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A very convenient way to solve this problem is reducing it to a minimum flow problem, for which well-known efficient algorithms are available (Ciurea and Ciupalã, 2004).
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This paper deals with fuzzy quantities and relations in multi-objective minimum cost flow problem.
We mathematically formulate the energy optimization problem as a multi-commodity minimum cost flow problem, and prove its NP-hardness.
To solve the problem, we reformulate it as a minimum cost flow problem plus several bounded variables.
In this paper, we show how the problem can be modelled as a minimum cost flow problem with side constraints.
We model this problem as a novel application of the minimum cost flow problem and show the applicability of the model for different types of layouts and priorities.
The results demonstrate that this framework is effective and overcomes the limitations of the multi-objective stochastic minimum cost flow problem (which becomes intractable for large-scale instances).
Based on this reformulation, we show that the basis of the reformulated problem is closely related with the minimum cost flow problem and design a kind of network simplex method to get the integrated optimal solution of the problem.
An embedded structure can be transformed to a generalized minimum cost flow problem, which is used as a sub-problem in a column generation approach, to solve the linear relaxation of the mixed-integer program.
We specify our approaches for a minimum cost flow problem and a network capacity design problem, both of which involve chance constraints for bounding the risk of demand shortages.
The models are based on a minimum cost flow problem over a layered network following an underlying year-planning managerial approach, with multi-period decision dependency and in the presence of uncertainty.
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