Article citationsMore>>

N. Kamiyama, A. Takizawa, N. Katoh and Y. Kawabata, “Evaluation of Capacities of Refuges in Urban Areas by Using Dynamic Network Flows,” Proceedings of the Eighth International Symposium on Operations Research and Its Applications, ORSC & APORC, Zhangjiajie, China, 2009, pp. 453-460.

has been cited by the following article:

• 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.