CC BY
27
UDK 65.147
Yurkov N.K., Mednikov V.I.
Penza State University
NEW APPROACH TO ENTERPRISE SAFE MANAGEMENT SYSTEM CREATURE
Summary. The article describes new approach to enterprise safe Management system creature based on its functions and recourses multilevel decomposition. Main interrelated indicators content was formulized.
Key words: market, safe Management, downturn, risk, thread.
Initial orientation. Nowadays neither progressive states nor protection branch theory haven't had justifiable ways to resolve the enterprises' problems ring "Non-competitive products - Enterprises' low-income - Small budget revenue - Insufficient budget funding for education -Poor training - Non-competitive products". These challenges are forcing control theory and practice to find eligible approaches to resolve some of these problems or to find the "Ariadne's thread" in order to gradually unravel the entire ring. Unfortunately contemporary theory and practice use particular criterions owing to what economic, information, internal, fair, external safety, physical protection and others take place and growth. Enterprises perform fundamental function in every state economic system and produce the significant part of gross domestic product. Because of it enterprises safe Management effectiveness is the subject of meticulous attention in our devising.
We are interested in two kinds of enterprise interactions: "market" and "influence" (Fig.1). Influence is unidirectional purposeful resources interaction, where one participant's resources carry out an un-authorized impact on the other participant's resources; herewith Earthquake and other "acts of God" are examples of un-authorized, but purposeless impact processes.
Fig.1. Two kinds of enterprises' interactions - market and influence;
unidirectional arrow indicates influence.
Market is two directional purposeful participant's recourse interaction - its exchange; herewith both directions are compulsory and simultaneous. Enterprise 2 represents the ambient of enterprise 1 in "market", i.e. its external environment.
Management performs the enterprise control in "market" by means of authorized influences on internal resources. Hence impact on the enterprise is an un-authorized control which performs by means of un-authorized influences.
Known math models define different enterprises, for example, BSC, as aggregations of processes, indicators, properties, resources and so on because of unresolved root problem: formalization of enterprise activity, of ambient activity (other enterprises represent an ambient) and of their interactions.
Unresolved problem of enterprise activity formalization has lead to appearance and growth of such areas of safety as economic, internal, communicatory, fire, environmental, external, information, etc.
We put emphasis on requirements to enterprise model as follows: scalable; assumption of resources non-stationarity or its dependence on external processes; the processes inertia reproduction in different details; possibility to find consistent estimations of enterprise's activity and resources.
New approach to Enterprise activity model creature. Most developed approaches to enterprise activity modeling use such indicators as geographic territory, where capital-intensive productions are located (physical protection [1]), or financial indicator (BSC [2]), or some defined internal potential (Miripolsky's model [3]).
Against these approaches we pursue the development way, which uses "function" as the indicator for enterprises description. Based on hierarchy structure of all Management systems, which haven't canceled so far, we avowed reasonable to use functions and seven resource components for enterprise decomposition, its ambient (environment) and their interactions decompositions (Fig. 2). The decomposition made it possible to refuse its industrial classification (defense, educational, social, etc.) and with that to describe it completely. Based on their decompositions we get their informative models.
Fig. 2. Four levels of participant (enterprise) functions and resources decomposition, where denoted functions: Assg. - assignment;
Cntr. - control; Supp. - supporting; Prot. - protection; Guar. - guard;
Coun. - counteract, and denoted resources: C. - communicative; Te. -technical; Env. - enterprise internal environment; Mo. - financial; Hu. -human resource; Ti. - resource of time; Pr. - protection.
Before the participant interaction math model building the compulsory decomposition of its functions and resources required. The lower decomposition levels the easier the complexity of
recourse and function components. The possibility for vertical decomposition in form of hierarchy set of these independent recourse and function components results from absence of these components cohesion on every level. These components independence is a consequence of:
1) self-dependence every of each;
2) internal process specialization every of each;
3) structure separateness every of each.
Our practice shown that different participants' decompositions usually have up to 4 levels (profiles) - "Branch", "Assignment", "Functional" and "Atomic". Examples: vertical holding
have four levels; retailer, agricultural enterprise or horizontal holding have the only two. The atomic (lowest) level represents prime processes which single human performs; herewith a human is an accounting unit of participant's human resource.
Every enterprise decomposition level has a quantitatively defined own amount of "manufacturing cycle" (MC). During this cycle participant manufactures (creates) some part of its activity main indicator in real or in value term. Thereby enterprise is replaced by its own equal multilevel internal environment which manufactures activity main indicator or its components.
During the formalization attempts we established that queuing theory, scheduling theory and game theory use "pure", i.e. full protected, enterprises and their interactions. Because of it these instruments were avowed as no applicable ones for the root problem resolve.
We have found the rational fractions are the most appropriate instrument for fulfilling specified (see above) including especially inertia.
