction degree among all supply and demand points. Since usually there exists no transportation pattern optimizing two objectives simultaneously, we propose an algorithm to find some non-dominated transportation patterns after defining non-domination. We then give the validity and time complexity of the algorithm. Finally, a numerical example is presented to demonstrate how our algorithm runs.
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机译:摘要:我们考虑具有随机和模糊因素的以下瓶颈运输问题。存在具有灵活供应数量的$ m $供应点和具有灵活需求数量的$ n $需求点。对于每个供求点对,根据正态分布,运输时间是一个独立的正随机变量。对供给量和需求量的满意度分别附加到每个供给点和每个需求点。它们由相应模糊集的隶属函数表示。在上述设置下,我们寻求一种运输模式,该运输模式将受机会约束的运输时间目标最小化,并将所有供求点之间的最小满意度最大化。由于通常不存在同时优化两个目标的运输方式,因此我们提出了一种在定义非支配性之后找到一些非支配性运输方式的算法。然后,我们给出了算法的有效性和时间复杂度。最后,给出一个数值示例来说明我们的算法如何运行。
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