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# Algoritms for Applied Vehicle Routing Problem

Student: Sergey Grevtsov

Supervisor:

Educational Programme: Applied Mathematics and Information Science (Bachelor)

The vehicle routing problem (VRP) is a classical problem in logistics that aims to design minimum-cost delivery routes from a centralized depot. A special case of the VRP arises in situations in which the network has a tree structure (TVRP). Such tree networks may be found in rurals, rivers, near main highways and when the cost of road construction and maintenance is much more than the routing cost. The heuristic first creates individual vehicle routes for every tree leaf and then working with such routes trying to append them by previous nodes or by merging with other routes. When all existed routes faces with capacity restriction and can not be appended by any possible nodes, but not evrery tree node is served, new vehicle routes created for every not served node. Then trying to merge this new routes. To find way over tree used a breath-first search method. The algorithm works with routes in parallel to make them more balanced. There are shown two strategies to work with vehicle routes, both works in parallel. For iteration taken the route which not checked yet node is most far from the depot in compare with other routes. First one working with route before it is changed (added node/merged with another route) or filled (can not be changed). Second one working with route until route changed or changed it is meta information (checked and failed to add node or failed to merge route). The heuristic algorithm was implemented on randomly generated networks.

Full text (added May 28, 2018)

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