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Posted by: 27.14.2014 Last Edit:27.14.2014

Deploed model of extremal system operation for solving optimal management problems

I. Lutsenko

Eastern-European Journal of Enterprise Technologies. - 2014. - Vol. 5/2(71). - P. 61-66.

DOI: 10.15587/1729-4061.2014.28592


1. Introduction


For solving optimal management problems, it is necessary to satisfy a number of conditions in relation to the managed system. The first condition is the possibility of independent management of feeding of raw materials and energy products to the input of the system under study, while ensuring the given quality of a primary useful product at the output of this system. The second condition is the possibility to take into account the wear of the basic technological mechanism in general. The third condition is the possibility of cost or expert estimation of input and output products of the system operation.

This is caused by the need to maximize the desired product of the system in the process of manufacture of the main useful product. The desired product in managed systems is the value added (price), but only extremal systems ensure a purposeful change of the desired product, and optimal systems ensure its maximization.

The above conditions are met in systems with batch feeding of raw materials, at the input of which there are raw material feeding system/systems, and at the output - output technological product buffering system/systems.

2. The analysis of literature data and formulation of the problem

Analysis of available publications shows that the continued interest is drawn to the research topic of operations. This indirectly indicates that the central questions remain open.

Conclusions of analytical publication on operations research show that there is a steady trend in demand for works with "rigorous use of empirical data, quantitative analysis and theoretical modeling" [1].

At the same time, it must be recognized that the main efforts are still focused on modeling physical processes of transformation [2-4].

Works, related to inventory management are no exception [5]. Despite the fact that this model is also used for trading systems management, research is focused on the quantitative parameters of products and practically do not affect the cost parameters that directly impact the efficiency of the operation.

Marketers, whose attention is directed at the system process management efficiency [6], which stimulates the development of a generalized model of the operation show great interest in the operations research. However, the lack of a reference point as the efficiency criterion leads to the need to be guided by a set of indicators in researches [7].

Constructing a mathematical model of the process under study is the first and fundamental step towards the operations research. Nevertheless, the analysis of scientific publications indicates that authors, as a rule, without the detailed development of the operation model immediately switch to research methods of private scientific or practical problems that have the ability to involve the developed mathematical apparatus.

For example, in the known work of Hemdi A. Taha [8] statement begins not with construction of a generalized model of the operation, but an introduction to linear programming, a description of the simplex method, etc.

The above analysis can be summarized by the words of Peter Drucker from his legendary work of 1964: "What is a transaction? Above all, how does one decide which of the many transactions within a business is the transaction that is representative of the actual cost structure? There is no set answer" [9].

3. The purpose and objectives of the study

For more accurate identification of system operations, it is necessary to develop a mathematical model that links together all the relevant quantitative parameters of technological products and their corresponding expert estimates in time.

This presupposes solving the following tasks:
- the construction of the registration model of the operation;
- the assessment of the model limitation and development of the conceptual model of the extremal managed system with a possibility to determine the wear of technological mechanism and reduce the registration signals of quantitative parameters for technological products to comparable values;
- the construction of the reduced registration model of the operation to comparable values;
- the construction of a generalized, deployed model of the operation;
- the comparative analysis of possibilities of registration and deployed models of operations.

4. Development of the deployed model of the system operation

As a result of the interaction of the technological product feeding systems, system under study and output technological product receiver systems, with respect to the system under study, the displacement of technological and information products is formed. Registration of the quantitative parameters of exchange products of these systems allows to create a basic registration system model of the operation.

As an example, let us consider a system operation of batch heating of the liquid using an electric heater. The choice of such a system as a demonstration model is caused by a good knowledge of the model of the heating process, its inertia (there is no need in parameters stabilization nodes) and popularity of wear model of electric heater.

Fig. 1 shows the structure of the managed system, which ensures fulfilling the first condition of optimal management. Сигнал регистрации движения специального продукта

Fig. 1. Structure of the managed fluid heating system with the batch feeding of cold fluid and management of its heating to a predetermined temperature


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