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In this paper, we present a new algorithm of the time-dependent shortest path problem with time windows. Give a directed graph , where V is a set of nodes, E is a set of edges with a non-negative transit-time function . For each node , a time window within which the node may be visited and , is non-negative of the service and leaving time of the node. A source node s, a destination node d and a departure time t0, the time-dependent shortest path problem with time windows asks to find an s, d-path that leaves a source node s at a departure time t0; and minimizes the total arrival time at a destination node d. This formulation generalizes the classical shortest path problem in which ce are constants. Our algorithm of the time windows gave the generalization of the ALT algorithm and A* algorithm for the classical problem according to Goldberg and Harrelson [1], Dreyfus [2] and Hart et al. [3].

The Vehicle Routing Problem (VRP) is a well-known combinatorial optimization problem. The classical definitions of vehicle routing problems often lack handling of uncertain parameters and flexibility of constraints. The most popular approaches to these aspects involve probability distributions for uncertainty and penalty-based goal function for flexibility. In this paper a different approach is proposed which involves fuzzy sets framework, modeling both imprecision and flexibility, and analyzing practical solution approaches for VRP with uncertain information. Several variants of the basic problem and fuzzy optimization problem formulations are described. The fuzzy VRP is obtained when some of the elements in the formulation are fuzzy. The main versions of VRP that have appeared in the literature are reviewed and the standard approaches for solving the corresponding models are described.

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.