CC BY
49
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Economic-mathematical methods and models
UDC 658.5.012.1.001.76 DOI: 10.5862/JE.240.9
A.N. Shichkov, N.A. Kremlyova, А.А. Borisov
DESIGNING THE OPERATION CYCLE OF A MANUFACTURING AND TECHNOLOGICAL SYSTEM
А.Н. Шичков, Н.А. Кремлёва, А.А. Борисов
ПРОЕКТИРОВАНИЕ ОПЕРАЦИОННОГО ЦИКЛА ПРОИЗВОДСТВЕННО-ТЕХНОЛОГИЧЕСКОЙ СИСТЕМЫ
In order to manage innovating projects, he paper offers a method for estimating the degree by which a manufacturing and technological system (ECO — system) has been converted during the operation cycle into an economic system. The operation cycle of a manufacturing and technological system is seen as a circular integrated set of vectors of cash or cash equivalent flows arising as a result of converting technological processes into products in the form of technological stages or end products with market cost. The operation cycle consists of two contours formed by five vectors of cash equivalent flows. The first contour is a right-angled triangle of vectors that is formed by: the vector of direct technological operation costs, the vector of tangible and intangible assets and their summation being the vector of manufacturing capital. The second contour is also a right-angled triangle of vectors formed by: the vector of direct technological operation costs, the vector of net income and their summation being the vector of sales value. The modules and directions of all vectors are variables. The level of converting technological processes into money equivalent flows has been offered to estimate by the conversion coefficients. The ideal manufacturing and technological system has some upper limits of the conversion coefficients of the operation cycle. Namely, the vector of sales value divided by the vector of a manufacturing capital and the vector of tangible and intangible assets divided by the net income vector are equal to one. The graphical interpretation of an ideal operation cycle is an equilateral triangle. In the operation cycle of a real manufacturing and technological system the conversion coefficients are less than one. Every criterion in this integrated set may change simultaneously when any innovation is implemented in a manufacturing and technological system.
IDEAL (REAL) OPERATION CYCLE; VECTOR FIELD OF ECONOMIC POTENTIAL (LIABILITIES; ASSETS); CONVERSION OF TECHNOLOGICAL PROCESSES; MANUFACTURING AND TECHNOLOGICAL SYSTEM; VECTORS OF CASH EQUIVALENT FLOWS.
Для управления инновационными проектами предложен способ оценки уровня конверсии в операционном цикле производственно — технологической системы (ECO — systems) в экономическую систему. Операционный цикл производственно — технологической системы рассматривается как замкнутый интегрированный комплекс векторов денежных или их эквивалентов потоков, возникших как результат конвертации технологических процессов в продукты в форме технологических переделов или конечных продуктов, имеющих рыночную стоимость. Операционный цикл состоит из двух контуров, сформированных векторами потоков денежных эквивалентов. Первый контур является прямоугольным треугольником векторов, сформированным: вектором прямых технологических операционных затрат, вектором материальных и нематериальных активов и их суммой, являющейся вектором производственного капитала. Второй контур является также прямоугольным треугольником векторов, сформированным: вектором прямых технологических операционных затрат, вектором чистого дохода и их суммой, являющейся вектором объема продаж. Модули и направления всех векторов являются переменными величинами. Уровень конвертации технологических процессов в потоки денежных эквивалентов предложено оценивать коэффициентами конверсии. Идеальная производственно — технологическая система имеет верхний предел коэффициентов конверсии операционного цикла. А именно, вектор объема продаж, деленный на вектор производственного капитала и вектор материальных и нематериальных активов деленный на вектор чистого дохода равны единице. Графической интерпретацией идеального операционного
цикла является равносторонний треугольник. В операционном цикле реальной производственно — технологической системы коэффициенты конверсии меньше единицы. Каждый критерий интегрированного комплекса изменяется когда (если) осваивается любая инновация.
ИДЕАЛЬНЫЙ (РЕАЛЬНЫЙ) ОПЕРАЦИОННЫЙ ЦИКЛ; ВЕКТОРНОЕ ПОЛЕ ЭКОНОМИЧЕСКИХ ПОТЕНЦИАЛОВ (ПАССИВЫ; АКТИВЫ); КОНВЕРСИЯ ТЕХНОЛОГИЧЕСКИХ ПРОЦЕССОВ; ПРОИЗВОДСТВЕННО-ТЕХНОЛОГИЧЕСКАЯ СИСТЕМА; ВЕКТОРЫ ПОТОКОВ ДЕНЕЖНЫХ ЭКВИВАЛЕНТОВ.
