ÓÄÊ: 656.615:004.272
Arsenyev Yu.N., Davidova T.Y.
OPTIMIZATION APPROACHES TO INVESTMENT
INTO THE INTELLECTUAL CAPITAL IN REGION, PROVISION OF SECURITY, QUALITY AND
RELIABILITY OF ENTERPRISES OPERATION
The territorial branch of the ARDIFE
in the town of
Tula State Teachers’ Training
University named after Leo Tolstoy
Consideration of the models of
optimization of investicial and financial objects
with an illustration then on concrete examples are considered, optimization
approaches to the utility value and assessed value of investmentinto
the intellectual capital of
the region with the multitude of features and alternatives.
Under certain enumeration of development alternatives of the
intellectual capital and economic performances stipulated by them, may emerge
situations of risk (scenario probabilities of process developments are
acquainted), uncertainty (probability values are impossible to obtain) and
obscurity (assertions which can’t unambiguously be assigned to valid or fallible).
By means of methods of information collection, processing, analysis and
predication it is possible to decrease the degree of expectation unreliability,
disbenefit of their consequences. Constructing models
and applying methods of investment estimation it is possible to optimize values
of objective functions taking into account changes of production parameters and
realization of enterprise production or intellectual capital. Alternatives of
changes of intellectual capital and enterprise development may correspond to
various values of objective functions. In cases of undominated
alternatives the choice of the best alternative is advisably to conduct on the
basis of the acquainted criteria [1].
Utility value of alternative solutions risk is mapped by the function of
risk priority, transforming miscellaneous investor’s risk attitude: positive
(convergence to risk), negative (fear of risk) or neutral (indifference to
risk). Under negative risk attitude the investor usually chooses under common
mathematical expectation that alternative which has smaller standard deviation.
As this takes place a part of information is lost, motivating the compilation
of detecting the function of risk priority. Replacing mathematical expectation
and moments of risk of the objective functions (CK) with expected utility
(profit) it is possible to correlate them with objectives, expectation of
degree achievement and accounting investor’s risk attitude. Bernulli’s
criterion is used to estimate the profit of a compromise of possible investment
with the search for the maximum of “moral expectation” for every alternative ,
determining utility function of unreliable results (expectations), for example
CK. In this process the reliable result (equivalent) is found which has similar
profit as two unreliable results and probabilities values of the occurrence of
an event. Utility function in the risk situation evaluates investor’s risk
attitude: under indifferent risk attitude reliable equivalent corresponds to
the value of the result to be expected, under positive (negative) risk attitude
the value of reliable equivalent is higher (lower) than the value of the result
to be expected.
Methods of optimization of investmentfinance include a multitude of
economic, mathematical and applied models. In action widely known models of
taking unit solutions under single objective function (multitude of static and
dynamic models) and programmed universal solutions (classical, technological,
compensatory and uncompensatory, MADMmethods , MAUTmethods, LIMAPmethods and MODMmethods with
programmed multiplelens solution of matters of vector maximum).
In conditions of expectation equivocation the most wellknown methods of
taking investmentfinancial decisions are methods of correction; sensibility
analysis; simulative and sensitive risk; solution trees.
Correction method specifies change in the range of assumed data of the
reckoning of investment (mathematical expectation value is often replaced by
discounts or risk premiums). When using cost of capital value for determining
utility value and risk assessment they raise interest rate or the rate of
current payouts, reduce the rate of current payments or working lifespan. This
guarantees that objective function will reach the maximum with high
probability. The disadvantage of this method consists in subjectivity of
determination and calculation of corrections in the integrated rather than
differentiated given data accounting of unreliability of the expectations and
their consequences.
Sensibility analysis method affords investor decisionmaking to take
into account the link between the assumed data and the values of objective
functions of alternatives, to answer the questions, relating changes of values
objective function under given variation of input quantities as well as
bandwidths where it’s possible to change the values of input quantities under
given worst value or the limit of values of the objective function. Sensibility
analysis is connected with the formation of the decisionmaking model and the
determination of its data, flavor and number of studied input quantities,
valuation of their influence to the end result in one or more periods of
planned interval of time, collation of choice alternatives and their valuations
of relative utility value. At determining relative utility value of investment,
focused on expansion of production they usually evaluate: the complex of
parameters (critical values of purchase costs, sale price of goods, overall
production and volume of sales, fixed costs or variable costs, rates of payouts
and expenses, interest rate, working lifespan, liquidation revenues). When
analyzing the sensibility it is necessary to: determine the values of input
quantities deviations from the assumed data; estimate the alternative values of
input quantities; calculate objective function values on their basis. Planning
production turnout with the overall production, equal to the volume of sales,
market entity chooses from the multitude of investment alternatives labeled by
the set of assumed data and calculates the cost of capital just as CK = A_{0} + ((p_{crit}  a_{vt})x_{t}  A_{ft})q^{t}
+ Lq^{t}, where t – time index; T –
maintenance end; A_{0} – purchase payments; p_{t} – selling
price in the point of time t; a_{vt}
– payments per unit in the point
of time t, determined by the sales(production) quantities; x_{t}
 sales(production) quantity in the point of time t; A_{ft} – payments
in the point of time t unaffected by the sales or production quantities; L
 liquidation revenue; q^{t} 
discount coefficient in the point of time t (q = 1 + i).
Having applied computer modeling CK it’s possible to find the critical
value of the upper and lower limits of the profitability of the best
alternative, its deviation and also its probability – basis for evaluation of
profit or risk of the alternative. Critical selling price is determined as p_{crit} = [A_{0} + (a_{v}x + A_{f})q^{t} + Lq^{t}]
