On the Formation and Optimization of the Production Management Structure

A. A. Tereshchenko, G. V. Soldatenko

(Presented by the scientific and technical seminar of the Department of AM)

It is known that the automation of managerial labor with the aid of modern computer technology is not a one-sided process of freeing engineering and technical personnel and employees from performing certain tasks. Along with the transfer of a number of functions and tasks to the computer, new tasks arise for the employees of the management apparatus, including the performance of procedures connected with the use of computer technology. Therefore, especially during the period of implementation and operation of an automated control system, the problem arises of forming and optimizing the organizational management structure so that the management apparatus becomes more advanced, efficient, and economical.

At present, in developing automated control systems, serious attention is being paid to questions of improving organizational structures. But in most cases heuristic methods are used for these purposes, which makes it possible to achieve only certain partial successes. To construct optimal management structures, a systems approach to their analysis and synthesis is necessary, and this is possible only by combining heuristic methods with the use of mathematical modeling and computer technology.

An optimal organizational structure is understood to mean such a set of its elements that fully corresponds to the functional management structure while making maximum use both of the working time of engineering and technical personnel and of their qualifications.

To formulate the basic principles for forming and optimizing the organizational structure, let us represent the enterprise as a system consisting of technical, economic, and social elements that are functionally and organizationally connected with one another. The diversity of connections and the complexity of enterprise management require its detailing, with a further characterization of its constituent parts.

At an enterprise, two interrelated systems may be distinguished—the controlling system (the subject of management) and the controlled system (the object of management).

The controlling system is a set of links and hierarchical levels of management. A management link is an isolated unit with definite management functions. Management levels are groups of management links at a definite level of the management hierarchy. The totality of levels and management links, in their dependence and subordination, constitutes the structure of the controlling system.

In the structure of the control system one may, conventionally, distinguish the functional and the organizational structure of management. The functional structure is a complex of management procedures together with their informational links. The organizational structure of management is the set of elements that facilitate the execution of management procedures and provide them with information. Fig. 1 and equation (1) show how the component parts of the control system are brought together and transformed.

\[ P_{\text{out}} = f(P_{\text{in}}, E, V), \tag{1} \]

where \(P_{\text{in}}\) and \(P_{\text{out}}\) are, respectively, input and output information;
\(E\) is the complex of management procedures;
\(V\) is the set of elements of the organizational structure.

The functional structure of management is represented in the form of a network model consisting of a set of management procedures necessary for achieving the stated goal and connected with one another by an order relation. At the same time, the labor intensity of each procedure is assumed to be known. The vertices \(E_i\) and arcs \(P_{iy}\) of such a network are, respectively, management procedures and their informational links.

There is a set \(E\), consisting of a finite number of management procedures,

\[ E=\{E_1, E_2,\ldots,E_n\}. \tag{2} \]

If to each element of this set one assigns zero or several elements from \(E\) (i.e., if we specify a law \(\Gamma\) representing this correspondence), then the symbolic specification of the model by means of vertices and a direct mapping of arcs is written as follows:

\[ M=(E,\Gamma). \tag{3} \]

Fig. 1. Model of the control system

Representation in the form of a network model of the functional management structure makes it possible to identify “bottlenecks” in the control system.

The formation and optimization of the organizational structure are based on the volume and content of the managerial labor of the employees of the management apparatus (i.e., management is represented as labor evaluated qualitatively and quantitatively). The quantitative side of management is reflected by the following expression for the case of manual management:

\[ T_{\text{u}}=\sum_1^m \sum_1^n \sum_1^k T_{nqij}, \tag{4} \]

where \(m\), \(n\), and \(k\) are, respectively, the number of functions, tasks in the \(q\)-th function, and management procedures in the \(i\)-th task;
\(T_{\text{u}}\) is the labor intensity of management;
\(T_{nqij}\) is the labor intensity of the \(j\)-th procedure.