Vector field of an economy ECO-system
In an innovation market economy all needs of people are bought and sold and, therefore, these needs have a market cost in cash or cash equivalent. Thus, from a physical and mathematical point of view, the economy is the field of economic potentials (Liabilities L and Assets A) where the «buy-sell» process (difference of potentials) is a dual process of forming cash flows with magnitude and direction. It is known that mathematical functions with magnitude and direction are vectors [1—3]. The gradient of potentials, i. e., Liabilities and Assets, forms the vector of cash or cash-equivalent flows. The engineering business is seen as an engine working on the basis of the gradient of potentials (Liabilities and Assets). In this case, liabilities and assets fulfill the functions of potentials of economic fields: «buy-sell» or «resources-results». For example, the results of business such as the assets of technological stages and taxes become liabilities in the subsequent technological stages (zones of financial responsibility) of enterprises and in the municipality budget. Therefore, the terms «liabilities and assets» determine the function of potentials.
In this context, we understand by production management [4] an economic system the infrastructure of which realizes the function of an engineering change order (ECO) [5] on the basis of the balance of supply and demand of products and services using different markets (fields of potentials).
An operation cycle is a circular integrated set of engineering and technological processes on the basis of mechanical, electrical, chemical, thermodynamical, optical and any other physical systems arising during the accounting period in the course of the ordinary activities of a manufacturing and technological system and as a result of the synergetic effect [6—8] are converted to an economic system in the form of cash-equivalent flows of sold products. In other words, an operation cycle is an integrated set of continuous processes ensuring the conversion of
technological systems into economic systems. In this sense, manufacturing and technological systems (ECO-systems) are the tools for the processes of conversion. It means that the manufacturing and technological system should be estimated in relation to the parameters of economic benefits. The main economic results of the conversion operation cycle are:
«Net income is an increase in the economic benefits emerging during the accounting period in the form of inflows or enhancements of assets or some decreases of liabilities that result in increases in equity, other than those related to contributions from equity participants» [9—11].
«Revenue is a gross inflow of economic benefits emerging during the accounting period in the course of ordinary activities of the entity. These inflows result in an increase in the equity of the shareholders, with investments calculated on the basis of the direct share in the equity»
[9—11].
«Profit is the residual amount that remains after expenses (including capital maintenance adjustments, where appropriate) have been deducted from income. Any amount over and above that is required to maintain the capital at the beginning of the period is profit» [9, 10, 11]. Net profit is the property of owners, members and participants of equity. It consists of two parts. Net profit is the amount required to pay for non-operating expenses and to pay dividends on the basis of shareholders' meeting decision. Therefore, managers of an enterprise try to reduce the need in a net profit. Maintenance adjustments capital is the main tool to manage the taxable base of operating profit. As a rule, innovative enterprises do not have a taxable base of operating profit.
The main function of operation management is to organize the production ensuring the manufacturing of products with the required structure of direct technological costs in an operation cycle and consumer properties having competitive advantages and, consequently, having market cost.
The priority structure of direct technological costs of the operation cycle:
According to Chapter 25 of the Tax Code of the Russian Federation, tax accounting should substantiate the planned net profit.
As for management accounting, it has to implement an operation cycle with a required coefficient of capitalization X:
X = ■
V„,
GoW
(1)
where Vsv is sales value of the operation cycle, G0 is the designed production volume and W0 is the designed unit costs.
If direct operating costs Coc of the operation cycle are equal to 100 %, then material costs Cmc should be equal to 30 %; additional costs Cac should be equal to 20 %; labor payment costs Clp should be equal to 25 % and finally, depreciation of tangible costs Cdc should be equal to 15 %.
The balance equation of costs in the operation cycle has the form:
100 % = Cmc / Coc + Cac / C + Cp / C +
+ Cdt / Coc = 30 % + 20 % + 35 % +15 %.
^dt
If additional costs Cad are 20
then the
amortization of intangible assets Cai is equal to 10 % and the summation of tax fixed assets Nfa, tax of land NL and other costs are approximately equal to 10 % too.
Namely,
Cac / Coc = 20% = Cai / Cac + + (...Nfa + Nl + ...)/ Cac = 10% + 10%.
