Mathematical model of structural and topological optimization of logistics networks

2021 ◽  
pp. 178
Author(s):  
Volodymyr Bezkorovainyi ◽  
Leonid Nefedov ◽  
Vladimir Russkin
Keyword(s):  
Mathematical Model ◽  
Optimization Problem ◽  
System Optimization ◽  
Topological Optimization ◽  
Distributed Objects ◽  
Topological Structures ◽  
Logistics Networks ◽  
Current State ◽  
Geographically Distributed ◽  
The Mathematical Model

The subject of research in the article is the topological structures of closed-loop logistics networks. The goal of the article is to increase the efficiency of centralized logistics networks by developing a mathematical model for a two-criteria problem of optimizing topological structures in the process of their reengineering. The article solves the following tasks: analysis of the current state of the problem of structural and topological optimization of logistics networks; formalization of the problem of optimization of logistics networks as geographically distributed objects; synthesis of objective functions of the mathematical model of a two-criterion optimization problem for centralized three-level topological structures of closed logistics networks at the reengineering stage; development of a system of constraints of the mathematical model of the problem of optimizing centralized three-level topological structures of closed logistics networks; a function for evaluating the overall utility of options based on the Kolmogorov-Gabor polynomial is offered. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: the analysis of the current state of the problem of system optimization of logistics networks, mathematical models and methods for its solution was carried out; formalization of the problem of structural and topological optimization of logistics networks as geographically distributed objects; a mathematical model of a two-criterion task of reengineering of three-level topological structures of logistics networks in terms of costs and efficiency with integrated points of production and processing has been developed (originality). Conclusions: Based on the results of the analysis of the problem of optimizing the topological structures of logistics systems, it has been established that the problems of direct and reverse logistics are still considered as conditionally independent, which does not allow obtaining effective global solutions. In the context of expanding the network of consumers, changes in delivery volumes, the introduction of environmental restrictions, it is proposed to reengineer the networks, which provides for their radical redesign. The formulated statement and the developed mathematical model of a two-criterion (in terms of cost and efficiency) optimization problem for three-level topological structures for combined production and processing points will increase the efficiency of logistics networks with reverse flows by reducing the cost of reengineering (practical value).

scholarly journals OPTIMIZATION OF TOPOLOGICAL STRUCTURES OF CENTRALIZED LOGISTICS NETWORKS IN THE PROCESS OF REENGINEERING

2021 ◽  
pp. 23-31
Author(s):  
Vladimir Beskorovainyi ◽  
Antonii Sudik
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Time Complexity ◽  
Large Scale ◽  
System Optimization ◽  
Distributed Objects ◽  
Computational Point ◽  
Topological Structures ◽  
Logistics Networks ◽  
Current State

The subject of research in the article is the topological structures of closed logistics networks. The purpose of the work is to create a mathematical model and methods for solving problems of optimization of topological structures of centralized logistics networks in the process of reengineering, taking into account many topological and functional constraints. The article solves the following tasks: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; formalization of the problem of system optimization of logistics networks as territorially distributed objects; development of a mathematical model of the problem of optimization of centralized three-level topological structures of logistics networks at the stage of reengineering; development of a method for solving the problem of optimization of centralized three-level topological structures of logistics networks at the reengineering stage; estimation of time complexity of the method of optimization of centralized three-level topological structures of logistics networks. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; the problem of system optimization of logistics networks as territorially distributed objects has been formalized; developed a mathematical model of the problem of reengineering three-level topological structures of logistics networks in terms of cost and efficiency for the case of combined production and processing points; methods of directed search of variants of construction of a logistic network which use procedures of coordinate optimization and modeling of evolution on the basis of genetic algorithm are developed; estimates of the accuracy and time complexity of optimization methods of centralized three-level topological structures of logistics networks are obtained. Conclusions: Based on the results of the study of methods for solving the problem, an approximation of their accuracy and time complexity was performed. In practice, this will allow you to choose a more efficient method for solving large-scale practical problems, based on the required accuracy, available computing and time resources. The method based on the coordinate optimization procedure has a significantly higher accuracy, but it is more complex from a computational point of view. The accuracy of the evolutionary method based on a genetic algorithm can be increased by increasing the number of iterations. The practical use of the proposed mathematical model and methods of reengineering the topological structures of centralized closed logistics systems by jointly solving problems for direct and reverse flows will reduce the cost of transport activities of companies. Keywords: closed logistics; logistics network; optimization; reengineering; structure; topology.

scholarly journals Introducing a Conditional Ghost Correction Into the Vector Method

1984 ◽  
Vol 6 (2) ◽  
pp. 117-123 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Mathematical Model ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Linear Equations ◽  
Singular System ◽  
Orientation Distribution ◽  
Mathematical Approach ◽  
System Of Linear Equations ◽  
Vector Method ◽  
The Mathematical Model

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

Multi-Objective Optimization Design of Screw Conveyor Using Genetic Algorithm

2013 ◽  
Vol 732-733 ◽  
pp. 402-406
Author(s):  
Duan Yi Wang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Optimization Design ◽  
Optimization Problem ◽  
Machine Design ◽  
Screw Conveyor ◽  
Optimized Design ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
The Mathematical Model

The weight minimum and drive efficiency maxima1 of screw conveyor were considered as double optimizing objects in this paper. The mathematical model of the screw conveyor has been established based on the theory of the machine design, and the genetic algorithm was adopted to solving the multi-objective optimization problem. The results show that the mass of spiral shaft reduces 13.6 percent, and the drive efficiency increases 6.4 percent because of the optimal design based on genetic algorithm. The genetic algorithm application on the screw conveyor optimized design can provided the basis for designing the screw conveyor.