/ xq^{t}].
The deviation of the given combination of values from the values of the
critical function testifies to the dependence of the utility value from the
values of input quantities and their compromise. If the
evaluations of the investment alternatives relative profit are necessary than
it’s more convenient to consider them mutually. Then it’s possible to
determine critical values combinations for every input quantity.
By comparison a range of investment projects it’s possible to find a
critical value CK whereby investment has common value of objective function
with the fixation of spectral band utility value and values of input
quantities. With the aid of critical values or variations of input quantities
values it’s possible to trace the influence of input data on the relative
profit of investment objects under ascendancy of analytical estimations number
[1].
Sensibility analysis method directs statement of costs for a number of
variants of investing production (production purchase) with regard for critical
values of production and expenses, comparison of critical volumes of production
and limits of alternative profitability and the choice of the best variant with
regard for unreliability of expected production volumes.
Decisionmaking algorithm on the basis of the simple risk includes
procedures: formation of decisionmaking
model; determination of probability distribution of unreliable input
quantities; account of the stochastic dependence between unreliable input
quantities; calculation of probability distribution for the objective function;
interpretation of the results. Under probability distribution of individual
input values discontinuous or abrupt distribution is used. Abrupt distribution
is usually applied under given type of distribution with the evaluation of its
parameters (mathematical expectation, standard deviation under normal
distribution, outermost and innermost limits at the triangular distribution).
The determination of probability distribution is sophisticated in case of
single investment. Probability correspondences between unreliable input
quantities are considered in pair or multiple regression coefficient and
correlation and probability distribution of input quantities.
Probability calculation of objective function is carried on analytical
(distribution of its values is calculated from input quantities distribution)
or simulative (multitude of accounts is fulfilled and using the method of
random numbers it’s necessary to choose samples from the probability
distribution of input quantities) method, then multitude of these accounts
gives the distribution of the objective function values. The basis of risk
evaluation is the distribution of calculated objective function values.
Absolute values of separate class frequencies are transferred in relative
values composing the base of probability distribution evaluation, distribution
function or the risk profile of the objective function.
Let us assume that funds are invested into projects A and B (table 1)
for environment enhancement and security assurance of manufacture functioning.
Unreliable input quantities are prices, payouts, operation revenue, production
and fulfillment volumes of A project. These
quantities, excluding production and fulfillment volumes of A
project, have triangular distribution (their distribution parameters – modal
(mod), minimal (min) and maximal (max) value limits are summarized in table 1).
It’s necessary to evaluate the investment risk into these projects. After
having calculated capital cost of projects A and B and constructed distribution
functions CK let us find optimum value of the objective value. Collocating and
pattern of distribution function testifies to average values of the objective
function and their dispersion. Values of mathematical expectation CK, its
standard deviation and negative profit probability (p) of projects A and B duly
comprised: M[CK_{A}] = 10,11 rub.; S_{A}
= 10,045; P_{óÀ} = 0,18; M[CK_{B}] = 9,67
rub.; S_{B} = 6,676; P_{ó}_{B} = 0,08. Investor accounting of the character of the
distribution function and calculated indexes is important for the exposure of
risk connected with investment and negative profit probability and it testifies
about absence of the absolute advantage of the alternatives. Project A has
higher values of mathematical expectation, standard deviation and negative
profit probability than Project B and stochastic domination is missing here.
Sensibility (sensitivity) and investment decisions risk may be evaluated
autonomously and in complex. Complex approach includes the analysis of:
unreliable input quantities and their distribution probabilities; stochastic
interdependencies between unreliable input quantities; input quantities
considered to be reliable.
Under sensitive risk analysis objective function value is given and
later with the help of imitation modeling because of random values of other
unreliable input quantities we calculate the critical value of input quantity
or the compromise of critical values from the input quantities range with the
search of their distribution. In comparison to common analysis of sensibility
sensitive risk analysis is distinguished by the fact that under systematic
variation of input quantities their probability distribution varies and that
gives a multitude of probability distributions of objective quantity and under
compatible analysis we determine critical value distribution instead of
critical value. Having applying for the data from table 1 sensitive risk
analysis method with the value change of the selling prices triangular
distribution (minimal, modal and maximal values) on 10% and 5% under the
constancy of probability distribution of all the other values we obtain selling
prices triangular distribution, values of their mathematical deviation and
standard deviation on the basis of imitation modeling (table 2). Investment
planning based on the solution tree method affords to find optimal decisions at
the beginning of the planned period and successive instants of time accounting
possible environmental conditions and their probabilities. Mathematical
expectation CK value usually arises as objective quantity. As this takes place
a set of decisions given maximum of mathematical expectation of capital cost is
considered to be optimal.
In the large the solution tree method is oriented towards the evaluation
of the flexible models under small number of unreliable quantities and their
values diapason in a single monetary objective function with decision,
containing only expected values of mathematical expectation CK without their
possible deviations. The compromise of sensitivity analysis method and solution
tree method gives additional possibilities of the best decision search under
conditions of uncertainty but under more difficult computer calculations.
Table 1. Indexes of investment projects A and B (thous rub.)
Input
alternative quantities 
Investment
indexes 

