In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to s...

In this paper, a capacitated vehicle routing problem with time windows (CVRPTW) is presented. In this work, a new idea for calculating the heuristic value to improve the performance of ant colony algorithms when solving capacitated vehicle routing problems with hard time windows is proposed. The performance of the model and the heuristic approach are evaluated by Solomon’s VRPTW benchmark probl...

We propose a novel algorithmic framework to solve an integrated planning and scheduling problem in supply chain management. This problem involves the integration of an inventory management problem and the vehicle routing problem with time windows, both of which are known to be NP-hard. Under this framework, algorithms that solve the underlying sub-problems collaborate rigorously yet in a comput...

time-dependent vehicle routing problem is one of the most applicable but least-studied variants of routing and scheduling problems. in this paper, a novel mathematical formulation of time-dependent vehicle routing problems with heterogeneous fleet, hard time widows and multiple depots, is proposed. to deal with the traffic congestions, we also considered that the vehicles are not forced to come...

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...