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A Parametric Approach to the Bi-criteria Minimum Cost Dynamic Flow Problem

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DOI: 10.4236/ojdm.2011.13015    2,806 Downloads   6,443 Views   Citations
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ABSTRACT

This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of minimum parametric cost flow problems with different objective functions. On each of the iterations, the flow is augmented along a cheapest path from the source node to the sink node in the time-space network avoiding the explicit time expansion of the network.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Parpalea, "A Parametric Approach to the Bi-criteria Minimum Cost Dynamic Flow Problem," Open Journal of Discrete Mathematics, Vol. 1 No. 3, 2011, pp. 116-126. doi: 10.4236/ojdm.2011.13015.

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