Современные информационные технологии/1. Компьютерная инженерия

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.