The vehicle routing problem with backhauls (VRPB) as an extension of the classical vehicle routing prob-lem (VRP) attempts to define a set of routes which services both linehaul customers whom product are to be delivered and backhaul customers whom goods need to be collected. A primary objective for the problem usually is minimizing the total distribution cost. Most real-life problems have othe...

In recent years, the size of combinatorial applications and the need to produce high-quality solutions quickly have increased steadily, providing significant challenges for optimization algorithms. This paper addresses this issue for large-scale vehicle routing problems with time windows, a class of very difficult optimization problems involving complex spatial and temporal dependencies. It pro...

Transportation in economic systems such as services, production and distribution enjoys a special and important position and provides a significant portion of the country's gross domestic product. Improvements in transportation system mean improvements in the traveling routes and the elimination of unnecessary distances in any system. The Vehicle Routing Problem (VRP) is one of the practical co...

In this paper we consider the Vehicle Routing Problem with Hard Time Windows and Stochastic Service Times (VRPHTWSST). We can describe the problem as follows. Consider a directed graph G = (V,A) where V = {0, 1, . . . , n} is the node set, and A = {(i, j) | i, j ∈ N} is the arc set. Node 0 represents a depot where a fleet of homogeneous vehicles is initially located and Vc = {1, . . . , n} is t...

A new model and solution for the energy minimizing vehicle routing problem with time windows (EVRPTW) and customers’ priority is presented in this paper. In this paper unlike prior attempts to minimize cost by minimizing overall traveling distance, the model also incorporates energy minimizing which meets the latest requirements of green logistics. This paper includes the vehicles load as an ad...