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3.3. Interaction and the coordination of interests strukturnyhpodrazdeleny high school

the Majority of educational programs is realised by institute is on-line, and with attraction of other structural divisions. It first of all concerns programs of the higher vocational training - blocks obshcheprofessionalnyh and special disciplines the block of general humanitarian both socially - economic disciplines and the block obshih mathematical and natural-science disciplines - basically other divisions are carried out by profile institute, and.
13 communications with it are represented expedient formation of some system of the estimations characterising degree vzaimnoju of participation of structural divisions in realisation of educational programs and level of an autonomy of structural divisions.
Volume of the academic loading (in hours) educational program g, realised in j th institute, we will designate Vjr, and volume of the hours which are carried out
v.
In this пр01рамме institute i - V; jr. Then the relation — characterises to -
lju 1-1*0 institutes in educational program realisation g j-ro institute. If the institute j carries out p educational programs, its total
In
The academic loading makes ^J7, »; thus loading volume, priho -
(). (3.3.1)
г-1
If in high school function m educational structural divisions the sum (т-1) factors of mutual participation will characterise a share of volume of study of institute j, carried out by others of structures -
nymi divisions; we name this size in factor of dependence of structural division Kz;, i.e.
= SH (3-3)
Or
«I
(3.3.3)
0~j)
IZ ^
= ^g ^
The remained study is carried out by institute], its share
IT
Makes (1]? A*v); we name this characteristic in factor avtono -
•• I
Mines of structural division To, ts.
Thus, To ^ = 1 - Kz; (3.3.4)
It is convenient to present the offered system of factors in a kind
Square matrix of dimension mxm:
I TO A Kli ^LJ - K\f—K\m
^ "21 К-Л1 To» - Kn K-p K-lu
TO * '
On the main diagonal factors of autonomy KL are placed; (j=l, m) all structural divisions; each line of a matrix represents a file of factors of mutual participation corresponding struktu rnogo divisions. It is obvious, that the sum of elements of each column of a matrix is equal 1. It is obvious also, that the sum of all elements of a column except for KAj is equal to factor of dependence of corresponding structural division.
The offered system of factors allows to estimate operatively, first, to possibility of divisions at formation of plans under the nomenclature and volume given OU, and secondly, is rather useful
At definition of system of financial mutual relations between divisions.
At joint realisation of educational programs before financial managers of high school there is a problem of distribution of received profit between the structural divisions participating in performance of given educational program, and the distribution mechanism should provide high enough motivation for corresponding divisions in decrease in own expenses. Such mechanisms name rational.
At once we will make a reservation, that here speech does not go about income division between high school in whole (the centralised deductions), on the one hand, and its structural divisions, with another.
A problem of the given research is distribution of a part of the income of realisation of educational program, being at the command educational divisions (we will designate this size).
Let's make a number of the assumptions simplifying the decision put
Problems.
We consider, that educational program includes three independent blocks of subject matters. For example, for programs of the higher vocational training as such blocks the block of socially-humanitarian disciplines, the block of is natural-scientific disciplines, the block of obshche-professional and special disciplines (association in last block of two traditional cycles of the State educational standards speaks that they, as a rule, are realised by one institute) can act.
We believe, that realisation of the listed blocks is carried out in time consistently.
Teaching of disciplines of each block spends one educational division. Division of educational division into smaller structures (chair) is not considered.
4. The cost price structure in educational divisions is identical and includes expenses on a payment, the uniform social tax, direct costs on the organisation of educational process, miscellaneous costs, etc.
In such statement the given problem is similar to a problem of the co-ordinated distribution have arrived in consecutive corporate associations [30].
Let's designate cost prices of realisation of blocks of educational program by educational divisions accordingly s С2 and Cj. The cost price of all educational program will be equal With = Ci + С2 + С3.
The profit distributed between divisions will make
P = TS - (WITH, + С2 +>) =-TS-S.
One of approaches to division of this profit between divisions is based on a principle «equal rentabelnostej» according to which the profit falling to rouble of expenses, for all divisions should be identical.
Let's designate TS TSz, Lb - incomes of corresponding educational blocks; it is obvious, that TS | + TSg + TSg TS.
Then the profit of each division will make accordingly: P; = TS, - With; П1-Ц2-С2; SH = TS} - With, '. (3.3.5)
To profitability of divisions will be equal:
sh sg with,
Equating profitability, we will make system of the equations: With, with,
With, with,
As a result of transformation of system of the equations it is received:
Yokes =
_ С\ц2 Sg
WITH,
~ TS-ts?
We substitute expression for TS} in vjuroe the equation:
ts _ S.SHCH
Sou
Taking into account the first equation:
TS, =, or

