DEVELOPMENT OF THE METHOD FOR TESTING OF EFFICIENCY CRITERION OF MODELS OF SIMPLE TARGET OPERATIONS

If we request such definitions as «efficiency”, and/or its analogs in the form of “KPI”, “BSC” in the search box of any browser, we can get the information array which contains more than 1 billion of the most diverse responses. Whether is it possible to select the index that really can represent the result, declared in the name among the given array of various indices? 11. Anokhin, A. N. The system approach to analysis and description of operator activity [Text] / A. N. Anokhin // Cybernetics and Systems. – 2008. – Vol. 1. – P. 82–87. 12. Адаменко, А. Н. Информационно-управляющие человеко-машинные системы: Исследование, проектирование, испытания [Текст]: справочник / А. Н. Адаменко, А. Т. Ашеров, И. Л. Бердников и др.; под общ. ред. А. И. Губинского, В. Г. Евграфова. – М.: Машиностроение, 1993. – 528 с. 13. Grif M. G. Methods of desingning and modeling of man–machine systems [Text] / M. G. Grif, O. Sundui, E. B. Tsoy // Proc. of International Summerworkshop Computer Science 2014, 2014. – Р. 38–40. 14. Падерно, П. И. Системный администратор локальной вычислительной сети. Задачи, требования, модель, отбор [Текст] / П. И. Падерно, Ф. Э. Сатторов // Вестник академии наук Республики Таджикистан – 2009. – Т. 52, No 6. – С. 437–442. 15. Lavrov, E. Mathematical models for the distribution of functions between the operators of the computer-integrated flexible manufacturing systems [Text] / E. Lavrov, N. Pasko, A. Krybidub, A. Tolbatov // Proceedings of the XIIIth International Scientific Conference TCSET’2016, 2016. – P. 72–77. 16. Lyubchak, V. Ergonomic support of man-machine interaction. Approach to designing of operators’ group activities [Text] / V. Lyubchak, E. Lavrov, N. Pasko // International Journal of Bio-Medical Soft Computing and Human Sciences. – 2011. – Vol. 17, Issue 2. – Р. 53–58. 17. Lavrov, Е. Planning of Group Activity of Маn-Operators in Information Systems [Text] / E. Lavrov, N. Pasko // International Scientific Conference “UNITECH ІІ”. Proceedings. – 2011. – Vol. 1. – Р. 371–376.


Introduction
If we request such definitions as «efficiency", and/or its analogs in the form of "KPI", "BSC" in the search box of any browser, we can get the information array which contains more than 1 billion of the most diverse responses.Whether is it possible to select the index that really can represent the result, declared in the name among the given array of various indices?
As an assessment indicator, it is logical to use an absolute measure "profit" or its cybernetic analog "the added value" (target product).But, one more problem is that the "added value" index needs such restructuring as a result of which the new type of such index will be able to identify certain cybernetic processes adequately.
It is connected to the fact that the functioning of the controlled systems (CS) which generate system operations is carried out in the environment of continuously changing external conditions.
Therefore, to realize verification of indices, relating to the identification of system operations and operational processes, it is necessary to create such models of system processes which display all important characteristics of controlled systems, including prognostic estimates from the use of new investments.
Of course, this task is unsolvable in a general view.However, its successful solution for a number of special cases is quite possible.
For this purpose, it is necessary to develop a system of tests which allow identifying the offered indices regarding the claims declared in the name.Each such test, for example, can represent a couple of operations of a certain class which efficiency shall be set beforehand, based on direct methods of estimation.
Actuality of work in this direction consists that for verification of the indicators declared as the "criterion of efficiency" will be possible to define a set of couples of models of simple target operations (MSTO) of different classes, with in advance known ratio of their efficiency.Thus, it is possible to define as "operability" of this or that indicator within the class of MSTO, from the point of view of an assessment of their efficiency, and its adequacy to the criterion of efficiency in case the developed indicator adequately "works" at the whole range of classes of reference MSTO.

