Geodesic
Chance constrained bottleneck transportation problem with preference of routes
Kybernetika, Tome 48 (2012) no. 5, pp. 958-967.

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This paper considers a variant of the bottleneck transportation problem. For each supply-demand point pair, the transportation time is an independent random variable. Preference of each route is attached. Our model has two criteria, namely: minimize the transportation time target subject to a chance constraint and maximize the minimal preference among the used routes. Since usually a transportation pattern optimizing two objectives simultaneously does not exist, we define non-domination in this setting and propose an efficient algorithm to find some non-dominated transportation patterns. We then show the time complexity of the proposed algorithm. Finally, a numerical example is presented to illustrate how our algorithm works.
Classification : 68Q25, 90C15, 90C35, 90C70
Keywords: bottleneck transportation; random transportation time; chance constraint; preference of routes; non-domination 
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     author = {Ge, Yue and Chen, Minghao and Ishii, Hiroaki},
     title = {Chance constrained bottleneck transportation problem with preference of routes},
     journal = {Kybernetika},
     pages = {958--967},
     publisher = {mathdoc},
     volume = {48},
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     year = {2012},
     mrnumber = {3086862},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a8/}
}
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Ge, Yue; Chen, Minghao; Ishii, Hiroaki. Chance constrained bottleneck transportation problem with preference of routes. Kybernetika, Tome 48 (2012) no. 5, pp. 958-967. http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a8/