Based on it participant's math model is represented by expression pypj sl+p: s: + ...+pnSn ts) =----------—^------------+ V (s)
г. 4- r. el -I- tv 4* 4- 4- r sn
where f(s) - production function on some level; pi - facts of main activity indicator realization; n - dimension of reference interval of time nAt; At - elementary interval of time; ri - facts of internal resource usage in order to manufacture pi; every ri is represented by column matrix [7 x 1], where 7 - number of resource components of ri (see Fig. 2); s = Re + jIm; Re - abscissa of absolute convergence; Re and Im - arguments (in this case orthonormal basis
exp(jnAt/T) of Laplace transform was used); 9(s) - Laplace transform of participant activity initial conditions, which include capital, territory, etc.
If we use a value terms for enterprise definition, rational fraction f(s) is right; if we use natural (real) terms, this fraction is improper. The model f(s) is sufficient for quantitative fulfilling the term "transparency of the company"; f(s) was used to base and to choose criterions and to find participants' activity estimations during two kinds of interactions we are interested in.
New safe Management system. Based on plenty publications we created the cognitive enterprise behavior model (Fig.3), which pertained and was invariant in Teacher's modeling, in combat vehicles or in religious conflicts, etc modeling. Crisis mechanism (see beneath) in enterprise economy was defined by using this model.
Fig. 3. The enterprise activity cognitive model. The model elements Functioning, Storing, Perception, Protection, Comparison represent internal processes. Other enterprises represent enterprise external environment or ambient.
This model confirmed that enterprise protection is as its inherent resource as inherent function. The features of Teacher's behavior and others' ones named above (ethical preferences, age manners, moral values, combat vehicle technical dates, etc.) locate in element "Storage" and define specific of their behavior, i.e. their functions performance. Owing to the cognitive model noted above well known BSC model in authors' terms is as show on Fig.4.
Pursuing enterprise multilevel decomposition (Fig.2) we modified BSC on Fig.4. It was transformed into model shown on Fig.5. Enterprise protection consists of selection and localization every influence and of counterwork against every influence, impact or attack on enterprise's resources.
Our judgments above show: owing to decomposition Management has possibilities to task every functional component and to check this task execution. These possibilities have changed enterprise's control:
made it possible to find reasons of impermissible influences to main activity indicator more precisely and to form adequate measures (including measures of precautions) for these reasons counteraction, owing to what
made it possible to select and localize un-authrised influences to enterprise recourses so made multilevel BSC-control more sensitive.
Fig.4. BSC-model in authors' terms.
Fig.5. BSC-model in enterprise multilevel decomposition terms; in this case "Environment" is market of BSC-enterprise products.
Structure realized multilevel enterprise protection and control shown on Fig.6.
This structure substantial distinction is as follows: every cell on every level has detached structure, purpose and process, communicates with level processor unit PU by CDDI protocol. These properties provide safe Management system reliability which approximately equal to the one of the single cell. Another difference is that structure has interfaces with bookkeeping accounts, with all internal processes and with activity main indicator P during enterprise's interactions in "market" or in "influence". The enterprise protection function (system) consists of two functions (subsystems) (Fig.2): guard (it has efficiency Eguar.) and
counteraction (it has efficiency Ecount.).
where denoted p - enterprise activity main indi
structure cator; f£
(template),
■,sg. (s) - level
assignment functions performing; p - decision concerning r on level; pstndr -
standard amount of p(s) on level chosen; r - level resources; "Branch", "Assignment", "Functional", "Atomic" are levels of enterprise this system.
The structure on Fig.6 consists of elementary protection and control cells shown on Fig.7. This cells' structure belongs to class of control systems with standard models. Substantial distinctions of the cell from known are as follows: 1) there is a check unit ("guard boundary") in input of element "+"; 2) authorized influences on any resource are, figuratively, "painted", so every cell distinguishes authorized influences on resources and its authors from un-authorized ones which are "no-painted". Besides the awesome cell property is adaptability we needed.
Control of performing function fasSg.(s) on some level bases on, for example, linear measure [p(s) - pstndr.(s)] usage, where pstndr.(s) is standard (paradigmatic) amount of p(s). Authorized influence uses this measure amount for decision about change Ar in resource [r(s) + Ar] (see control element p on Fig.6 and Fig.7) . In such a way control loop in the parameter p(s) is closed on the level you chosen.
Every cell of the structure on Fig.6 analyzes m attributes di (i c [1, m]) of influence on resource, including all pertinent Managers' digital signatures. In general case these attributes have different importance for control or flow of documents hence for enterprise activity. Thanks to these attributes the "guard boundary" into elements "+" makes decision eUa. concerning "authorized or not" influences in accordance with criterion, for example,
eua.=di &d2&d3&-&dm=1.
This method reduces the probability Pua i of un-authorized influence on resource to a value, equal to multiplication nPuai, where i c [1, m], Puai - un-authorized influence probability defined by using each attribute d± in contemporary enterprises' protection and control systems.
