Page 11 - Azerbaijan State University of Economics

Adalat Muradov, Nazim Hajiyev, Safwan Al Salaimeh, Salim Istyaq: Software Design for
Integrated Computerized Management Systems

In most cases production functions is system static models; for their synthesis and
analysis are accepted methods of mathematical statics, integral and differential
calculus. Balance models using linearity and independent factors i.e. (∑ ) =
/
/
∑ ( );
/
/

Example of balance models are models binding qualified sources of resources and
production capacity and loading equipment. They are given by a system of linear
equation
BBBBBB
− ∑ 0 = , = 1, . for example: inter branch balance can be described
/
/
.62
/. .
by this balance mode, here xi – number of products, produced by branch; yi –
number of products reaching for domestic consumption; aij – number of products i-
th branch; that goes for production in j-th branch; aij, xj – the total number of
products i-th branch.

This model is valid for many kinds of resources and production levels. Balance
model can be transformed into a linear programming problem, for example- cost
minimization for movement of goods from one branch to another. To solve these
problems accepted theory of mathematical statics and linear algebra.
Model exchange plan formed as a optimization for example: the problem of
formation of production program of the enterprise, known range of products ( =
BBBB
, ) , the value of the party xi; limit j-th recourse; Aj- profit per unit i-th product ci.

Must maximize the total profits of the enterprise

∅( ) = ∑ →
/
/ /

BBBB
under the constraints: resource ∑ J ≤ , = , on the technical and
/
/
H
/62
economic indicators ∑ J ≥ ;
/L /
L
/62

S
for the production of products ≤ ≤ , where Tif – during operation time of
/
/
R
equipment, f-th type, necessary for the production of one product i-th type, Bf – fund
operating time of equipment f- th group; F- the number of groups of equipment; Cif
–p-th technical and economic characteristics i-th type of products; Zp – required
level p-th of technical and economic indicators; and – number of products,
/
/
determined in accordance with demand and the higher authority.

Mathematical apparatus synthesis models exchange planning is linear and integer
programming. Exchange model used for an overall schedule planning, taking into
account the load of each workplace impossible to implement of high – dimensional
problems must be enlarged intermediate planning, which are designed to coordinate
all services of the enterprise. Its purpose – distribution of the production program for
11