ECONOMIC OPTIMIZATION OF TECHNICAL PARAMETERS

A. S. BATURIN

(Presented by the scientific seminar of the Department of Economics)

With the introduction, during the ninth five-year plan, of automated control systems (ACS), the possibilities for using electronic computers (ECM) for engineering calculations and for optimizing products under development are expanding.

In this connection, optimization of technical decisions in engineering activity acquires special importance. It should also be borne in mind that modern requirements for new products have become very high. New products must be at the level of invention and possess high economic efficiency, since a substantial leap in labor productivity growth can be obtained through the introduction of fundamentally new optimal solutions.

One of the main directions in the optimization of new products is the economic optimization of technical parameters. The essence of this question may be briefly presented as follows. In developing a new product, all parameters may be divided into two groups. Optimized (controlled) parameters are those parameters that the design engineer can change and thereby influence the economy of the product. Such parameters may include: current strength, voltage, pressure of steam, gas, or liquid, speed, productivity, operating modes, weight, dimensions, reliability, etc. The optimized parameters vary within certain limits, which are predetermined by the initial conditions. Non-optimized (uncontrolled) parameters do not permit their alteration (with the exception of certain tolerances for a parameter). These parameters may include a number of input and output parameters of the product that are predetermined by the initial conditions. Examples of uncontrolled parameters may be: output power of the product, input or output current frequency, etc.

The same parameters, when developing one product, may be optimized, while for another they may be fixed. Everything depends on the initial data for the development and on the conditions under which the new product will be used. The optimized parameters enter into the objective function and are unknowns, while the uncontrolled parameters are included among the constraints of the problem being solved.

In addition, in engineering developments it is important to distinguish two kinds of relationships: physico-technical and cost relationships. Physico-technical

relationships are governed by the processes that occur in the product (electric current, magnetic field, mechanical motion, motion of liquid, steam, gas, etc.). The physicotechnical relationships in a product are complex and often make it impossible to find a rigorous analytical solution. For this, numerical solution methods and modern computers can be used. Cost parameters are linked with physical ones, since a change in physical parameters leads to corresponding changes in the price of the product and in the magnitude of operating expenses. Cost parameters remain unchanged only within short time intervals, while over long periods of time they undergo changes. This is explained by the fact that prices for raw materials, materials, semifinished products, and products, as well as tariffs for electric power, do not remain unchanged over a long period of time. Owing to the growth of social labor productivity, the development of new natural resources, and scientific and technical progress, they tend to decrease. In calculations that take development prospects into account, this must be considered.

Of great importance in the optimization of technical parameters is the optimality criterion. From the economic point of view, the most acceptable criterion is the minimum of the sum of annual reduced costs, determined by the formula:

\[ Z_{\mathrm{g}} = C + E_{\mathrm{n}} \cdot K \tag{1} \]

where \(Z_{\mathrm{g}}\) is the annual reduced costs, \(\dfrac{\text{rub.}}{\text{year}}\);

\(C\) is the annual operating expenses, \(\dfrac{\text{rub.}}{\text{year}}\);

\(E_{\mathrm{n}}\) is the normative coefficient of comparative economic efficiency, \(\dfrac{\text{rub.}}{\text{rub. year}}\);

\(K\) is the one-time capital investments, rub.

It is evident from formula (1) that the sum of annual reduced costs includes both operating expenses and capital investments, which is an important advantage of this criterion. Variation of the technical parameters most often affects the cost indicators of a product in a contradictory way. Thus, an increase in a technical parameter may lead to a reduction in operating expenses and, at the same time, to an increase in capital investments, or vice versa. When many parameters are varied, the picture of changes becomes more complicated. The optimal value of the parameters is characterized by the minimum of annual reduced costs.

The formula for annual reduced costs (1) becomes more complicated for optimizing a specific product, since annual operating expenses (\(C\)) and capital investments (\(K\)) must be expressed through operating factors and the parameters being optimized. This, in turn, makes the process of finding the optimum more complex and leads to the need to choose the most advantageous solution method.

In order to optimize the parameters of a product, it is necessary to conduct experiments by means of which to establish the interrelations of physicotechnical and cost parameters. Several methods may be used for this.