The net income D0, including net profit P0 and capital maintenance adjustments Cma is the summation of depreciation of tangible assets Cdt and amortization of intangible assets Cai. Herewith, the fund formed from Cdt should be used only for simple reproduction, while the fund formed from Cai is the resource for funding the extended reproduction of fixed assets.
Years
Fig. 1. Simple and extended reproduction of fixed assets Ufa of a manufacturing and technological system
Management accounting tends to increase the parameters of the operation cycle on which a coefficient of capitalization depends. It means that labor payment in the structure of assets in the operation cycle increases up to 35 %. In this case, an innovative enterprise will have competitive advantages on a labor market in a municipality. Besides, tax payments to all levels of budgets are prioritized for innovative enterprises of the municipality. Therefore, there is a tendency to try to achieve tax payments of 20 % in the structure of assets in management accounting.
Operating profit tax is the exception from the general rule. The fact is that the amortization of intangible assets decreases the taxable base of operating profit taxes; therefore, innovative enterprises with intangible assets do not pay the tax of operating profit. However, if enterprises have intangible assets, such enterprises pay more land taxes than enterprises without intangible assets.
The system of equations for an ideal operation cycle of ideal manufacturing and technological system
The equation for the cost of manufacturing and technological capital (balance cost of a manufacturing and technological system) consists of the summation U of tangible Ufa and intangible assets Uia and direct technological operation costs GO J^O:
Q = U + Go Wo.
(2)
The equation of manufacturing and economic
capital (economic system) consists of the sales value Vsv of products and services equal to the summation of direct technological operation costs G0W0 and net income D0:
(3)
Vsv = GoWo + Do,
where any technological equipment, any manufacturing and technological system and any production enterprise have their characteristic GW in the form of parabola:
W = aG2 + bG + c.
(4)
Project parameters of the manufacturing and technological system:
G0 = -b /2a; W0 = (4ac - b2) / 4a.
Vector of direct technological operation costs G0W0
The designed parameters of business are: G0 is the production volume in physical units (unit/year);
W0 is the unit costs (rub/unit). If AG and AW are the limits of change of parameters in business, then coefficients a, b, c of equation (4) are found in three points from the range of change of production volume G and unit costs W.
Table 1
Example of the dependence of unit costs W on production volume G for a furniture enterprise [12]
Parameters of the manufacturing and technological system First year Second year Third year
Production volume, G, thousand m3/year 22.4 26.4 26.2
Unit costs of production, W, thousand rub./m3 10.5 10.7 10.4
Based on Tab. 1, the system of equations is formed in order to find the numerical value for a, b, c (4):
501.8a + 22.4b + c = 10.5;
697.0a + 26.4b + c = 10.7;
686.4a + 26.2b + c = 10.4;
then W = 0.29 G2 - 13.90G + 176.30.
G0 = 13.90/2-0.29 = 24.31 thousand m3/year;
W0 = (4-0.29-176.30 - 13.90)/4-0.29 = = 7.47 thousand rub/m3.
AW
G
► Go
Fig. 2. Characteristic GW of any manufacturing and technological system
Productivity balance of technological and economic systems of the operation cycle
It is necessary to design an MTS that ensures the equality of the productivity of the wear of fixed assets and the productivity of operating costs. In this case the balance cost of fixed assets Ufa should be estimated by costs approach. The balance equation of productivity has the form:
U,
fa
GqWq
fa
Rg
GQWQ Rq
(5)
where RG is the business constant determining annual resources of the useful life of fixed assets in hour/year; R0 is business constant determining the annual resources of work time in hour/year. The equation (5) can be written in the form:
* - A =
GqWQ
Rg u
(6)
fa
where k is business constant determining its industry and which can be determined by industry. For example, a business relating to the metallurgical industry has k = 0.5, an engineering enterprise has k = 1.0, enterprises related to the «Gasprom» business have a numerical value of the constant k equaling 0.27. The business constant of forest industry enterprises has the value of 0.8.
Constant of business k for an enterprise as an integrated set of manufacturing and technological systems
Balance cost of fixed assets of an enterprise is equal to the summation of balance cost of each technological stage (MTSs):
Ufa=U1 + U2 + ... + Ui. (7)
Operating costs of all technological stages are equal to the summation of operating costs of each technological stage (MTSs):
Coc=C1 + C2 + ... + Ct. (8)
These equations may be presented in the form:
c.