Fig.7. Structure of cell of enterprise safe Management system, where resource r(s) is represented it's components denoted: rc. - communicative; rte. - technical; renv. - enterprise internal environment; rmo. - financial; rhl!. - human resource; rti. - resource of time; rpr. - protection;
Ar -change in resource r(s); f&ssg.(s) - assignment function; p(s) - activity main indicator or its component; Pstndr.(s) - standard amount of p(s); p - decision concerning Ar.
Each cell performs its specific function fassg. (s), which was formalized as P0i+PnSiI + - + PniEin
£-*» =-------------------------
+ ri 1 311 + ■ ■ ■ + rE 1 3jT)
where Eg
guard subsystem efficiency and Ec
(2)
counteraction
subsystem efficiency
(see above) . The control function fc:
(s) of the "atomic" or other levels was formalized as
where patom‘ - authorized control influence on the resource; [ri] - resource amount (in form of column-matrix for every si) of the function fassg.(s) performing; k - quantity of cells, which are specified by the responsibility of the level Manager (Fig.8). This way we can formalized top Managers' function with their behavior preferences or features (element "Storing" on Fig.3).
Fig.8. Manager control function realization on "atomic" level.
Useful fact is as follows: multilevel enterprise decomposition has disappeared a lot of ways for unauthorized (impermissible) influences on its activity and coincidently has opened a lot of ways for enterprise protection.
Some enterprise activity estimations. Dynamic criterion of participant success in market is the scalar
P/MCproduser = P/MCconsumerf (4)
where P is an amount of product, which "Producer" has manufactured; MC - participant's manufacturing cycle; "producer" and "consumer" - indexes relatively "Producer" or "Consumer"; dynamics P/MC may be quantitatively equal, for example, (1 - 2) % a year. If we use dynamic criterion, we describe the participant activity on short interval of time ("under magnifying glass"), so we must use the dynamic programming.
In order to account for purposes of every participant interactions, vector criterion was used. This is conjugacy of collinear combined dynamic vector (P/MC)producer and dynamic vector
(P/MC) customer .
The procedure of selection and localization un-authorized influence on participant activity in market or in influence was realized by means of rectangular window, which is sliding on the process p(t) by computing d2p(t)/dt2.
Crisis mechanism in enterprise economy [4] was defined by using cognitive model (Fig. 3). Recession or downturn in "Producer's" activity appears and continues if it couldn't receive enough resource "Mo." (Fig.2) in order to buy all resources needed to manufacture products P in next MC. This is necessary "Producer" crisis condition, i.e. the scalar MCproducer < MCconsumer. "Consumer" has downturn too if condition MCproducer > MCconsumer occurs. Because MCconsumer is usually lengthening gradually, "Consumer's" effective dynamic is falling, and when MCconsumer=1,5MCproducer, "Producer" gets "downtime" as a result. It occurs when (P/1,5MCproducer)MCproducer=0,67 P (pay attention to Fig.8).
Crisis sufficient condition differs from enterprise to enterprise and from branch to branch. We have found this condition for average enterprise-producer in such form:
Recession length / MCproducer. c (2; 1600). (5)
"Impact Equation" is Pua(s) = vuar(s)f(s), where Pua(s) - amount of the main activity indicator as a result of un-authorized influence to resource; "ua" means "un-authorized"; vUa - variation, i.e. impact; r(s) - resource or resource component was impacted; f(s) - function performing.
"Based safety equation" in "Influence" is as follows:
ppr.(s) = auavua f(s) r(s), (6)
where aua - anti-variation against vua , i.e. counteraction un-authorized influence vua. We have set un-authorized influences vua on resources may already now be put in analytical form into "main safety equation".
factor, was defined through effectiveness Eguar. of "Counteraction" function (Fig. 1)
risk = (1 - Eguar.Ecount), (7)
enterprise activity, including subjective Guard" function and effectiveness Ecount. of
th (1 Eguar.Ecount. ) thresh. , (8)
where the threshold (thresh) is established statistically or set by expert way, or by calculation.
We recognized Risk and Threat competent to spread on enterprise influences on "itself".
The relation between resource protection effectiveness Eprot., their informative manifestation Kinf. and resource perviosness PN of un-authorized influences was formalized by equation
Eprot. = (1 - Kinf.)Eguar.(1 - PN)Ecount. . (9)
Resource informative manifestation Kinf. represents the description method or existence mode, etc. of enterprise resource material or tangible manifestation; pertinent example: apartment
price. Resource perviosness "PN" of un-authorized influences from the outside characterizes every resource internal property to resist these influences, or not to be subject to impacts, or no perceive these influences, impacts, etc.
Conclusion.
The material above represents interrelated quantitative relationships, "based safety equation" and terms contents concerning new approach to enterprise safe Management system creature. We have found certain ways of this work further development.
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