Matrix method for the multi salesmen problem (TSP) with several vehicles

Despite the considerable progress made in a transport logistics research, an actual problem today is an optimization of time spends on search for optimal solution [1]. This article describes a method that can be used to simplify and solve the cargo routing problem with several vehicles. The method offers easier and faster solution compare to other known methods. The cargo routing problems are based on the classic traveling salesman problem (TSP). TSP is an NP-hard problem [2]. The task is to find a shortest possible route that visits each travel point exactly once with a return to the starting point given a list of points and their pairwise distances. Modern computer technology is widely used to solve this type of problems. However, practical matters require a more complex undertaking [3]. One of the variations of routing problem is a routing with several vehicles and various cargo limitations [4]. Linear and integer programming methods are often incompatible for this type of problems due to the complexity and vast volume of data processing. Approaches that can be used include an introduction of heuristic methods (hypotheses) [5], [6]. This technique leads to a decomposition of the problem [7]. This article discusses a procedure of division of the routing problem with several vehicles to a problem with one vehicle with matrix approach.