U
fa
Cl Ui
C2
~rr~U fa Ui + ^U2 +... + ;
U2
Cl
Ui
KtsUfa = *1U1 + *2U2 + ... + *iUi ;
KtsUfa = ki (U1 + U2 + ... + Ui ).
k - k
mts ~ Hi
where k - —. ' Ui
Constant of business k of each technological stage is equal to the constant of businesses k of each MTS of the enterprise.
Five vectors of cash equivalent flows which implement the conversion of manufacturing and technological processes are the following:
Vsv, rub/year, is the sales value including taxes to budgets of all levels.
G0W0 is the direct technological costs including
— operating direct technological costs: the construction materials; energy resources; spare parts; repair and technological tools;
— labor payment including taxes and payments. D0 is the net income for simple and extended
reproduction of business including
— the capital maintenance adjustments consisting of the depreciation of tangible assets and the amortization of intangible assets;
— net profit to support joint stock capital in the form of dividends.
Q is the manufacturing capital including
— the direct operating technological costs G0W0 and the fixed assets and intangible assets U.
The mathematical model of the operation cycle in an ideal manufacturing and technological system
Eqs. (2) and (3) can be written in the form:
Vv
G0W0 + Do
Q
U + GoW o
= 1, = 1.
(10) (11)
Consequently, Eqs. (10) and (11) may be equated:
Q
Vsv,
U + G0W 0 G0W0 + D0
(12)
Eq. (12) in a dimensionless form is the following:
G0W. + D0
Q Ufa + Ua + G0W0
GW0- + Ui- + a + p UL k + a + p UL + (13)
U fa U fa U fa _ U fa U fa
1 + + G0W0
Ufa Ufa
1 + k +
Ua
U
If Vsv/Q = v is the conversion coefficient, k = G0W0/Ufa is the characteristic of business, D0/Ufa = m is the coefficient of capital maintenance adjustments, then the parametric equation (13) of the operation cycle of the ideal manufacturing and technological system has the form:
k + m
S = •
1 + k +
Ua
U
fa
P0 U-
where m = —— + a + B —^.
Ufa Ufa
(14)
(15)
Analysis of parametric dependence (14)
for the ideal manufacturing and technological
system
If the limit of the coefficient of capital maintenance and fixed assets adjustments m tends to one, then the limit of the conversion coefficient in a technological system will also tend to one. In this case dependence (13) can be written in the form:
U■ P0 U ■
k + a + P+ = 1 + k + -a,
Ufa Ufa Ufa
U P
a + (p - 1)^ + = 1,
)Ufa Ufa ' D0 = Ua+Ufa = U,
(16)
where a is the depreciation rate of tangible assets (fixed assets); p is the amortization rate of intangible assets; Uia is the balance cost of intangible assets in the MTS equal to its balance cost estimated by the income approach Um a minus the cost of the MTS estimated by the costs approach Ufa.
The upper limit of the conversion coefficient of the ideal manufacturing and technological system is equal to one:
L imSm = L imm
k + m
* U
1 + k +—-U
= 1. (17)
fa
fa
An integrated set of systems the parameters of which are described by equation (17) is the following:
The technological machine (TM) is the technological equipment which presents an integrated set of tangible and intangible assets, consisting of mechanical, electrical and/or chemical
engineering solutions, tools for manufacturing the elements of technological (operation) stages or whole technological (operating) stages having a market cost.
The manufacturing and technological system (MTS) is an integrated set of technological machines (tangible and intangible assets) providing the manufacturing of technological stages and/or end products with a market cost. The results of this operation cycle are net income and sales value.
The enterprise is an integrated set of manufacturing and technological systems; the results of the operation cycle are net revenue, sales value and tax payment to budgets of all levels.
Municipality is an integrated set of a system of industrial enterprises, the results of operation cycles of which are the budgets necessary and sufficient for ensuring the life activity of people in the municipality.
The subjects of the Russian Federation.
Parameters of an operation cycle
of real manufacturing and technological systems
Operation cycle of metallurgical enterprises
Three metallurgical enterprises, JSC «Severstal», JSC «Magnitogorsk metallurgical company» and JSC «Novolipetsky metallurgical company», are similar in their technological and economic parameters.
The technological similarity of enterprises is
determined by similar manufacturing and technological systems that produce steel sheets of practically equal volume and equal sales value.
Economical similarity of enterprises is confirmed by the equal numerical value of business characteristics and net income.
