Engineering
sciences/12. Automated
control systems in manufacturing process
Ph. D. Borovska
T. N.
Vinnitca National Technical
University, Ukraine
Constructing of
innovative development models
Introduction. Innovative development is proved to be the necessary
condition of survival for production systems of any scale. It is known that
since 80s, Japan has spent on innovations and scientific research fractions of
percent more than the USA. By the year 2000 the USA had abandoned the own
production of some types of electronic equipment, the share of Japanese cars
had drastically grown on the markets of the USA. Today effective innovative
strategy is carried out by the organizations of India and China. Quite natural
practical problem regarding optimal distribution of resources of production
facilities between proper production and innovative developments arises.
Formulation
of the problem, dealing with the elaboration of innovative development models. The purpose of the given research is to elaborate the extended mathematical model of the production system taking into account the development of innovations, creation on their basis of new products and means of production,
manufacturing of the constantly renovated industrial
products on systematically updated production capacities. Classic approach
to the construction of innovative development model – from statistics, experiments, approximations - is unproductive or impractical for the production systems. At the initial stages innovation
does not have any statistics. G. Forrester
offered and realized in simulation models of an enterprise and city another
method of construction of the model of a large system – from credibly revealed
regularities of functioning and development of large systems. Statistics
is applied at the stages of verification of the model.
Ways
of
problem solution. In sufficiently large production systems usually there are subdivisions,
engaged in research and development of new products, technologies and equipment,
subdivisions, engaged in modernization and creation of production capacities,
and subdivisions, producing the finished goods. In the model of the first approximation
we consider the production system, consisting of three subsystems:
"innovations", "development", "production" [1, 2].
In the following approximation it is possible to examine the
"incomplete" production systems, buying the equipment and
technologies, consider the processes of innovations distribution, etc. We
assume the existence in each subsystem of stochastic dependence "resources
– product", average of which is reduced meets to nonstrict
monotonous and nonstrict positive limited dependence - generalized production
function. Choice
of basic model structure of the
production system. In Fig. 1 the diagram of the production system is presented taking
into account its development.
Fig. 1. Diagram of the production system
Basic
model of generalized production function. In the
first approximation we consider the set states of models of functional subsystems
- innovations, development, production. In Fig. 2 an «informative block» – working
mathematical model and results is presented. In the debugged model it is simple
to enter inertia, delay, effects of utilization and saturation of necessities.
The specific feature of manufacturing of «product» in these subsystems is
different, however, general «mechanisms» and properties allow to build basic
parametric model, which can be adjusted on the specific feature of subsystems
of «innovation», «development», «production». Basic model is realized in the environment
of mathematical package
Operators
of parametrical connections in the system of "innovation, development,
production". The most difficult for formalization element of three -level
production system is connections between subsystems (Fig. 1).
Fig.
2. Basic model of generalized production function
To be more precise, it is transformation of the
output of the previous subsystem in the changes of production
function ( PF) of the following subsystem. For example, the subsystem «development»,
having spent dY resources, modified the subsystem «production», that led
(Fig. 3):
- to the increase of production capacity A by dA;
- to the increase of «steepness» of production function a by the value da;
- to the decrease of threshold (permanent) expenses s, by ds.
We will consider the scenarios of realization of the changes of
"production" subsystem: - scenario 1: simple expansion of production
- machine-tools, reactors, workplaces operate in parallel; - scenario 2:
reduction of production expenses - variable and constant without a change of
production capacities.
Fig. 3. Changes of production function of the
developing system
We will consider more suitable for formalization scenario of small continuous
changes. The statement of generalized PF change
can be presented in the form:
where 
, 
are the states
of PF, 
are increments
of PF, 
is an
operator. Complex nonlinear connections of nonlinear systems caused the necessity
of creation of stand for research and better understanding of the essence of
innovative development. Part of stand is presented in Fig. 4.
Generalization of the results.
The problem is solved – basic working model of innovative development of the
production system is constructed. The next stage is to construct on the base of
verisimilar and operational concept a working tool. We will consider the
alternative variants of the programmatic module «chain»:
- 
is a function which takes the functions of
innovations, development, production, total resource and returns the volume of
output of end products and new functions of development and production;
- 
is a function which takes the parameters of
functions of innovations, development, production, total resource and returns
the output of end products and new values of PF parameters. Exactly this function
is used in the example in Fig. 4. On the base of these functions it is possible
to realize: 
optimum equivalent production function of the
system "innovation, development, production", which takes the
structure of vRs, consisting of the
interval of the system resource change, its initial distribution; matrix of
parameters of production functions of subsystems Mpse and a number of steps K,
and returns dependence of end products output of the system on the total
expenses on condition of optimization of resource distribution between
subsystems.
Fig.
4. Stand for the analysis of the system «innovation, development, production»
On the base of function Op3 of
the three-level system it is possible to put forward and solve variational
problem of optimal development during certain planned period. Another direction
of function Op3 application: it is possible to obtain the influence functions of
subsystems «innovation», «development» on the
production.
Referenses
1. Áîðîâñüêà Ò. Ì. Ìåòîä îïòèìàëüíîãî
àãðåãóâàííÿ â îïòèì³çàö³éíèõ çàäà÷àõ: ìîíîãðàô³ÿ / Ò. Ì. Áîðîâñüêà, ².Ñ. Êîëåñíèê,
Â.À. Ñåâåð³ëîâ.
– ³ííèöÿ: ÓͲÂÅÐÑÓÌ-³ííèöÿ, 2009. – 229 ñ. – ISBN 978-966-641-285-3.
2. Ìîäåëþâàííÿ
³ îïòèì³çàö³ÿ ïðîöåñ³â ðîçâèòêó âèðîáíè÷èõ ñèñòåì ç óðàõóâàííÿì âèêîðèñòàííÿ
çîâí³øí³õ ðåñóðñ³â òà åôåêò³â îñâîºííÿ: ìîíîãðàô³ÿ / [Áîðîâñüêà Ò.Ì., Áàäüîðà Ñ.Ï.,
Ñåâåð³ëîâ Â.À., Ñåâåð³ëîâ Ï.Â.]; çà çàã. ðåä. Ò.Ì. Áîðîâñüêî¿. – ³ííèöÿ: ÂÍÒÓ, 2009. – 255
ñ. – ISBN 978-966-641-312-6.