A QUANTITATIVE APPROACH TO ANALYZING THE ACTIVITIES OF A UNIVERSITY AND ITS DEPARTMENTS

V. Z. Yampolsky

(Presented by the scientific-technical seminar of the Department of ACS and the Management Laboratory)

An operational approach to problems of managing organizational systems presupposes the existence of a definite goal and of a quantitative criterion characterizing the degree of its achievement. After the list of factors influencing the formulated criterion of operational efficiency has been determined in one way or another, and this influence has been expressed by means of definite mathematical relations, it becomes possible to carry out a mathematical formulation of the problem with the aim of finding its optimal solution.

What is essential here is the quantitative determinacy both of the criterion of operational efficiency and of the entire set of parameters and factors.

As has already been noted, the processes of functioning of complex and large systems of organizational management are characterized by the interaction of both quantitative and qualitative parameters and factors. This applies fully to a system of the university type, where the intangible nature of the basic processes and the high uncertainty of such categories of quality of functioning as “knowledge,” “ability,” and “skills” create additional difficulties in formulating and solving operational problems. There are various points of view regarding the necessity, possibility, and legitimacy of a quantitative approach to the analysis and planning of the activity of such a complex and specific mechanism as a university; therefore this question deserves some discussion.

The necessity of a quantitative approach follows above all from the obvious fact that analysis of many aspects of a university’s activity in qualitative terms suffers from lack of concreteness. As is noted in this connection in [1], leaders of higher education institutions (ministers, rectors, deans, etc.) justify their appointment only if they manage—that is, plan, control, evaluate the concrete results of a university’s activity, and on this basis adjust the plans, structure, and character of its functioning. The performance of all these functions is possible only when objective quantitative measures are available.

The objective necessity of introducing quantitative criteria was recognized by the Ministry of Higher and Secondary Specialized Education of the RSFSR as early as 1966 and was embodied in a system of indicators for evaluating the activity of universities. In accordance with the basi-

areas of university work, the system consists of five sections characterizing, respectively, the level of staff qualifications, the results of research, educational, and extracurricular work, and the level of teaching of the social sciences.

The system of indicators can thus be regarded as a set of \(n\) quantitative criteria characterizing the principal aspects of a university’s activity. The multi-purpose nature of this activity, as well as the real difficulties of constructing generalized, adequate, and representative measures, led to the introduction into the system of a sufficiently large number of indicators (\(n = 39\)). Each of the indicators in the system, directly or indirectly (but always in quantitative form), characterizes some aspect of a university’s activity. Thus, indicator \(P_{11}\) of the system characterizes the quantitative side of the performance of contract and budget-funded research projects by the university’s academic staff, while indicator \(P_{13}\) indirectly determines the qualitative side of this process by recording the percentage of work carried out in response to government resolutions.

The set of measures of the quantitative and qualitative aspects of the principal dimensions of a university’s multifaceted activity constitutes the essence of the system of quantitative indicators. With its introduction, the goals toward which one should strive in managing a university as a system acquired quantitative definiteness, and the problem of analyzing the activities of universities and their subdivisions was shifted from the plane of subjective opinions and judgments to the more objective plane of quantitatively substantiated decisions.

The use of quantitative indicators gave impetus to the development of analogous approaches at the intra-university level \([2—5]\). Statistical material began to accumulate in universities and in the ministry, with the aid of which studies were begun on university development, on questions of planning, forecasting, and other aspects of management. Thus the prerequisites were created for moving to a higher stage in the study of the “university” system on the basis of the use of mathematical methods and electronic computers.

Turning to the substantiation of the possibility of a quantitative approach to the analysis of complex social objects, among which the university is included, it is first of all necessary to note that the very striving to construct artificial quantitative measures (indicators) for these purposes is not as radical as is sometimes asserted.

In principle, there are no special logical or methodological obstacles to the quantitative measurement of qualitative attributes. The history of human knowledge knows many examples in which an attribute regarded in one epoch as purely qualitative, in another epoch received an adequate quantitative description \([6]\). This tendency is also currently observed in the field of concrete social research. Quantitative measurements and mathematical methods are increasingly becoming the language of sociology, the basis for modeling complex social processes and phenomena \([7]\).

At the same time, one cannot fail to notice that there are significant practical difficulties in constructing adequate quantitative measures for organizational systems. As a rule, in such systems there are no, or not enough, “directly countable” objects of study, that is, objects whose numerical expression is a priori fixed by everyday usage. There arises a need for “artificial” quantitative characteristics—indicators. It should be borne in mind that when indicators are used, what is measured is no longer the objective properties themselves—

properties existing independently of the measurement procedure, but “constructed” properties, the so-called “dispositional properties.” Therefore, the process of constructing a system of indicators must be preceded by sufficiently complete and deep professional-logical knowledge of the system under study, expressed in terms of a qualitative description. The process of construction itself must ensure that the indicators are formulated in quantitative terms so as to take into account all the most important elements of the qualitative description.

