scholarly journals MATHEMATICAL MODELS OF DECISION SUPPORT IN THE PROBLEMS OF LOGISTICS NETWORKS OPTIMIZATION

2021 ◽  
pp. 5-14
Author(s):  
Vladimir Beskorovainyi ◽  
Oksana Draz
Keyword(s):  
Mathematical Model ◽  
Decision Support ◽  
Mathematical Models ◽  
General Problem ◽  
Network Optimization ◽  
Optimization Problems ◽  
Final Choice ◽  
Logistics Networks ◽  
Current State

The subject of research in the article is the process of decision support in the problems of logistics networks optimization. The goal of the work is to develop a set of mathematical models of logistics network optimization problems to increase the efficiency of decision support systems by coordinating the interaction between automatic and interactive procedures of computer-aided design systems. The following tasks are solved in the article: review and analysis of the current state of the problem of decision support in the problems of logistics networks optimization; decomposition of the problem of decision support for the optimization of logistics networks; development of a mathematical model of the general problem of network optimization in terms of economy, efficiency, reliability and survivability; development of a set of technological mathematical models for the correct reduction of many effective options for building logistics networks for the final choice, taking into account difficult to formalize factors, knowledge and experience of the decision maker (DM). The following methods are used: systems theory, utility theory, optimization and operations research. Results. Analysis of the current state of the problem of logistics networks optimization has established the existence of the problem of correct reduction of a subset of effective options for their construction for ranking, taking into account difficult to formalize factors, as well as knowledge and experience of DM. The decomposition of the problem into tasks is performed: definition of the principles of network construction; network structure selection; determination of the topology of network elements; choice of network operation technology; determination of parameters of elements and communications (means of cargo delivery); multi criteria evaluation and selection of the best option for building a network. A mathematical model of the general problem of network optimization in terms of economy, efficiency, reliability and survivability is proposed. To coordinate the interaction between automatic and interactive network optimization procedures, it is proposed to use a combined method of ranking options, which allows you to identify and correctly reduce the subset of effective options for ranking DM. To implement the method, mathematical models of problems of the procedure of ranking options in the technologies of project decision support have been developed, which allow to combine the advantages of the technologies of the ordinalistic and cardinalistic approaches. Conclusions. The developed set of mathematical models expands the methodological bases of automation of processes of support of multi criteria decisions on optimization of logistic networks, allows to carry out correct reduction of set of effective options of their construction for the final choice taking into account factors, knowledge and experience of DM. The practical use of the proposed models and procedures will reduce the time and capacity complexity of decision support technologies, and through the use of the proposed selection procedures - to improve their quality across a variety of functional and cost indicators.

scholarly journals Determination of intersecting curve between two surfaces of revolution with parallel axes by use of auxiliary planes and auxiliary spheres

2002 ◽  
Vol 2 (4) ◽  
pp. 267-272
Author(s):  
Ratko Obradovic
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Coordinate System ◽  
Surfaces Of Revolution ◽  
Surface Of Revolution ◽  
First Case ◽  
Intersecting Curve

In this paper the space intersecting curve between two surfaces of revolution with parallel axes of surfaces have been determined. Two mathematical models for determination of intersecting curve between two surfaces of revolution have been formed: auxiliary planes have been used in the first mathematical model and auxiliary spheres have been used in the second model (Obradovic 2000). In the first case each auxiliary plane intersected with each surface of revolution on circle and two points of intersecting curve are obtained as intersecting points between these two circles. In the second case centres of two locks of auxiliary spheres are put on axes of surfaces of revolution (centre of first lock is on axis of the first surface of revolution and centre of second lock is on axis of the second surface of revolution) on saine z coordinate (when axes of surfaces of revolution are parallel with z axis of coordinate system). First lock sphere intersects the first surface of revolution on w1 parallels and second lock corresponding sphere intersects the second surface of revolution on w2 circles. It is possible to find a relationship that for selected radius of the first lock sphere can determine the radius of second lock sphere and real points of intersecting curve have been determined by use of these two spheres. The points of intersecting curve between two surfaces of revolution are obtained by intersection between w1 circles from the first surface with w2 circles from the second surface (Obradovic 2000).

