Journal of Mathematical Sciences: Advances and ApplicationsAuthor'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
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.
minimum cost flow, combinatorial optimization, time-varying, time-windows.
