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.
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.