FORMATION OF LEVEL AGENDA PROGRAMS COMPETENCY OF THE PERSONNEL OF THE ORGANIZATION

2018, vol. 18, no. 2, pp. 112–120 112 At the present time, the requirements to the quality of education on the part of the state, applicants and employers are significantly increased, the competition among universities is becoming more acute, and the economic conditions of the universities are changing. All this raises the problem of finding new sources of increasing the competitiveness of a higher educational institution (HEI). In the documents of international organizations, domestic legislative and regulatory acts on higher education, it is noted that the most important condition for improving the quality of higher education is the competence of the teaching staff. Competences are stable characteristics of the human personality, predetermining the behavior of a person in a variety of situations and work tasks [1]. Modern research shows that recruitment through the competence model leads to an increase in staff efficiency, compared to other selection methods. At present, a multidimensional (holistic) approach to competence is becoming widespread [2], which offers more opportunities for integrating business requirements, human resource management technologies and the educational process. The competence model is the basis for the adoption of any personnel decisions and procedures such as hiring, attestation, office travel, skills development, motivation and payment systems. The current state of the problem does not allow to simulate the optimal trajectory of increasing the competence of personnel within the existing limitations for a particular organization [3]. In this regard, it is important to develop a model support for the assessment process and increase the level of competence of the faculty of the university. DOI: 10.14529/ctcr180211

The article considers the task of increasing the level of competence of the personnel of the organization. The approach is based on the technology of developing development management systems (RMS technology), created in the Institute of Control Sciences of the Russian Academy of Sciences with the participation of leading consultants in strategic management. The main stages of the RMS technology are considered as applied to the task of increasing the level of competence of the organization, such as a comprehensive assessment of the level of competence of the organization, assessing the potential for increasing the level of competence of personnel, developing a program to increase the level of competence, building a program implementation schedule.
Consider a comprehensive assessment of the level of competence of an organization from several departments. For definiteness, let it be an institution consisting of x departments (Fig. 1).

