MAGAZINE  №5 (94) October 2019


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



 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.



 Electronic version

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


MAGAZINE  №4 (93) August 2019


Valeyev R.S.

Valeyeva A.F.

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

CATEGORY Analytics and reviews Optimization and mathematical modelling



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.

 Electronic version


Published in Analytics and reviews

MAGAZINE  №2 (91) April 2019


REMPEL W. - M. Sc., Research Associate, University of Applied Sciences (Cologne, Germany)

ZOLLER C.S. - Dr.-Ing., Professor University of Applied Sciences (Germany, Cologne) 

CATEGORY Transportation in logistics Production logistics Optimization and mathematical modelling


In-house material supply is one of the core factors for the flexibility and efficiency of manufacturing companies. This paper describes a procedure for planning and optimising tugger train systems for material supply. For this purpose a vehicle routing problem is developed, which should minimize the replenishment lead-time of the entire system by defining the routes and assigning the tugger trains. The paper describes the application of the heuristic model under different decision possibilities of the system design. The model offers the possibility to select different trip strategies, demand signal types, and afterwards optimise tugger train systems with a desired number of vehicles. Thus, the model optimises the performance of tugger train systems according to the individual requirements and objectives of a company.

 Electronic version


Published in Production logistics


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