Experiments can be conducted directly on the product, but then it is necessary to manufacture it and sometimes not just one, but several products with different parameters, and then carry out tests to identify the regularities in the variation of technical parameters and cost-

indicators for determining the optimum. In this case, all products must perform their functions under specified operating conditions. Carrying out such work requires large expenditures, as well as a long period of time. Therefore the method of optimization directly on the product is uneconomical and often difficult to implement. In practice this method is used rarely. It should be noted that, in this case, the product itself must not be changed in the course of the experiments.

It is more expedient, for optimization, to use models that replace the product being developed. Models may be analogs: physical ones (substitution circuits), graphical ones (graphs, diagrams), or symbolic ones (mathematical models). The choice of one model or another depends on the type of product being developed, as well as on other factors connected with carrying out the optimization.

For the economic optimization of technical parameters, mathematical models of linear, nonlinear, integer, and, in a number of cases, stochastic programming may be used [1, 2, 3]. In addition, the base-point method [4] may be applied; it has been considered with respect to power engineering, but can also be used in other branches when it is possible to formulate the function of annual reduced costs in terms of the optimized parameters and to transform it into an equation in dimensionless criterion form.

A more advanced method is the combination of product calculation and its optimization on a computer. In this case we have machine design [5], in which substitution circuits described by mathematical equations may be used. Experiments according to the program are carried out on a computer. The time required for product development and optimization is reduced many times over. The results of calculations are issued in the form of graphs, tables, drawings, or in another form. Machine design of products produces a leap in the growth of labor productivity, while new optimal products help increase the efficiency of social production.

In many cases, during optimization it is necessary to select significant parameters, and also to resolve the questions of how to vary the optimized parameters, how many experiments to conduct, and in what sequence to conduct them. It is important not to carry out superfluous experiments that do not make a noticeable contribution to increasing the accuracy of the results. The task arises of planning the experiments in the best possible way so as to ensure sufficient accuracy of the results and not do unnecessary work. To solve this task one may use the mathematical planning of experiments [6].

Thus, the achievements of modern economics, mathematics, and computer technology make it possible to carry out machine design and economic optimization of the technical parameters of products under development. However, to realize these very promising possibilities, it is necessary to train and retrain teaching staff and engineers.

Technical higher educational institutions can do much in this direction: revise curricula, introduce new courses and sections so that graduating engineers will be familiar with the problems of optimization and machine design. Both technical and economic departments must take part in solving this problem. It should be taken into account that at present our higher educational institutions graduate engineer-mathematicians who are specialists in solving applied problems by mathematical methods. Therefore engineers in technical specialties should study only the fundamentals of economic optimization and machine design, and should also acquire

the ability to solve the simplest problems. Along with this, they must be able to formulate complex problems for mathematical engineers.

Such a shift will help improve the quality of the training of engineers and will improve the use of automated control-system technology.

No less important is the inclusion of questions of economic optimization and machine-aided design in the programs of faculties for advanced training of certified engineers.

A solution to this problem cannot be conceived without the development of textbooks and teaching aids, as well as corresponding programs for various specialties. It would be desirable for this work to be coordinated centrally, in order to avoid unnecessary duplication. This does not rule out competitions for the corresponding textbooks and programs, which are developed by institutes and then the best of them are published in mass editions.

Nor should one overlook the need for additional equipment with the appropriate technology—computers and other equipment—for organizing the educational process in higher educational institutions.

It is also necessary to retrain the corresponding instructors at technical higher educational institutions, since independent mastery requires a great deal of time.

It is more expedient to carry out the retraining of instructors through special departments and higher educational institutions.

Solving the problem of introducing economic optimization and machine-aided design into the educational process is an important direction in implementing the achievements of scientific and technological progress. This will influence the growth of the productivity of engineering labor, the introduction of optimal products, and the improvement of the efficiency of social production.

REFERENCES

1. L. V. Kantorovich, A. B. Gorstko. Optimal Decisions in Economics. Moscow, “Nauka,” 1972.

2. V. E. Likhteinshtеin. Models of Discrete Programming. Moscow, “Nauka,” 1971.

3. A. A. Korbut, Yu. Yu. Finkelshtein. Discrete Programming. Moscow, “Nauka,” 1969.

4. Yu. D. Arsen’ev. Similarity Theory in Engineering Economic Calculations. Moscow, “Vysshaya shkola,” 1967.

5. V. N. Il’in. Machine-Aided Design of Electronic Circuits. Moscow, “Energiya,” 1972.

6. V. V. Nalimov, N. A. Chernova. Statistical Methods for Planning Extremal Experiments. Moscow, “Nauka,” 1965.