A Mathematical Model to Describe the Inner Contour of Moineau Stators

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Ekrem Oezkaya ◽  
Moritz Fuss ◽  
Dirk Biermann
Keyword(s):  
Mathematical Model ◽  
Machining Process ◽  
Hole Drilling ◽  
Deep Hole ◽  
Deep Hole Drilling ◽  
Hole Drilling Method ◽  
Current State ◽  
Drilling Method ◽  
Large Length

Abstract Bore holes with a large length to diameter ratio of up to l/d = 100 are typically produced using the single-tube deep hole drilling method also named BTA (Boring and Trepanning Association) deep hole drilling method. However, there are various technical applications requiring deep, complex, epitrochoid-similar and helical inner contours, such as stators used in Moineau motors and pumps. According to the current state of the art, epitrochoid-similar contours for small diameters with large drilling depths can only be produced using a special machining process which is referred to a chamber-boring process. In this paper, a developed mathematical model will be presented that describes the epitrochoid-similar contour exactly. This allows the determination of the position-dependent speed and acceleration of the tool, which are necessary for designing the joints and components of the tool system. In addition, this mathematical model can be used for a subsequent Laplace-transformation, so that could be used for a further optimization of the process dynamic in the future.

Introduction

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Batch Process ◽  
Mixed Integer ◽  
Optimization Models ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Location Allocation ◽  
Primary Focus

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. A plethora of applications in all areas of science and engineering employ mathematical models. A mathematical model of a system is a set of mathematical relationships (e.g., equalities, inequalities, logical conditions) which represent an abstraction of the real world system under consideration. Mathematical models can be developed using (i) fundamental approaches, (ii) empirical methods, and (iii) methods based on analogy. In (i), accepted theories of sciences are used to derive the equations (e.g., Newton’s Law). In (ii), input-output data are employed in tandem with statistical analysis principles so as to generate empirical or “black box” models. In (iii), analogy is employed in determining the essential features of the system of interest by studying a similar, well understood system. The variables can take different values and their specifications define different states of the system. They can be continuous, integer, or a mixed set of continuous and integer. The parameters are fixed to one or multiple specific values, and each fixation defines a different model. The constants are fixed quantities by the model statement. The mathematical model relations can be classified as equalities, inequalities, and logical conditions. The model equalities are usually composed of mass balances, energy balances, equilibrium relations, physical property calculations, and engineering design relations which describe the physical phenomena of the system. The model inequalities often consist of allowable operating regimes, specifications on qualities, feasibility of heat and mass transfer, performance requirements, and bounds on availabilities and demands. The logical conditions provide the connection between the continuous and integer variables.

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 OPTIMIZATION PROBLEMS OF MATHEMATICAL MODELLING OF A BUILDING AS A UNIFIED HEAT AND POWER SYSTEM

2020 ◽  
Vol 16 (1) ◽  
pp. 156-161
Author(s):  
Yuri Tabunshchikov ◽  
Marianna Brodach
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Energy System ◽  
Heat Energy ◽  
Objective Functions ◽  
Outdoor Climate ◽  
Energy Flows ◽  
The Mathematical Model ◽  
The Pontryagin Maximum Principle

The mathematical model of a building as a single heat energy system by the decomposition method is represented by three interconnected mathematical models: the first is a mathematical model of the energy interaction of a building’s shell with an outdoor climate; the second is a mathematical model of energy flows through the shell of a building; the third is a mathematical model of optimal control of energy consumption to ensure the required microclimate. Optimization problems for three mathematical models with objective functions are formulated. Methods for solving these problems are determined on the basis of the calculus of variations and the Pontryagin maximum principle. A method for assessing the skill of an architect and engineer in the design of a building as a single heat energy system is proposed.

scholarly journals Some insights into an integrative mathematical model: a prototype-model for bodyweight and energy homeostasis

2016 ◽  
Vol 7 (3) ◽  
pp. 1271
Author(s):  
Jorge Guerra Pires
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Literature Review ◽  
Differential Equations ◽  
Mathematical Models ◽  
Quantitative Methods ◽  
Energy Homeostasis ◽  
State Of The Art ◽  
Prototype Model ◽  
Current State

