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A Parametric Approach to the Bi-criteria Minimum Cost Dynamic Flow Problem
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Open Journal of Discrete Mathematics·Volume 01 (2011)·Pages 116–126·Published 28 October 2011·DOI10.4236/ojdm.2011.13015
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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.
KeywordsDynamic NetworkParametric CostBi-Criteria Minimum Cost FlowSuccessive Shortest Path
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