I
Ц2С1 = С2Ц~С1Ц2-С2Ц2;
Ц2 (With, + С2 + Sz) = С2 TS, hence
M - = SM With,//42 Q + With, + • Cj With
By analogy it is possible to receive, that with with.
For simplification of the further calculations we will accept size TS for unit (TS = 1). And esbsstoimosti s С2, Cj and incomes of educational blocks Hi, Lb, Ц1 we will define in shares from unit.
Then the decision of system of the equations of signs-more a simple kind:
Profits of divisions according to expressions (3.3.5) will make:
P,-? - With, П2 = - Sg; P, = f - Sz. (3.3.7)
Let's define, at what values With, С2 and С3 divisions receive the greatest profit. In case of the first division for this purpose it is necessary to find value Ct, at which function
Addresses in a maximum.
Realising standard procedure of search of an extremum, we differentiate expression P | (With |) on Ci and it is equated the received derivative to zero:
g S V _ (With, +Сг + With,)-with s-s. [With, + - Cj + a sou ' J (> +сг+сзу с2 '
From last expression it is found Ci:
It is easy to show, that at With | - With (1-) profit Hi addresses in a maximum.
Similarly,
С2 = WITH (1-); С3 = WITH (1-). (3.3.8)
Let's remind, that at such equal values Ci, С2, Cj reception by divisions of the maximum profit is provided.
Let's define under these conditions the cost price of all educational nrenramm For this purpose we will combine found values Ct, С2 and С3.
We receive:
Ci + С2 + With, - 3 With (1-) or
WITH = 3 WITH (1-);
3 (1-С)-1; WITH - |.
Accordingly sebestoimosto blocks will make:
WITH,-S2-WITH,-WITH (1-С) = |.
And incomes according to (3.3.6) will be equal:
ts,-ts, = ts, = 1.
Thus, a problem of divisions in case of method use «equal rentabelnostej» is "exit" on cost price level
— TS. In this case the aggregate profit of educational program TS remaining p the order of divisions, shares between them fifty-fifty.
If the real cost price of any educational block more low
2
-TS sootvetstvujushemu to division it is favourable it is artificial to overestimate to this size, having reduced thus high school profit as a whole.
If now to assume, that educational program realise - sh divisions, and to keep a consecutive principle of work we will receive the consecutive educational chain consisting from m of links.
Believing cost prices of parts of the educational program realised by each division, equal (it follows from previous consideration), i.e. With,-S3 =... = Q, we will find value With, (j = 1,2..., m). According to (3.3.8):
Cj = With (1-), but With = mCj;
Then
Cj = the hardware, (1 - mCj); Cj =—7 G - 1*2.... m). ' (3.3.9)
From
At the level of the cost price corresponding to expression (3.3.9). The structural division has the maximum profit. The general cost price will make thus
С_ From - 1/l — 1
= tts - sh — =.
t t
The high school profit will make:
Г1 = Ц-С=1 - =-.
t t
Accordingly, profitability budeg is equal:
R ^ L = 1 With from-1 '
Thus, we receive, at first sight, paradoxical situa-tsiju: at enough long educational chain profitability of educational program is close to zero.
Summarising the aforesaid, it is possible to assert, that the principle «equal reitabelnostej» practically is not applicable, if the high school contains "malozatratnye" divisions, or the quantity of the divisions participating in realisation of educational program, is very great.
Other way of division of profit between divisions is based on the account of stationary indicators any enough, characteristic for division, for example, number of workers of division, a share of the teachers having scientific degrees and ranks and so forth the Profit is distributed proportionally to these indicators.
If а^сь.аj - shares have arrived the division, defined by the such
In the image, and and, + ag + and} = I P |, П2 and Pz it is possible to find from parities:
П1 = а1 {the TS-sou, ТЬ=ссгЩ-С); П1 = а3 (TS-S). (3.3.10)
If n educational prozramme participate m structural divisions and if their shares of profit are equal («, =«, =... = am - ~),
m
TS - 1 (TS-S), j = 1, 2..., m (3.3.11)
m
From parities (3.3.10) it is obvious, that at such approach of division are interested in decrease in costs, but the formula (3.3.11) shows, that at enough long educational chain such interest decreases.
It is represented logical as shares and to use factors of mutual participation Kjj, i.e. to distribute profit according to the contribution of division to realisation given educational profammy. In this case, if the basic executor of educational program is the division], aiaK|j; a2 K2j;.... And; =Кл;.... a^k ^;. Then the profit of divisions can be found from parities: P, =Кц (TS-S); n2=I
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A source: Romanova Irina Borisovna. Ensuring competitive features of higher education institutions in the regional educational services market: theory and practice. 2006

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