**MAGAZINE №5 (94) October 2019**

**AUTHORS**** VALEEVA A.F., VALEEV R.S., GONCHAROVA Y.A.**

**CATEGORY **Optimization and mathematical modelling Transportation in logistics Industrial companies’ corporate logistics

**ABSTRACT**

** **Due to an increased volume of cargo transportations the development of the mathematical and software for resolving the routing problems is being actual, whereas the objective is costs reduсtion when cargo is delivered to customers. The problem of cargo's homogeneous delivery to various customers is considered in the paper, which is significant component in supply chain.

The mathematical model accounting such restrictions as a vehicle carrying capacity, the time windows, the planning horizon, a bunch of depots, the split delivery, a heterogeneous vehicle fleet, a possibility of backhauls, the quality and cost of roads, the type of roads, speed limits, as well as goods disposition within a vehicle during the construction of the rational delivery routes is represented. For the given NP-hard combinatorial optimization problem, the heuristic method on the basis of the ant colony algorithm based on population that allows to obtain the rational delivery routes for homogeneous goods with account of restrictions listed is developed.

Herewith, the results of the numerical experiments, which verify the efficiency of the proposed approach based on the developed software are presented.

**Keywords: **vehicle routing problem 3D Packing problem uniform load vehicle loading Ant colony optimization algorithm evolution algorithm

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**MAGAZINE №4 (93) August 2019**

**AUTHORS**** **

Goncharova Y.A. - Cand.of Tech.Sc., Software engineer, Research and Production Center «GeoTek» (Ufa, Russia)

**CATEGORY **Analytics and reviews Optimization and mathematical modelling

**ABSTRACT**

The paper reviews well-known routing problems (*Vehicle Routing Problem, VRP*), that are an essential part of the transport logistics. The mathematical models of various routing problems’ classes are given: with account to a transport vehicle’s carrying capacity (*TV*); with the time windows; with split delivery; with a given planning time horizon (periodic problem); with backhauls; with satellite facilities. Since the routing problems are the NP-hard objectives of combinatorial optimization, for the sake of their practical application in the sphere of the transportation management the various heuristic algorithms are being developed. The known metaheuristics are expounded in the paper that present the local search algorithms as well as constructive algorithms, namely, the genetic algorithm; the evolutionary strategies; the ant colony algorithms’ series; the alternating neighbourhood search algorithm. Herewith, the attention is paid to the solution coding and to some neighbourhood constructing solution operations. Since in practice the routing problems are closely connected with the goods disposition within the transport vehicles (the 3D packing problem), the approximate algorithms which provide obtaining the goods packing map are described. The given review of various routing problems’ classes and the effective methods of their solution aid in practical problems of the effective routes search for the goods delivery to various customers. So, Part 2 of the paper describes the mathematical model and the methods of one practical task resolving that is processed together with the 3D packing problem of goods inside car transport vehicles.

**Keywords: **

**MAGAZINE **№2 (64) April 2015

**AUTHOR **VALEYEVA A.F., VALEYEV R.S., TARASOVA T.D., GAZIZOVA E.I.

**CATEGORY **Optimization and economic-mathematical modeling Transportation Inventory Management Warehouse Logistics

In this paper we consider the problem of a homogeneous product delivery to various customers in connection with the objectives of inventory management, transportation, and warehousing. The mathematical model and the general scheme of an algorithm for the assigned problem solution are introduced. A particular attention is paid to the problem of inventory management. At the same time we propose to combine the various models of this problem into a single subsystem: deterministic, probabilistic and simulation, which is a modification of the well-known model.

**Keywords: **