scholarly journals Multiobjective dynamic programming in bipolar multistage method

2021 ◽  
Author(s):  
Tadeusz Trzaskalik
Keyword(s):  
Dynamic Programming ◽  
Decision Processes ◽  
Reference Points ◽  
Multistage Process ◽  
Optimality Principle ◽  
Hierarchical Classes ◽  
Large Size ◽  
Optimality Equations ◽  
Sustainable Regional Development ◽  
The Given

AbstractThe multicriteria Bipolar method can be extended and used to control multicriteria, multistage decision processes. In this extension, at each stage of the given multistage process two sets of reference points are determined, constituting a reference system for the evaluation of stage alternatives. Multistage alternatives, which are compositions of stage alternatives, are assigned to one of six predefined hierarchical classes and then ranked. The aim of this paper is to show the possibility of finding the best multistage alternative, using Bellman’s optimality principle and optimality equations. Of particular importance is a theorem on the non-dominance of the best multistage alternative, proven here. The methodology proposed allows to avoid reviewing each multistage alternative, which is important in large-size problems. The method is illustrated by a numerical example and a brief description of the sustainable regional development problem. The problem can be solved by means of the proposed procedure.

scholarly journals Bipolar sorting and ranking of multistage alternatives

2021 ◽  
Author(s):  
Tadeusz Trzaskalik
Keyword(s):  
Reference System ◽  
Fixed Number ◽  
Decision Processes ◽  
Reference Points ◽  
Hierarchical Classes ◽  
Multicriteria Decision ◽  
Numerical Example

AbstractThe present paper proposes an extension of the multicriteria Bipolar method, introduced by E. Konarzewska-Gubała, and its application to the control of multistage, multicriteria decision processes with a fixed number of stages. At each stage, two sets of reference points are determined, which constitute a reference system for the evaluation of stage decisions. At the end of the process, multistage alternatives—compositions of stage alternatives—are evaluated. The procedure proposed, which includes elements of the Electre methodology, allows to assign each multistage alternative to one of the six predefined, hierarchical classes, and then to perform ranking within each class. The purpose of the paper is to present and substantiate the dynamic Bipolar procedure. An essential part of the paper is a numerical example which illustrates the notions and relationships introduced.

scholarly journals THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION

2019 ◽  
pp. 132-138 ◽  
Author(s):  
A. Tarasenko ◽  
I. Egorova
Keyword(s):  
Dynamic Programming ◽  
Nonlinear Programming ◽  
Optimal Solution ◽  
Optimal Distribution ◽  
Optimality Principle ◽  
Numerical Example ◽  
Maximum Profit ◽  
Cost Forecasting ◽  
Method Of Dynamic Programming ◽  
Minimum Costs

The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. The problem of optimal distribution of funds among enterprises for the expansion of production has been formulated, which would give the maximum total increase in output. The solution of the task has been presented in the case, when the number of enterprises is 3. It has been shown, that the Bellman optimality principle allows you solve applied problems of cost forecasting with obtaining the optimal solution-maximum profit at minimum costs.

An Introduction to Dynamic Programming

1961 ◽  
Vol 16 (04) ◽  
pp. 261-274
Author(s):  
Brian Gluss
Keyword(s):  
Dynamic Programming ◽  
Small Body ◽  
Decision Processes ◽  
Theory And Practice ◽  
Rand Corporation ◽  
The Past ◽  
Multi Stage ◽  
The Subject ◽  
New Research ◽  
General Mathematical Theory

Dynamic programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory.In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitledDynamic Programming[1], have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of [1]), and linear programming (chapter VI).

scholarly journals Effect of Inclusions on the Corrosion Properties of the Nickel-Based Alloys 718 and EP718

Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1177 ◽  
Author(s):  
Ekaterina Alekseeva ◽  
Andrey Karasev ◽  
Pär G. Jönsson ◽  
Aleksey Alkhimenko
Keyword(s):  
Corrosion Resistance ◽  
Alloy 718 ◽  
Corrosion Properties ◽  
Electrolytic Extraction ◽  
Operational Conditions ◽  
Large Size ◽  
Size Number ◽  
Resistance To Deformation ◽  
The Given ◽  
Harmful Effects

Inclusions in steels and alloys are known to lower the resistance to deformation, as well as to lower the mechanical, corrosion and other properties. Studies of inclusions in nickel-based alloys are important since these materials could suffer from corrosion degradation in harsh operational conditions. This, in fact, could lead to a pitting initiation around the inclusions. Two industrial Ni-based alloys (alloy 718 and EP718) were investigated to determine the harmful effects of different inclusions on the corrosion resistance of Ni-based alloys. Specifically, the inclusion characteristics (such as composition, morphology, size, number and location) were determined for inclusions collected on film filters after electrolytic extraction and dissolution of a metal matrix around different inclusions on surfaces of metal samples after electrolytic extraction (EE). It was found that both Ni-based alloys contain various inclusion types: carbides (large size NbTi-C and small multicomponent carbides), nitrides TiNb-N and sulphides (TiNb-S in EP718 alloy). The most harmful effects on the corrosion resistance of metal were detected around sulphides and small carbides containing Mo, W, Cr. Dissolution effects were also observed around large carbides and nitrides, especially around inclusions larger than 10 µm. Moreover, the dissolution of a matrix around inclusions and clusters located on the grain boundaries were found to be 2.1–2.7 times larger compared to inclusions found inside of grains of the given alloy samples.

scholarly journals Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Time Scales ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Optimality Principle ◽  
Bellman Equations ◽  
Special Cases ◽  
Hamilton Jacobi Bellman

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

MODERNIZATION OF PUBLIC ADMINISTRATION: FOREIGN EXPERIENCE

2015 ◽  
Vol 4 (4) ◽  
pp. 119-124
Author(s):  
Матвеева ◽  
Ekaterina Matveeva
Keyword(s):  
Public Sector ◽  
Public Administration ◽  
Russian Federation ◽  
Reference Points ◽  
Foreign Experience ◽  
Administrative Reforms ◽  
The Russian Federation ◽  
The Given

Research of foreign experience of enforcing administrative reforms allows to reveal the primary directions of modernization, which laid the basis of changes in public sector of a number of the leading countries. Systematization of the given directions and their comparison to the directions of reforming of system of public administration in the Russian Federation allows to allocate the general and private elements, to prove priority of the realized actions, to formulate priorities and reference points.

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