In this paper, we present a review with some limited of exacts, heuristics and metaheuristics methods for the vehicle routing problem time windows (VRPTW). Over the past 20 years vehicle routing problem with time windows has been an area of research that has attracted many researchers. In this period a number of papers have been published on the exact, heuristics and metaheursitics methods of the routing problem with time windows. This problem has model character in many branches of mathematics, computer science, and operations research. Metaheuristics support managers in decision-making with robust that provide high-quality solutions to important applications in business, engineering, economic and science in reasonable time horizons.

In this paper, we present a new algorithm of the time-dependent shortest path problem with time windows. Give a directed graph ( )

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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 ρ satisfies a time-varying and time-windows constraint with the minimum cost of