project
A 
project
B 

Purchase
payments A_{0} 
130 
95 

Interest
rate i, % 
10 
10 

Liquidation
revenue L 
Input
quantities values 

Min Mod
Max Min Mod
Max 0
20 50 0 12 30 

Selling
price, r, rub. 
92
100 105 
92
100 105 

Payments
for production unit: Independent
from production a_{v}, rub. *
dependent on production A_{f} 
45
50 60 15
16 17 
45 50 60 11,5
12,5 13,5 

Quantity of sales and production x_{t}:  in period t = 1  in period t = 2  in period t = 3  in period t = 4  in period t = 5 
900 1000
1200 950 1050
1150 1000 1100
1200 950 1050
1150 900 1000
1100 
800 8000 800 800 8000 800 800 8000 800 800 8000
800 800 8000 800 
Table 2. Capital
costs of project A realization (triangular
distribution)
Imitation
Circle 
Triangular
distribution parameter Min Mod Max 
Mathematical
expectation CK 
Standard
deviation CK 

1 
82,8 
90 
94,5 

28490 
9,986 
2 
87,4 
95 
99,75 

9374 
10,162 
0 
92 
100 
105 
10208 
10,045 
3 
96,6 
105 
110,25 
29620 
10,253 
4 
101,2 
110 
115,5 
49516 
10,858 
Bibliography
1. Arsenyev Yu.N., Davidova T.Yu. Hybrid intellect systems. Economics. Management. Education.  M.: High School, 2008.  566 p.