Methods for optimizing the delivery of goods to consumers by several vehicles

Freight transport is one of the most important sectors of the national economy. The increase in the efficiency of the logistics company is ensured by the accurate organization of supplies, as well as the timely delivery of goods to the points of the route. That is why there is a need to optimize the delivery of goods. A delivery task is a transport task of delivering oversized cargo from a distribution center to a multitude of recipients located in the area of operation of a transport company. It is a generalization of the well-known traveling salesman problem, from which it differs in the condition of the limited carrying capacity of the vehicle used and, as a consequence, the need to repeatedly return to the base to replenish the transported cargo. This article proposes to supplement the traditional formulation of the problem with the requirement to distribute customers among several simultaneously operating vehicles (TC) so that the maximum lead time is minimal. This takes into account not only the interests of the delivery contractor, but also the customers. The solution to the problem consists of two stages. On the first one, in some known way, rational ring routes for each vehicle are determined, minimizing the total mileage. Based on the results of the stage, the time for passing each route is calculated. At the second stage, the problem of reducing the maximum travel time of routes is solved by using several vehicles delivering at the same time. To do this, it is necessary to optimally distribute vehicles along individual routes. It is proposed to use the algorithm for solving the well-known problem "Packing items into containers" to solve this problem. This problem belongs to the class of NP-hard problems in the strong sense and does not have an exact solution algorithm for arbitrary input data. This paper proposes a complex solution method combining the well-known First fitted (FF) algorithm, the original First fitted with reordering (FFR) algorithm, and S. Martello's lower bounds and P. Thoth to control the optimality of the obtained solution. Test calculations have shown the effectiveness of this approach for a moderate dimension of the problem.