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Uncertain minimum cost multicommodity flow problem

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Abstract

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.

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Acknowledgments

The research was supported by the National Natural Science Foundation of China Grants (Nos. U1404701, U1304706 and 61273044), the State Key Laboratory of Rail Traffic Control and Safety (No. RCS2014ZT22), the Fundamental Research Funds for the Central Universities (No. 2014RC038) and the Soft Science Research Program of Henan Province (No. 152400410447).

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  1. School of Management, Henan University of Technology, Zhengzhou, 450001, China

    Sibo Ding

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  1. Sibo Ding
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Correspondence to Sibo Ding.

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The authors declare that they have no potential conflict of interest to this work.

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Communicated by V. Loia.

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Ding, S. Uncertain minimum cost multicommodity flow problem. Soft Comput 21, 223–231 (2017). https://doi.org/10.1007/s00500-015-1871-6

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