Volume no :55, Issue no: 1, January (2019)

AN ALGORITHM OF A MINIMUM COST FLOW PROBLEM WITH TIME-VARYING AND TIME-WINDOWS

Author's: Nasser A. El-Sherbeny
Pages: [1] - [20]
Received Date: April 2, 2018; Revised April 14, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121950

Abstract

The Minimum Cost Flow Problem (MCFP) is a logical and distribution problem which is one of the classical combinatorial optimization and an NP-hard problem. We propose a new version of a MCFP, this version is a Minimum Cost Flow Problem on a Time-Varying and Time-Windows (MCFPTVTW). A mathematical model of the MCFPTVTW is presented. The objective is to find an optimal schedule to send a flow from the source vertex s to it’s the sink vertex satisfies a time-varying and time-windows constraint with the minimum cost of the arc and a minimum waiting times at vertices subject to the constraint that the flow must arrive at the sink vertex with time Finally, an algorithm of the MCFPTVTW is presented.

Keywords

minimum cost flow, combinatorial optimization, time-varying, time-windows.