Uncertain minimum cost multicommodity flow problem

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• 作者：Sibo Ding
• 关键词：Uncertainty theory ; Uncertain programming ; Uncertain variable ; Minimum cost flow ; Network optimization
• 刊名：Soft Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：21
• 期：1
• 页码：223-231
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1433-7479
• 卷排序：21

文摘

This paper investigates the minimum cost multicommodity flow problem with uncertain costs and uncertain capacities. Uncertainty theory is used to deal with indeterminacy factors in uncertain network. An (\(\alpha \), \(\beta \))-minimum cost multicommodity flow model is formulated. Some properties of the model are analyzed. An equivalence relationship between the (\(\alpha \), \(\beta \))-minimum cost multicommodity flow and the minimum cost multicommodity flow is proved. Then, a global optimal algorithm is developed for finding the (\(\alpha \), \(\beta \))-minimum cost multicommodity flow and the minimum cost multicommodity flow, and obtaining the uncertainty distribution of total shipping cost. Finally, two examples are presented to illustrate the algorithm.