Geometrical interpretation of the operation cycle in the form of a vector triangle allows to combine two approaches to estimate technological and economic similarities of enterprises.
The main criteria of technological and economic similarities of enterprises are parametric equations.
Parameters determining the economic ECOsystem of a manufacturing and technological system of an enterprise:
— operating profit, P = Vsv/r, where V is the sales value with a value added tax (+18 % if products are sold on domestic market), r is the return on sales (40—15 %);
— operating profit tax, Np = (P — Nfa)yp (yp is the tax rate on operating profit: 20 % in budgets of two levels is equal to 2 % + 18 %) [14];
Table 2
The initial economic parameters of three similar metallurgical enterprises that manufacture steel sheets [13]
Parameters in mln $ USA JSC «MMC» JSC «NLMC» JSC «Severstal»
Cost of equity capital, A in 2006 (19.04.2006) in 2002 7892.94 725 1o.9 (1o.1) 13964.22 1575 8.9 (9.8) 7452.8o 1214 6.1 (11.3)
Sales value, Vsv, $/year 538o.oo 17o7 3.2 4468.73 1322 3.4 5o55.17 1747 2.9
Return on sales, r = P/V ■ 100 % 24.6 % 15.7 % 1.6 41.6 % 23.9 % 1.7 35.2 % 17.7 % 2.o
Net profit, P0 947.oo 179.2 5.3 1385.34 2o7.3 4.7 1212.oo 19o.9 6.4
— fixed assets tax, Nfa = yfaUfa (y/a is the tax rate on fixed assets: 0—2.2 %) [14];
— planned net profit, P0 = (P — Nfa)(1 — yp);
— operating costs, Coc = Vsv — P;
-balance cost of fixed assets, Ufa = Co/k (k is the business characteristic, for metallurgical enterprises k = 0.5);
— depreciation of tangible assets, Cdt = aUfa (a is the depreciation rate of tangible assets: for a>f a should be greater than ^fa);
— amortization of intangible assets, Cai = pUia (P is the amortization rate of intangible assets: as rule PUfa = (P — P0), then p = (P — P0)/Um);
— balance cost of intangible assets, Uia
(Um = U
fa(ia)
Ufa, where Ufa(ia) is the fixed assets estimated by income approach); — net income, D = P0 + Cdt + C^.
Graphical interpretation of parameteric equation (14) developed on the basis of the Pythagorean Theorem [15, 16].
Eqs. (10) and (11) will be written in the form:
F
(GW,)2 + D2 Q2
Ufa + (GoW 0)2
= 1,
= 1.
(17)
(18)
Consequently, Eqs. (17) and (18) may be equated:
Q2
V2
Ufa + (GoW o)2 (Go Wo)2 +
Do2
Table 3
The analysis of the parameters of the enterprise on the basis of Eq. [14]
JSC «MMC» JSC «NLMC» JSC «Severstal»
cost oi equity capital
on stock market, mln $ 2002 2006 2002 2006 2002 2006
725 7892.94 1575 7892.94 1214 7452.80
Sales value, Vsv 1707 5380.00 1322 4468.73 1747 5055.17
Q = Ufa + GoWo 4296.33 11884.57 3090.4 6853.52 4274.1 9597.87
V = VJQ 0.40 0.45 0.43 0.65 0.41 0.53
G. WQ 1334.33 3771.43 990.40 2411.85 1334.10 3046.45
Balance cost, Ufa 2962 8113.14 2160 5519.42 2940 6551.42
k = G0 Wç/Ua 0.45 0.47 0.46 0.44 0.45 0.47
Net income, D0 242.2 1154.15 285.1 1578.52 293.8 1441.31
^ = VS/GQWQ 1.28 1.43 1.42 1.85 1.31 1.66
Y = (GQWQ+DQ)/VsV 0.92 0.92 0.92 0.89 0.93 0.89
m = Dq/GQWQ 0.18 0.30 0.30 0.65 0.22 0.47
m = Do/Ufa 0.08 0.14 0.13 0.29 0.10 0.22
vv = (k + m)/(k + 1) 0.38 0.42 0.42 0.53 0.40 0.48
Unit costs, W, $/r 143.8 122.7 151.3
Constant of business
k = G.Wo/Ufa 0.49 0.47 0.49
V = Vsv/Q 0.42 0.43 0.37
m = D0/Ufa 0.10 0.13 0.10
Conclusion. Parametric analysis of the operation cycle of the ideal manufacturing and technological system allowed to formulate an integrated set of criteria for innovative tasks of an engineering business.