Fig. 1. The organizational structure of the institute
Each employee (teacher) of the institute has a certain level of competence. To assess this level, formal indicators (summaries, academic degrees, length of service, etc.), subjective (expert) assessments, including interviews and interviews, results of attestation are used. Assume that the level of competence is assessed on a three-point scale: normal level -1, elevated -2, high -3.
The level of competence of the Institute's personnel will be assessed as follows. Let n -number of the higher teaching staff; n 1 -number of the higher teaching staff having a normal level of competence; n 2 -the number of the higher teaching staff having an elevated level of competence; n 3 -the number of the higher teaching staff having a high level of competence. We denote by 1 2 3 2 3 Y n n n    the sum of the levels of competence of the institute's the higher teaching staff. We introduce the boundary values: this is a low level of competence and organizational measures are required. If А 0 ≤ Y < А 1 , then the institute has a normal level of competence of the higher teaching staff. If А 1 ≤ Y < А 2 , then the institute has an increased level of competence. If Y ≥ А 2 , then the institute has a high level of competence. To assess the level of competence of PPP as a whole, the matrix convolution apparatus is applicable. We define the dichotomous structure (binary tree) of the pairwise aggregation of the competence levels of the institutions' higher teaching staff. In Fig. 2 shows an example of such a structure for the case of the four institutions. First, an integral assessment of the level of competence of institutes 1 and 2, as well as 3 and 4 is determined. Then a comprehensive assessment of the level of competence of the combined institutes I and II is determined. It is desirable to unite close (in terms of direction, in the number of students or in the institutions' number of the higher teaching staff. The definition of aggregated estimates is based on 3×3 matrices. An example of such an aggregation matrix for estimating institutions 1 and 2 is shown in Fig. 3. The choice of matrices is determined by the university's policy (priorities of institutions). Thus, from the matrix in Fig. 3 that the institute 1 has a certain priority before the institute 2. Indeed, in the evaluation of the second institute and the second one, the integral estimate is 2, and in the reverse picture (the score of 1 from the first institution and the estimate of 2 from the second) the integral estimate is 1. Having method of assessing the level of competence of the institution as a whole, it is possible to solve the problem of increasing this assessment.
The assessment of the potential for increasing the level of staff competence (the higher teaching staff) is based on the integration of many activities aimed at improving the level of competence -internships, participation in conferences, invitations to leading scientists, writing textbooks and monographs, preparing dissertations, developing incentive mechanisms for raising the level of competence, etc. Each the event will be evaluated by two characteristics -the cost of the event and the effect of the event (that is, an increase in the indicator of the competence level of the unit).
We denote by c i -expenses, а i -effect i-th's event, Y 0 -existing level of competence; ∆ -the amount by which the level of competence needs to be increased; s ij -minimum costs required for the transition i-th of structural subdivision in group j. Ratio determines the effect of i-th's event.
We number the measures in order of decreasing efficiency. Then, based on these data, you can solve two problems. If you want to increase the level of competence by the required amount, then using this data you can determine what minimum amount is required for this. Conversely, if there is a certain amount allocated to increase the level of competence, then based on the same data, you can determine what the maximum increase in the level of competence can be obtained.
If Y 0 < А 1 , то разность ∆ 1 = А 1 -Y 0 determines the minimum increase in the level of competence required to transition to the group of enhanced competence; а ∆ 2 = А 2 -Y 0 -determines the minimum increase in the level of competence required to transition to a group of high-level competencies.
Consider the task of forming a program to increase the level of competence. Without loss of generality, we assume that the existing level of competence is equal to one and the minimum cost matrix is defined. A variant of raising the level of competence is the aggregate x = (x i ) of assessments of the level of competence of institutions to which a comprehensive assessment corresponds π(x). Then the task is set: to determine the x, providing the required value of the integrated assessment π(x) with minimal costs. The algorithm for solving the problem is based on the method of dichotomous programming [1]. In fact, there may exist so-called multi-purpose measures, the implementation of which gives effect at once for several institutions. Such events include, for example, the organization of conferences, the invitation of leading scientists with lectures, etc. Let us consider two approaches to solving the problem in the presence of multi-purpose measures.
1 approach. If the number of multipurpose activities is not large, then it is possible to consider all options for entering the program of multi-purpose activities (such options 2 q , where q -the number of multi-purpose events). With a fixed variant of entering into the program of multi-purpose measures, we obtain the problem considered above with single-purpose measures. Of all the options, then the best one  is chosen. With a large number of multipurpose activities, the method of enumerating all the variants of their entry into the program becomes time-consuming. 2 approach. We apply the branch and bound method to obtain lower bounds based on the network programming method by I.V. Burkova [4]. To do this, we divide the costs of each multipurpose event arbitrarily into several parts according to the number of institutions in which this exercise gives effect. After this, we get the task with single-purpose measures. The task of determining the division of costs for multi-purpose activities, in which the lower estimate of costs is maximum, is called a generalized dual problem.
The obtained estimate is used in the method of branches and boundaries. However, after each branch, you can try to improve the estimate by adjusting the breakdown of costs. In some cases, this method reduces the number of branches. For this purpose the theorem on obtaining lower bounds is used: "The solution of the problem with single-purpose measures gives an estimate from below for the original problem".
The "cost-effect" method provides an approximate solution to the problem of including an event in a program. With a large number of events, the error is not significant. However, with a small number of measures, the error can be significant [5]. In this case, it is expedient to apply the exact algorithm of dichotomous programming.
Another factor that should be taken into account is associated with so-called interdependent activities. When you include a pair of interdependent activities, an additional (synergistic) effect arises in the program (the effect of a couple of activities exceeds the sum of the effects of these activities). This circumstance can be taken into account by constructing a graph of interdependencies.
Definition of the graph of interdependencies: The vertices of the graph correspond to the activities, two vertices i, j are connected by an edge if the corresponding measures are interdependent. The length of an edge is equal to the additional effect d ij.
First, we consider a particular case of a problem where the graph interdependent can be a matching (a graph whose no two edges have a common vertex). In this case, the problem is effectively solved by the method of dichotomous programming (for integer values of the parameters). In Fig. 4 shows an example of a graph of interdependencies of five vertices, which is matching.
To solve the problem, we take the structure of the dichotomous representation of the problem, such that the vertices connected by an edge are considered at the lower levels of the dichotomous representation tree (Fig. 5). Let us consider the general case. A subgraph is called a subgraph of a graph, which is matching. A paragraph with the maximum number of vertices is called the maximal paragraph.
The idea of the algorithm is as follows. Remove a number of vertices from the graph of interdependencies so as to obtain a paragraph. Further, as in the case of multi-purpose events, we consider all Example. There are six activities, the data of which are given in Table 1. Consider the graph (Fig. 6).
It is easy to verify that the edges (1, 2) and (3,4) have minimal 12 34 1 r r   . We include, for example, an edge (1, 2) in a paragraph, removing the vertex 6.
We obtain the part (see Fig. 4). Since one vertex is removed, it is necessary to consider two variants (see Table 1).
1 option. Activity 6 is not included in the program. In this case, the minimum costs are 13. Correct the target setting 6 30 26 a     . 1 step. We consider measures 1 and 2. We are considering the combined event II and activity 5 ( Table 2).
The results are tabulated (Table 3).  2 step. We consider activities 3 and 4. The solution is given below ( Table 4). The results are tabulated (Table 5).   3 step. We are considering the combined event II and activity 5.
We are considering the combined event II and activity 5 ( Table 6). 4 step. We consider the combined activities I and III. The solution is given below (Table 7). The optimal solution is determined by the cell (37; 13) with costs 13 + 2 = 15. We choose the first option.
The final stage in the formation of the program is the construction of a calendar plan for its implementation. Let the integral program financing schedule be given. The task is to determine the timing of each event, so that the required funding of activities at any given time does not exceed the funds allocated to this time. As a criterion of optimality, we take the value of the lost profit.
First you need to check the financial feasibility of the program. To do this, we construct a rightadvanced implementation plan (all activities are completed at a given point in time) and an integral schedule for its financing.
Terms of financial realizability of the program: an integral right-shifted financing schedule should not be higher than the integral schedule for financing the program at any one time.
The task is a complex optimization problem that does not have effective, accurate methods of solution. Therefore, we propose a heuristic algorithm, based on the priority rules of measures.
To justify the proposed priority rules for events, we consider two particular situations. 1 situation. The integrated financing schedule is such that the activities can only be carried out sequentially. We get the well-known task of determining the sequence of performance of measures, minimizing lost profits. It is proved that in this case it is optimal to carry out activities in the order of decreasing priorities: where i  -duration of the event i.
2 situation. Financing is carried out for periods, and each activity can be fully executed in one period ( i    , where  -duration of one period). In this case, a solution close to optimal is obtained on the basis of the "cost-effect" method, that is, the implementation of activities in the order of priorities: So, we have two priority rules for events. A heuristic algorithm was proposed in [6], in which a linear combination of these rules is proposed: Value α is chosen arbitrarily, which can lead to the loss of a number of options. We propose to consider all variants of priorities (their number does not exceed 2 1 n c  ; 2 n c -number of combinations from n to 2).
To determine these priorities for each pair of measures, we define the boundary value i from equation  , priority is greater for an event with a larger r, regardless of size α. The transition of α boundary points ij  leads to a change of priorities.