Let us note that measuring some attribute \(i\) of object \(j\) by means of a definite quantitative indicator \(P_i\) (that is, obtaining the estimate \(p_{ij}\)) is a sufficiently adequate mapping of this object onto the set of natural numbers, since the necessary conditions for order relations are preserved. However, when measuring a set of attributes \((i=\overline{1,n},\ n \geqslant 2)\), the set of all \(n\)-dimensional vectors \((p_{1j}, p_{2j}, \ldots, p_{nj})\) becomes partially ordered, and this circumstance introduces uncertainty into the assessment of the preferability of objects. Thus there arises the need to construct definite decision-making rules concerning the preferability of objects evaluated by a vector of \(n\) criteria. Let us note that although by their original nature indicators are simply certain definitions, they subsequently become an object of empirical control. Therefore, claims as to the correctness of quantitative analysis should be referred no less to the rules on the basis of which the analysis and assessment of the activities of higher educational institutions are carried out using the system of indicators. Consequently, in order to increase the correctness of quantitative analysis, it is necessary, when constructing a system of indicators, to strive to take into account the restrictions arising from the conditions of applicability of particular decision-making rules, and, when choosing rules, to take into account the properties of the adopted system of indicators.

Modern methods of decision-making under conditions of certainty in the case of \(n\) \((n \geqslant 2)\) criteria widely use the concepts of utility theory [6]. Utility is considered here as one of the most important categories reflecting the value aspect of the decisions being made. Being a quantitative or ordinal measure, utility allows the person or body responsible for making a decision to assess the preferability of \(n\)-dimensional vectors describing the objects being analyzed (alternatives, items, subdivisions, etc.).

The formalization of utility relations consists in specifying some utility function \(U(\vec P_j)\), which assigns to each \(j\)-th object a scalar estimate according to the vector \(\vec P_j\) of its estimates for each of the criteria. In practice, additive utility functions of the form

\[ U(\vec P_j)=\sum_{i=1}^{n} V_i p_{ij}, \tag{1} \]

are most widely used, where \(U\) is a real-valued utility function;
\(p_{ij}\) is the estimate of object \(j\) according to criterion \(i\);
\(V_i\) is a positive constant characterizing the utility (“weight”) of criterion \(P_i\);
\(n\) is the number of criteria according to which the complex decision is made.

The legitimacy of describing \(n\)-dimensional vectors \(\vec P_j=(p_{1j}, p_{2j}, \ldots, p_{nj})\) by an additive form of type (1), as applied to the problem of evaluating complex objects, is substantiated in the work of Fishburn [8]. The basic condition for the applicability of additive evaluation procedures is the independence of the utilities evaluated by the criteria \(P_i,\ i=\)

$= \overline{1,n}$. It is important to clarify that what is at issue is not the statistical (causal) independence of the evaluations of an object according to different criteria, but the independence of the utilities evaluated by them. In [8], conditions of independence are formulated and a theorem is proved on the possibility, in this case, of using additive weighted sums as a method for aggregating evaluations according to local criteria.

Guided by the arguments of [8], one may, on the basis of a professional-logical analysis, assert that in the indicated sense the indicators of the system for evaluating the activity of higher educational institutions are independent, since the evaluations $p_i$ are unambiguously established with their help for any object $j = \overline{1,m}$ independently of other evaluations of this object. In addition, the utility of this evaluation is defined as $V_i p_{ij}$, where $V_i$ is an a priori introduced measure of the utility of $P_i$, likewise not connected with the specific properties of the objects being evaluated. All this makes it possible to regard the indicators of the system as independent in the sense of the utilities evaluated by them (the results of the activity of a higher educational institution) and, consequently, an additive utility function of the form (1) is applicable to them, according to which the utility of a sum of evaluations is equal to the sum of the utilities. It should be borne in mind, however, that the use of an additive utility function imposes certain restrictions on the process of constructing indicators, the most important of which is ensuring the conditions of transitivity and independence of the utilities evaluated by them.

The practice of using quantitative indicators for solving various problems of managing a higher educational institution also puts forward a number of other requirements for the system of indicators. Among them are the requirements of representativeness, comparability, and unambiguity (see [3]).

The foregoing discussion shows that many processes in the functioning of a higher educational institution can, by means of a comprehensive professional-logical analysis and methods for analyzing a priori information, be described by a set of quantitative measures and used in the interests of increasing the objectivity of decisions made. A quantitative description creates the prerequisites for using rigorous mathematical methods of investigation and, in this sense, is more precise and less subject to the influence of subjectivism, but it is poorer in qualitative content. Moreover, in a higher educational institution it is far from always possible, for all aspects of the processes under study, to formulate adequate quantitative measures. Therefore one should not overestimate the role of mathematical methods in decision-making, and the results of quantitative analysis should be used only in combination with an analysis of the qualitative aspects of the processes and phenomena under study.

LITERATURE

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2. V. S. Smirnov. Scientific organization of labor in an institute. Leningrad, newspaper “Politekhnik,” No. 17 (2074), May 21, 1968.

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4. A. A. Vorob’ev, V. Z. Yampol’skii. Planning and analysis of the activity of a higher educational institution. Vestnik vysshei shkoly, No. 2, 1970.

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6. J. von Neumann, O. Morgenstern. Theory of Games and Economic Behavior. “Nauka,” 1970.

7. Modeling of Social Processes. Moscow, “Nauka,” 1970.

8. P. S. Fishburn. Independence in utility theory with whole product sets. Oper. Res., No. 13, 1965.