Transportation planning has been established as a key topic in the literature and practices of social production, especially urban contexts. To consider traffic environment factors, more researchers are taking time-varying factors into account when scheduling their logistic activities. The time-dependent vehicle routing problem (TDVRP) is an extension classical Vehicle Routing Problem with Time...

This paper provides a review of the recent developments that had a major impact on the current state-ofthe-art exact algorithms for the vehicle routing problem (VRP). The paper reviews mathematical formulations, relaxations and recent exact methods for two of the most important variants of the VRP: the capacitated VRP (CVRP) and the VRP with time windows (VRPTW). The paper also reports a compar...

Vehicle routing problem with time windows (VRPTW) is a special kind of vehicle adding constraints and has variety applications in logistics. Many researchers have attacked the VRPTW by approximate solutions. Ant colony optimization (ACO) classical method to solve but are not used consider customer selection. Most ACO-based algorithms can suffer from complexity such as trapping local optimum. In...

Given a fleet of vehicles assigned to a single depot, the vehicle routing problem with time windows (vrptw) consists of determining a set of feasible vehicle routes to deliver goods to a set of customers while minimizing, first, the number of vehicles used and, second, total distance traveled. A large number of heuristic approaches for the vrptw have been proposed in the literature. In this pap...

 The Shortest-path problem with timewindows and capacity constraints (SPPTWCC) is a problem used for solving vehicle-routing and crewscheduling applications. The SPPTWCC occurs as a sub-problem used to implicitly generate the set of all feasible routes and schedules in the columngeneration formulation of the vehicle routing problem with time windows (VRPTW) and its variations. The problem is ...

This study has extended a vehicle routing problem, with time-windows (VRPTW), by considering the randomness of the perishable food delivery process, and constructing a SVRPTWmodel, to obtain optimal delivery routes, loads, fleet dispatching and departure times for delivering perishable food from a distribution center. Our objective was to minimize not only the fixed costs for dispatching vehicl...

In this paper, two different heuristics for the vehicle routing problem with time windows (VRPTW) are presented: the Sequential Insertion Heuristic and the Cluster and Sequential Insertion Heuristic. Both are based on the Lagrangian relaxation of the constraints which require each customer to be serviced exactly once. They were evaluated based on the classical six test problem sets described in...

We present a hybrid search technique based on metaheuristics for approximately solving the vehicle routing problem with time windows (VRPTW). The approach is two phased; a global customer clustering phase based on genetic algorithms (GAs) and a post-optimization local search technique based on tabu search (TS). We also devise a new crossover operator for the VRPTW and compare its performance wi...