The integrated set of similarity criteria has the form:
1. S = Vsv / Q < 1 is the conversion criterion
of the operation cycle in the ideal manufacturing and technological system equal to the ratio between the sales value of products and services sold and the cost of manufacturing capital. The conversion criterion of a real operation cycle is less than 45 %. V
2. X = —< 2 is the criterion of
GqW.
capitalization of the operation cycle equal to the ratio between the sales value of products and services sold and the direct technological costs. Its numerical value cannot be more than 2 in an ideal operation cycle. The criterion of capitalization of a real operation cycle reaches only 1.5.
3. M = D0 / U < 1 is the criterion of capital maintenance adjustments equal to the ratio between the net income and the balance cost of the summation of tangible and intangible assets. The numerical value of this criterion for the operation cycle in an ideal manufacturing and technological system equals one. As a rule, intangible assets do not exist in the structure of manufacturing capital or their amount is very small; therefore M << 1.
Eq. (19) in a dimensionless form is the following:
VV = (GQW,)2 +D02 Q2 Ufa +(GqWQ)2 '
(20)
If Vsv/Q = v is the conversion coefficient, k = G0W0/Ufa is the characteristic of business, D0/Ufa = m is the coefficient fixed assets maintenance, then the equation (24) will have the form:
[ (Q )]2 = (GqW,)2 +[Dq(U )]2
if (GqWq)2 = [Dq(U )]2 (25)
then 2[Dq(U)]2 = [[(Q)].
V2 D02 (G0W0)2 U2 Q
Fig. 3. Graphical interpretation of the operation cycle of the ideal manufacturing and technological system
4. u = —— < 1 is the criterion of net income
W
equal to the ratio between the net income and the direct technological costs. The criterion cannot be more than one for a real operation
cycle in a manufacturing and technological system.
Every criterion in this integrated set may change simultaneously when any innovation is implemented in the manufacturing and technological system.
REFERENCES
1. Ilin V.P. Lineynaya algebra: ot Gaussa do superkompyuterov budushchego. URL: http://www.web citation.org/6GVpuiIrY (data obrashcheniya: 04.03.2016). (rus)
2. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. M.: Nauka, 1968. 399 s. (rus)
3. Krasnov M.L., Kisilev A.I., Makarenko G.I. Vektornyy analiz. M.: Nauka, 1978. 160 s. (rus)
4. Zherebov E.D., Babkin А.В. The technique of formation of the production program at strategic planning of development of the industrial enterprise. St. Petersburg State Polytechnical University Journal. Economics, 2009, no. 4(81). рр. 145-150. (rus)
5. Arena. The ABCs of Engineering Change Orders. Online Article, 2013. URL: http://www.arenasolutions. com/resources/articles/engineering-change-order (accused August 22, 2013).
6. Ivanova V.S., Balankin A.S., Bunin I.Zh., Oksogoyev A.A. Sinergetika i fraktaly v materialovedenii. M.: Nauka, 1994. 384 s. (rus)
7. Kapitsa S.P., Kurdyumov S.P., Malinetskiy G.G. Sinergetika i prognozy budushchego. M.: URSS, 2003. 288 s. (rus)
8. Khaken G. Sinergetika. M.: Mir, 1980. 406 s. (rus)
9. MSFO FM [elektronnyy resurs] URL: http://ms
fofm.ru/ (data obrashcheniya 04.03.2016). (rus)
