Abstract
Vehicle routing problem and traveling salesman problem are classical problems in operational research; this modification of those problems consists of a transport among nodes of the communication network using cyclical routes of vehicles with a given capacity. A transportation demand is given by the place of pickup, the place of delivery and quantity of goods. The goal is to find cyclical routes of a minimal length which ensure the transport requirements. In the paper there are two models proposed for the problem, both are demonstrated on an example. The problem is based on a case study from practice.
Highlights
Traveling salesman problem and vehicle routing problem and their modifications are frequently solved practical examples
The column generation method is used for selecting routes in the mathematical model
The following variables are defined in the model: yij Ն 0, integer – number of vehicles going through the arc (i, j) in the direction from i to j (i, j ϭ 0, 1, ..., nϩ1, i j), xikjlՆ 0, amount of goods transported from the node i to the node j (i, j ϭ 0, 1, ..., nϩ1, i j; k, l ϭ 1, 2, ..., n, k l)
Summary
Traveling salesman problem and vehicle routing problem and their modifications are frequently solved practical examples In such problems the goal is to assure pick-up or/and delivery of goods in a distribution network. While in those applications it is necessary to find cyclical routes starting and ending in a depot, in the studied problem it is required to transport goods between nodes of the network. In the practice time windows are often given for each node in the network and the order of pickup and delivery processes has to be defined, because the goods being loaded as the last ones will be unloaded as the first ones. Let us consider the distribution network with 4 nodes; the distance matrix C and the transportation requirements matrix Q are given: R.
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