in this paper we address the vrpcd, in which a set of homogeneous vehicles are used to transport products from the suppliers to customers via a cross-dock. the products can be consolidated at the cross-dock but cannot be stored for very long as the cross-dock does not have long-term inventory-holding capabilities. the objective of the vrpcd is to minimize the total traveled distance while respe...

centralizing and using proper transportation facilities cut down costs and traffic. hub facilities concentrate on flows to cause economic advantage of scale and multimodal transportation helps use the advantage of another transporter. a distinctive feature of this paper is proposing a new mathematical formulation for a three-stage p-hub location routing problem with simultaneous pick-ups and de...

In recent years, great efforts have been made to reduce greenhouse gas emissions by vehicles. Petroleum products produces greenhouse gas emissions, therefore reducing the use of these products can make a major contribution to reducing pollution. The Fleet Size and Mix Vehicle Routing Problem is one of the most widely used routing branches. In this problem, there are vehicle with different capac...

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...

The vehicle routing problem with the capacity constraints was considered in this paper. It is quite difficult to achieve an optimal solution with traditional optimization methods by reason of the high computational complexity for large-scale problems. Consequently, new heuristic or metaheuristic approaches have been developed to solve this problem. In this paper, we constructed a new heuristic ...

In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods...

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