Ñîâðåìåííûå èíôîðìàöèîííûå òåõíîëîãèè/1. Êîìïüþòåðíàÿ èíæåíåðèÿ
cand. tech. sci. Semakhin A.M.
Kurgan State University,
Russia
MATHEMATICAL
MODEL OF INFORMATION SYSTEM IN COMPLETE STATEMENT OF THE PROBLEM
In case of deficiency of resources the
mathematical model has the inadmissible decision and the system of restrictions is
not compatible. For elimination of a problem formulate a
problem in complete statement. In mathematical model add a new variable /1/.
The mathematical model of a choice of the
project satellite Internet looks like corporate information system
under restrictions (1)
where is a target parameter, unit of
measurement;
is investment
expenses of i project in j period of time, million. roubles;
is available means of
financing in j period of time, million. roubles;
is a share of financing of the
investment project;
is a number of the
investment project;
is a number of the
period of time, year.
Let's assume, that
the total share of financing should be not less sizes .
The mathematical
model in this case looks like
under restrictions (2)
Table 1
The optimum decision of mathematical model in complete statement of a
problem
Variable |
Size
of variables |
Dual
estimation |
Extremum
of criterion function |
|
0,4838 |
0,0000 |
0,85 |
|
1,0982 |
0,0000 |
|
|
0,1279 |
0,0000 |
|
|
0,0000 |
0,1083 |
|
|
0,0000 |
0,2086 |
|
|
0,8547 |
0,0000 |
|
|
0,0000 |
0,0779 |
|
|
0,0000 |
0,0395 |
|
|
0,0000 |
0,0766 |
|
|
0,5316 |
0,0000 |
|
|
0,0000 |
0,5000 |
|
|
|
|
The mathematical
model has the inadmissible decision since the system of restrictions is incompatible.
Pass to mathematical model in complete statement. Enter the additional variable
, defining a share of financing, which can be executed at available
means of financing.
The mathematical
model in complete to statement of a problem looks like
under restrictions (3)
Table 2
The optimum decision of a problem
Variable |
Size
of variables |
Dual
estimation |
Extremum
of criterion function |
|
0,4838 |
0,0000 |
0,99 |
|
1,0982 |
0,0000 |
|
|
0,1279 |
0,0000 |
|
|
0,0000 |
0,1259 |
|
|
0,0000 |
0,2426 |
|
|
0,9938 |
0,0000 |
|
|
0,0000 |
0,0906 |
|
|
0,0000 |
0,0459 |
|
|
0,0000 |
0,0890 |
|
|
0,5316 |
0,0000 |
|
|
0,0000 |
0,5814 |
|
|
0,0000 |
-0,5814 |
The optimum
decision of mathematical model in complete statement of a problem is resulted
in table 1.
Projects 1, 2 and 3 are financed. Shares of financing 0,4838, 1,0982, 0,1279
accordingly.
The final share of financing makes 85 %. We shall increase scheduled
value of a total share of financing on 0,85 and we shall substitute
in complete model. The optimum decision is resulted in table 2.
Variable is approximately equal 1. We
shall replace in mathematical model (2) in the fifth restriction the right part
on 1,7 and we shall find the optimum decision. The optimum decision is resulted
in table 3. Projects 1, 2 and 3 are financed. Shares of financing 0,4979, 1,0702
and 0,1318 accordingly. Projects 4 and 5 are not financed. The maximal value of
criterion function (net present value) 1,7349 million roubles is equal.
Table 3
The optimum decision of a problem
Variable |
Size
of variables |
Dual
estimation |
Extremum of criterion
function NPV, million roubles |
|
0,4979 |
0,0000 |
1,7349 |
|
1,0702 |
0,0000 |
|
|
0,1318 |
0,0000 |
|
|
0,0000 |
2,0675 |
|
|
0,0000 |
1,6790 |
|
|
0,0000 |
0,2490 |
|
|
0,0000 |
0,4667 |
|
|
0,0608 |
0,0000 |
|
|
0,5562 |
0,0000 |
|
|
0,0000 |
0,7584 |
The mathematical
model in complete statement of a problem allows to define the greatest possible
percent of financing at available money resources.
References:
1. Kochkina E.M., Radkovskaya
E.V. Methods Of Research And Modelling Of National Economy. - Ekaterinburg,
Publishing house Ural State Economic University, 2001. - 93 p.