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Uncertain minimum cost multicommodity flow problem
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DOI：10.1007/s00500-015-1871-6.png)
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Abstract
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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 (, )-minimum cost multicommodity flow model is formulated. Some properties of the model are analyzed. An equivalence relationship between the (, )-minimum cost multicommodity flow and the minimum cost multicommodity flow is proved. Then, a global optimal algorithm is developed for finding the (, )-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.
Keywords:
Uncertainty theory
Uncertain programming
Uncertain variable
Minimum cost flow
Network optimization
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