The ambition of this document is to set in evidence the prerequisite for integrative (mathematical) models, mechanism-based models, for appetite/bodyweight control. For achieving this goal, it is provided a scrutinized literature review and it is organized them in such a way to make the point. The quantitative methods exploited by the authors are called differential equations solved numerically; they are discussed briefly since it is not our goal herein to handle details. On the current state of the art, there is no mathematical model to the best of the author’s knowledge targeting at integrating several hormones at once in mathematical descriptions: even for single hormones, the literature is either occasional or do not exist at all; it is depicted some results for simple models already built. As it can be seen, the functions and roles seem fuzzy, most hormones seem to be piloting the same undertaking. The key challenge from a mathematical modeling perspective is how to separate properly the mechanisms of each hormone. The kind of pursuit presented herein could initiate an imperative cascade of mathematical modeling applied to metabolism of bodyweight control and energy homeostasis.

scholarly journals The Mathematical Modeling of Ca And Fe Distribution In Peat Layers

2015 ◽  
Vol 2 ◽  
pp. 40
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis ◽  
Aigars Gedroics
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Trace Elements ◽  
Mathematical Models ◽  
Organic Material ◽  
Low Concentrations ◽  
The Mathematical Model ◽  
Research Show

Bogs have been formed by an accumulation of peat - a light brown-to-black organic material, built up from partial decomposition of mosses and other bryophytes, sedges, grasses, shrubs, or trees under waterlogged conditions. The total peatlands area in Latvia covers 698 918 ha or 10.7% of the entire territory. Knowledge’s of peat metals content are important for any kind of peat using. Experimental determination of metals in peat is very long and expensive work. Using experimental data mathematical model for calculation of concentrations of metals in different points for different layers can help to very easy and fast to find approximately concentration of metals or trace elements. The results of the research show that concentrations of trace elements in peat are generally low. Concentrations differ between the superficial, middle and bottom peat layers, but the significance decreases depending on the type of mire. The mathematical model for calculation of concentration of metals in different points for different 3 layers in peat blocks is developed. As an example, mathematical models for calculation of Ca and Fe concentrations have been analyzed.

scholarly journals DEVELOPMENT OF A DECISION SUPPORT SYSTEM (DSS) BASED ON MATHEMATICAL MODELS OF SOCIODYNAMICS

2018 ◽  
Vol 64 ◽  
Author(s):  
A.A. Pravda ◽  
T.V. Selivyostrova
Keyword(s):  
Mathematical Model ◽  
Decision Support ◽  
Decision Support System ◽  
Mathematical Models ◽  
Support System ◽  
Analysis Method ◽  
Hierarchy Analysis ◽  
Labor Resources

Development of DSS that reproduces the decision on the migration of the Ukrainian citizen abroad. Solves the problem of choosing a migrant between several countries with the help of a mathematical model of multi-criteria choice. The model is based on the algorithm of the hierarchy analysis method. The DSS forecasts the volume of migration, and provides monitoring of the volume of labor resources in Ukraine. The results of the DSS are provided in analytical and graphical forms.

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 Mathematical aspects of nutrition systems projecting for dietary therapy

2017 ◽  
Vol 11 (1) ◽  
Author(s):  
G. Krutovyi ◽  
A. Zaparenko ◽  
A. Borysova
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Calcium Deficiency ◽  
Dietary Therapy ◽  
The Creation ◽  
Prevention And Therapy ◽  
Content Optimization

The mathematical toolkit created and used for the design of durable nutrition systems aimed at the prevention and therapy of the diseases caused by calcium deficiency is analyzed. In particular, these are: the complex of mathematical models of the expendable diets and methods of the ingredients content optimization in them, mathematical model of daily diets optimization, and formalizationed method of fast and light determination of a diet’s biological value.The ways for the improvement of the developed mathematical toolkit aimed at the creation of the nutrition systems with higher level of both nutrients balance and provision of daily needs in them on the basis of using unconventional floury products enriched with the deficient nutrients, functionals for balancing the connected groups of nutrients are determined, as well as the introduction of aggregated restrictions on these groups of nutrients to the models (both products and rations).

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