TITLE:
A Parametric Approach to the Bi-criteria Minimum Cost Dynamic Flow Problem
AUTHORS:
Mircea Parpalea
KEYWORDS:
Dynamic Network, Parametric Cost, Bi-Criteria Minimum Cost Flow, Successive Shortest Path
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.1 No.3,
October
17,
2011
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.