8.
Mathematical methods in economics.
Doctor of Science Pistunov IM
State Higher Educational Institution
"National Mining University"
Research
and development of methods to reduce energy consumption Closed Joint Stock
Company "Erlan"
The work developed economic model selecting optimal heating of
industrial facilities to reduce energy consumption.
To construct a mathematical model of optimization criteria have been
established, the analysis of the most important characteristics of the
components of the heating system, normalized variables of the object, the
analysis of the criteria for the final model limitations.
Mathematical
model
(1)
(2)
(3)
mi,
- each type of equipment through ³ = [1;8]; n – the number of types of equipment, n = 8, ѳ – unit
price of equipment i-th type, ̳ –power equipment i-th type, CP³ – coefficient of performance i-th type of equipment, Ñå
– electricity tariff, UAH. / Wt, à – utilization of power equipment
Application of criteria in the
construction of a linear function
(4)
(5)
– ³-th criterion
problem; 
- the optimum criterion; 
- normalized value
criterion.
An
analysis of the calculations this method optimal set of heaters is 86 pieces.
heat fans TCC TV 01-30 and 2 pcs. industrial infrared heaters Frico IR45 total
cost of 70200 USD.
Application
of the guaranteed result 
, 
.
The results of calculations of the system by this
method coincide with those obtained at maximizing the second criterion. That
is, the heating system is composed of 166 pieces of equipment.
Application of normalized convolution of partial
criteria
(6)
The results of calculation and the amount of
equipment-type coincide with the results obtained using the method of
guaranteed results:
In the calculations for different options
coefficient significance criteria were also obtained similar results heating
industrial premises.
Application of converting one of the criteria to
limit
(7)
Calculations heating different values of the
coefficient of power equipment
Determination of Pareto-optimal solutions
²íø³ mi = 0.
Given the condition of the equipment in the system must be of the same
type, the number of heaters define a model. Because of the solution x5 = 83, x6
= 4, it is acceptable for the company to purchase and install 88 units. Thermal
models of industrial fans TCC TV 01-30.
Calculating economic impact the introduction of new heating industrial
premises
Indicator heating facilities old heating facilities
Electricity consumption per month, W 264 000 434 783
The cost of electricity consumed, rub. / Month. 41 817.6 68 869.62
The cost of the new equipment is 70 400 UAH. taking into account savings
from reduced power consumption of the equipment payback period is 3 months, ie
one heating season.
Thus, the technique of saving in the next season will increase revenue
by 27 thousand UAH.