Geodesic
Stochastic bottleneck transportation problem with flexible supply and demand quantity
Kybernetika, Tome 47 (2011) no. 4, pp. 560-571.

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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.
Classification : 68Q25, 90C15, 90C35, 90C70
Keywords: bottleneck transportation; random transportation time; flexible supply and demand quantity; non-dominated transportation pattern 
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     author = {Ge, Yue and Ishii, Hiroaki},
     title = {Stochastic bottleneck transportation problem with flexible supply and demand quantity},
     journal = {Kybernetika},
     pages = {560--571},
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     volume = {47},
     number = {4},
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     zbl = {1228.90136},
     language = {en},
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Ge, Yue; Ishii, Hiroaki. Stochastic bottleneck transportation problem with flexible supply and demand quantity. Kybernetika, Tome 47 (2011) no. 4, pp. 560-571. http://geodesic.mathdoc.fr/item/KYB_2011__47_4_a4/