Vehicle Routing Problem with External Carrier

The Vehicle routing problem with private (internal) and common (external) carrier is a modification of classic logistic problem. The following contribution studies this problem, assuming that primary carrier secures transport to customers by utilizing its own vehicles, whose capacities and costs per 1 km of transport are given and is the same for all vehicles. Also, there is given the matrix of the shortest distances between nodes (depot and customers). On the other hand, external carrier's costs depend only on transported quantity measured by weight of goods or by the number of containers/pallets. External carrier's costs do not depend on the vehicle's type, traveled distance etc. A mathematical model designed in this article is reformulated to a VRP model, where the routes may not contain all nodes. As following, there is a description of the original heuristics, which can be modified differently and three of those modifications are suggested. The results of numerical experiments for tasks of various size are presented at the end of the article. There are results of three heuristic modifications as well as results of the model solution, which due to NP difficulty and size of tasks could not be completed (the calculation was interrupted or collapsed after some time).