With the introduction of an ACS and the transfer of the solution of certain tasks to a computer, the labor intensity of automated management consists of the labor intensity of manual management \(T_{\text{r}}\) and the labor intensity of machine management \(T_{\text{m}}\):

\[ T_{\text{u}} = T_{\text{r}} + T_{\text{m}}. \]

This shows that the labor intensity of management will change, i.e., a redistribution of management functions will occur between ele-

...methods of the organizational structure and computers, causing it to change. This poses the problem of finding a management structure under the conditions of an automated control system.

The substantive part of managerial labor is revealed by classifying management procedures according to the following principal characteristics:

the relation to a particular management function;
the relation to a particular object of management;
the level of complexity;
the possibility of formalizing the decision;
the name of the procedure.

The first two characteristics are used to form the links of the control system. The third characteristic is used to form the levels of management. The fourth characteristic indicates the possibility of automating the procedure, and the fifth indicates the number of management procedures of the same type.

From a number of procedures classified in this way, related groups are formed, on the basis of which the organizational structure is formed according to the following basic principles:

formation of each element of the organizational structure (subdivision, group, etc.) as a unified whole headed by one person;

establishment, for each element of the organizational structure, of a principal goal that does not contradict the fulfillment of the goal of the management system as a whole;

subordination of a definite number of executors to one manager;

drawing a distinction between functional and administrative duties;

clear definition of administrative duties and their distribution among employees;

maximum decentralization of responsibility while simultaneously ensuring clear administrative control;

grouping of secondary duties and their distribution among the elements of the organizational structure as additional ones, which makes it possible not to create new subdivisions.

Organizational modeling requires a systems approach, in which not individual elements are considered, but the entire organizational structure as a whole. Since, however, it is difficult to examine the management system as a whole in detail because of the large number of management procedures and elements of the organizational structure, first an enlarged model of the organizational structure as a whole is constructed, and then local models of structural subdivisions are elaborated in greater detail.

The model of the organizational management structure is obtained in the form of a graph, the vertices of which may represent an individual subdivision or manager. The directed edges of the graph reflect administrative and functional connections. If only administrative connections are plotted, then, in the case of a hierarchical management system, the model has the form of a tree branching from top to bottom.

Management procedures, according to the periodicity of their performance, may be divided into several time periods: daily, ten-day, monthly, quarterly, etc. In addition to periodic management procedures, nonperiodic and random ones may arise (commissioning of facilities, an accident, etc.). Accordingly, the model of the functional management structure consists of several partial models:

\[ M = M_1 + M_2 + \ldots + M_n. \tag{5} \]

where \(n\) is a number indicating into how many periodicities the management procedures have been divided.

It follows from this that the functional part of the management system changes daily. The organizational structure, reflecting the statics of management, cannot change so often [1]. Therefore, when forming the organizational structure it is necessary to take into account all possible changes in the functional structure and, by applying probabilistic methods, to determine the mathematical expectation of the average reserve of employees of each profession and of the required qualification [2, 3].

The labor resource of the organizational structure is also not constant because of random factors (illness, dismissal, etc.). Therefore, the problem arises of the optimal allocation of the labor resource from the organizational structure that has been formed. The problem of optimizing the use of resources can be solved using the apparatus of dynamic programming [4].

In allocating the resource, a shortage of it may occur, which leads to the nonperformance of certain management procedures by the directive deadline. For this reason, the problem of determining the priorities of management procedures is introduced into the resource-allocation program. The division of procedures by priority is based on their importance and the urgency of their execution.

Thus, the approach set forth in this paper makes it possible, using economic-mathematical methods and computers, to form an organizational structure and carry out its optimization.

LITERATURE

1. O. V. Kozlova, I. N. Kuznetsov. Scientific Foundations of Production Management. Moscow, “Ekonomika,” 1968.

2. A. Kaufmann. Methods and Models of Operations Research. Translated from the French. Edited by D. B. Yudin. Moscow, “Mir,” 1966.

3. A. Kaufmann, R. Faure. Let Us Engage in Operations Research. Translated from the French. Edited by A. A. Korbut. Moscow, “Mir,” 1966.

4. R. Bellman, S. Dreyfus. Applied Problems of Dynamic Programming. Translated from the English. Edited by A. A. Pervozvanskii. Moscow, “Nauka,” 1965.