10. Shichkov A.N., Kremleva N.A., Borisov A.A.
Innovation and innovating management for engineering business. Ed. by A.V. Babkin. St. Petersburg, Izd-vo Politekhn. un-ta, 2015, pp. 614-630. (rus)
11. Shichkov A.N., Kremleva N.A., Borisov A.A., Polovinkina V.D. Management Accounting of Cost of Innovative Business of Municipality: basic terms, concepts and definitions. Ed. By A.V. Babkin. St. Petersburg, Kult-inform-press, 2015, pp. 392—412. (rus)
12. Yegorov V.N. Razrabotka ekonomicheskikh mekhanizmov innovatsionnogo razvitiya derevopererabatyvayushchego predpriyatiya: avtoref. dis. ... kand. ekon. nauk. M., 2008. 22 s. (rus)
13. Kolokolnikov O.G. Antikrizisnoye upravleniye i proyektirovaniye organizatsiy na osnove innovatsiy: avtoref. dis. ... kand. ekon. nauk. SPb., 2007. 22 s. (rus)
14. KonsultantPlyus. URL: http://www.consultant. ru/document/cons_doc_LAW_28165 (data obrashcheniya 04.03.2016). (rus)
15. Yelenskiy Shch. Po sledam Pifagora. M.: Detgiz, 1961. 487 s. (rus)
16. Littsman V. Teorema Pifagora. M.: Gos. izd-vo fiz.-mat. lit., 1960. 115 s. (rus)
СПИСОК ЛИТЕРАТУРЫ
1. Ильин В.П. Линейная алгебра: от Гаусса до суперкомпьютеров будущего. URL: http://www.web citation.org/6GVpuiIrY (дата обращения: 04.03.2016).
2. Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. М.: Наука, 1968. 399 с.
3. Краснов М.Л., Кисилев А.И., Макаренко Г.И.
Векторный анализ. М.: Наука, 1978. 160 с.
4. Жеребов Е.Д., Бабкин А.В. Методика формирования производственной программы при стратегическом планировании развития предприятия // Научно-технические ведомости Санкт-Петербургского государственного политехнического университета. Экономические науки. 2009. № 4(81). С. 145-150.
5. Arena. The ABCs of Engineering Change Orders. Online Article, 2013. URL: http://www.arenasol utions. com/res ources/articles/engineering- change - order (accused August 22, 2013).
6. Иванова В.С., Баланкин А.С., Бунин И.Ж., Оксогоев А.А. Синергетика и фракталы в материаловедении. М.: Наука, 1994. 384 с.
7. Капица С.П., Курдюмов С.П., Малинецкий Г.Г.
Синергетика и прогнозы будущего. М.: УРСС, 2003. 288 с.
8. Хакен Г. Синергетика. М.: Мир, 1980. 406 с.
9. МСФО ФМ. URL: http://msfofm.ru/ (дата обращения: 04.03.2016).
10. Шичков А.Н., Кремлева Н.А., Борисов А.А. Реструктуризация экономики: теория и инструментарий: монография / под ред. А.В. Бабкина. СПб.: Изд-во Политехн. ун-та, 2015. С. 614-630.
11. Шичков А.Н., Кремлева Н.А., Борисов А.А., Половинкина В.Д. Инновации и импортозамеще-ние в промышленности: экономика, теория и практика: моногр. / под ред. А.В. Бабкина. СПб.: Культ-информ-пресс, 2015. С. 392—412.
12. Егоров В.Н. Разработка экономических механизмов инновационного развития деревопере-рабатывающего предприятия: автореф. дис. ... канд. экон. наук. М., 2008. 22 с.
13. Колокольников О.Г. Антикризисное управление и проектирование организаций на основе инно-
ваций: автореф. дис. ... канд. экон. наук. СПб., 2007. 22 с.
14. КонсультантПлюс. URL: http://www.consul tant.ru/document/cons_doc_LAW_28165 (дата обращения: 04.03.2016).
15. Еленьский Щ. По следам Пифагора. М.: Детгиз, 1961. 487 с.
16. Литцман В. Теорема Пифагора. М.: Гос. изд-во физ.-мат. лит., 1960. 115 с.
SHICHKOV Aleksandr N. - Vologda State University.
160000. Lenina str. 15. Vologda. Russia. E-mail: shichkov-an@yandex.ru
ШИЧКОВ Александр Николаевич — заведующий кафедрой Вологодского государственного университета, доктор экономических наук.
160000, ул. Ленина, д. 15, г. Вологда, Россия. E-mail: shichkov-an@yandex.ru
KREMLYOVA Nataliia A. — Vologda State University.
160000. Lenina str. 15. Vologda. Russia. E-mail: kremleva-n@yandex.ru
КРЕМЛЁВА Наталия Анатольевна — доцент Вологодского государственного университета, кандидат экономических наук.
160000, ул. Ленина, д. 15, г. Вологда, Россия. E-mail: kremleva-n@yandex.ru
BORISOV Aleksandr A. — Vologda State University.
160000. Lenina str. 15. Vologda. Russia.
БОРИСОВ Александр Алексеевич — доцент кафедры управления инновациями и организации про-изводсва Вологодского государственного университета.
160000, ул. Ленина, д. 15, г. Вологда, Россия.
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