Research on Multi-Objective Transmission Planning in Electricity Markets

2012 ◽  
Vol 516-517 ◽  
pp. 1429-1432
Author(s):  
Yang Liu ◽  
Xu Liu ◽  
Feng Xian Cui ◽  
Liang Gao
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Genetic Algorithms ◽  
Electricity Markets ◽  
Optimization Problem ◽  
Nsga Ii ◽  
Transmission Planning ◽  
Multi Objective ◽  
Complex Optimization ◽  
The Mathematical Model

Abstract. Transmission planning is a complex optimization problem with multiple deciding variables and restrictions. The mathematical model is non-linear, discrete, multi-objective and dynamic. It becomes complicated as the system grows. So the algorithm adopted affects the results of planning directly. In this paper, a fast non-dominated sorting genetic algorithm (NSGA-II) is employed. The results indicate that NSGA-II has some advantages compared to the traditional genetic algorithms. In transmission planning, NSGA-II is feasible, flexible and effective.

CURRENT STATE AND PROBLEMS CONCERNING LOCALISATION TECHNOLOGIES OF OIL PIPELINES FOR THEIRS REPAIR WITH TERMINATION OF OPERATING

2018 ◽  
pp. 170-178
Author(s):  
Y. G. Melnychenko ◽  
G. G. Melnychenko ◽  
T. Y. Dodyk
Keyword(s):  
Mathematical Model ◽  
Critical Analysis ◽  
Transient Flow ◽  
Flow Calculation ◽  
Oil Pipeline ◽  
Current Technology ◽  
Advantages And Disadvantages ◽  
Current State ◽  
Oil Pipelines ◽  
The Mathematical Model

The critical analysis of current technology of onshore oil pipeline sections releasing from product for theirs repair are undertaken. Its shortcomings are established. The overview of modern plugging devices for oil pipelines sections localization while being repaired is provided, in particular the advantages and disadvantages of each considered one were analyzed. On the basis of this review an optimal plugging pig construction for oil pipeline sections isolation is proposed.The advantages and disadvantages of the proposed device are given. The necessity of simulation of plugging pigs motion in the pipeline is proved. The mathematical model of the plugging device movement along the main oil pipelines is formulated. The methodology of transient flow calculation during plugging pigs motion and stopping in the oil pipeline was proposed.

scholarly journals Shakedown of Composite Frames Taking into Account Plastic and Brittle Fracture of Elements

2015 ◽  
Vol 15 (4) ◽  
pp. 5-21 ◽  
Author(s):  
Piotr Alawdin ◽  
George Bulanov
Keyword(s):  
Mathematical Model ◽  
Cyclic Loading ◽  
Brittle Fracture ◽  
Optimization Problem ◽  
Shakedown Analysis ◽  
Composite Frames ◽  
Composite Frame ◽  
Plane Frames ◽  
Low Cyclic Loading ◽  
The Mathematical Model

abstract In the paper the mathematical model of the optimization problem of limit and shakedown analysis for composite plane frames, containing elastic-plastic and brittle elements under low-cyclic loading, is proposed. It is assumed that the load varies randomly within the specified domain, and limited plastic redistribution of forces in such structures occurs. An example of the shakedown analyses of the composite frame is given.

scholarly journals OPTIMIZATION OF UNIT LOAD FORMATION TAKING INTO ACCOUNT THE MASS OF PACKAGING UNITS

2014 ◽  
Vol 32 (4) ◽  
pp. 73-80
Author(s):  
Kamil Popiela ◽  
Mariusz Wasiak
Keyword(s):  
Mathematical Model ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Vertical Axis ◽  
Unit Load ◽  
Unit Formation ◽  
Proposed Model ◽  
Axis Rotation ◽  
The Mathematical Model

This article presents a mathematical formulation of the optimization problem of loading unit formation taking into account the mass of packaging units. Proposed model can be applied to optimize the arrangement of non-uniform cubical loading units in loading spaces. The model ensures possibility of defining various dimensions, masses, resistances of particular packaging units and their vertical axis rotation. Within the constraints of formulating optimization problem, taking into account masses and resistances ensures that all packaging units will rest on a pallet or on other packaging units, and the surface of contact between loading units guarantees stability of units arranged in subsequent layers. The mathematical model was verified. The paper provides an appropriate calculation example.

scholarly journals Design of State Rail and Bus Transportation Scheme with Bi-Level Optimization Model

2017 ◽  
Vol 15 (4) ◽  
pp. 2-9 ◽  
Author(s):  
K. Pavlova ◽  
T. Stoilov
Keyword(s):  
Mathematical Model ◽  
Optimization Model ◽  
Optimization Problem ◽  
Transportation Network ◽  
Rail Transport ◽  
Maximal Flow ◽  
Passenger Transport ◽  
The Mathematical Model ◽  
Transportation Route ◽  
Bus Transportation

Abstract The increase of the rail public transportations is searched in directions for redistribution of the passenger travels between rail and bus transportation. The rail transport benefits by increasing it schedule for places where the transportation capacities on appropriate directions is not achieved. A mathematical model has been derived to assess the potential of the rail passenger transport to increase his capacity and efficiency. This potential has been evaluate in comparison with the competition of the bus transportation. A specific transportation route has been chosen from Sofia to Varna and the potential for increase of the rail transport has been evaluated. The mathematical model uses bi-level optimization problem, related to the evaluation of a maximal flow in a transportation network.

scholarly journals Development of the mathematical model of the problem of reengineering topological structures of large-scale monitoring systems

2015 ◽  
Vol 4 (4(76)) ◽  
pp. 49
Author(s):  
Владимир Валентинович Бескоровайный ◽  
Ксения Евгеньевна Подоляка
Keyword(s):  
Mathematical Model ◽  
Large Scale ◽  
Monitoring Systems ◽  
Topological Structures ◽  
The Mathematical Model
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