Analysis of literature data and problem statement
The class of absolute indicators which display the measure of its value added occupies a special place among the indicators characterizing the purposeful activity of the controlled system.
Practice shows that the economic «profit» is one of the most important performance indicators of the results of management [1].Another important indicator is the «resource efficiency», or just «efficiency».
Experts in the field of control hold continuous debates concerning what is the entity of this index and what is the ratio and/or relationship between such concepts as profitability [2], result, performance, efficiency, effect, productivity, etc.
Such discussions are in many respects connected to the fact that the index "profit" is used as a universal "tool", without considering the features of those system processes for which assessment it is used.
Considering single-digit compliance of minimum cost to the maximum profit in a number of production operations, the issues of efficiency control are defined as the cost management [3], and optimization problems -as a search of the minimum cost or maximum profit [4].
Nevertheless, a number of works note that efficiency is the synergy effect of profit [5] and therefore, it is necessary to consider the cumulative effect of the profit in the efficiency determination [6].In this regard, the concept "capitalization" is actively used [7].
In the paper [5], the need of creation of the model of the controlled system for the efficiency determination by direct methods on the basis of the index "profit" is marked, in fact, the concept "supersystem" as a management company is introduced.However, the attempt of the development of the direct evaluation method of efficiency doesn`t rely on the basic cybernetic entity "operation", but on the macroeconomic entity "enterprise".
As a result, the indices characterizing both the material, and the parallel cash flows duplicating them, and without considering the dynamics in time are a part of the developed index of efficiency.Now for the efficiency assessment, the independent choice of the criterion of efficiency from a packet of indices which are identified as KPI [8] and further development of this direction in the form of the system of indices BSC [9] is offered to the enterprises.
Numerous debates and publications connected to the development of efficiency criteria and the use of various indices as the criterion of efficiency point to the need for creation of a technique which use will allow resolving the issue of preliminary testing of the developed indices which are positioned as criteria of efficiency.

Purpose and objectives of research
The purpose of the work is the development of a method for testing of criteria of efficiency of models of simple target operations and processes.
Achieving this goal leads to solving a number of tasks such as: -development of a method of an assessment of efficiency of simple target operations with the use of a direct method of estimation of the processes equivalent generated by them from the point of view of efficiency; -definition of classes of models of simple target operations and definition of restrictions for these classes from the point of view of a possibility of use of couples of models of operations as an efficiency comparison standard; -testing of the known relative indicators for the ability to identify the efficiency of a set of classes of simple target operations.

Development of the conceptual and axiomatic definitions of the theory of estimation of models of simple target operations
In case of creation of the theory on the basis of the postulational method, the concepts which aren't defined within this theory which properties and the relations are described by a system of axioms and postulates are introduced.
To formulate conclusions of the developed theory, it makes sense to use the predicate logic language, therefore, we will define the underlying sets with which we will work, and introduce the symbolic notation of the main objects (object variables) and their properties or relations (predicate variables): M -set of the operations researched within this theory; Μ  -set of system processes; ' Μ -set of synchronized operations; ' Μ  -set of synchronized processes;  -set of input products of system operation; '  -set of input exchange products of system operation; ' ⊂  ;  -set of output products of system operation; '  -set of output exchange products of system operation; ' ⊂   .Object variables for nomenclature of the basic concepts within this theory: x -operation; x  -the system process including one or more operations of one class; c -technological products of operation; ' c -exchange products of operation; r -input products of operation; p -output products of operation; rs -expert estimation of one input product of operation; ps -expert estimation of one output product of operation.The predicate variables denoting the properties and the relations of objects of this theory: ( ) E x -efficiency of x operation.We will define basic concepts of this theory: Definition 1.The operated process of transformation of products is called cybernetic operation or just operation.
Definition 2. System is the object that is continuously generating certain cybernetic operations.Definition 3. Cybernetic operation is called system operation if it includes other cybernetic operations, each of which uses the input intrasystem products and forms the output products which transformation is directed to the achievement of the one system purpose.
Definition 4. System operation, the input products of which are presented in the form of the corresponding expert estimates is called the target system operation or target operation The supersystem is a class of systems the output product of which are the functioning systems of one class that transfer the target products to the supersystem (Fig. 1).
We will formulate the main statements within this theory which do not require justification in the form of postulates and axioms.
Postulate 1.For any target system operation, the moment of its beginning and the moment of its end can be defined Postulate 2. Input and output products for any target system operation can be quantitatively defined.

Postulate 3. Carrying out any cybernetic operation requires the use of quite certain i input raw products
Postulate 4. The result of carrying out the cybernetic operation is a formation at the exit of the system j of output consumer products of the operation 1 P , 2 P , 3 P each of which can be also quantified  ( ) Postulate 5.Each amount of a raw product i RQ and each amount of a consumer product j PQ of the cybernetic system we can establish the corresponding exchange product with quantitative parameters Definition 10.For any target operation, it is always possible to define a cumulative expert assessment of its input and output products.
The expert assessment of input products of the target operation is always more than zero, and the expert assessment of output products of the operation is higher than the expert assessment of input products of the operation.
Based on the D10 and P1, it is possible to define the concept of the added value of the target operation ( ) and the coefficient of the added value ( ) In this case, ( )  .Thus, the added value of the operation is defined as it is possible to define the time of the target operation ( ) Postulate 7. The model of the simple target operation can always be defined by the three parameters as follows (Fig. 2).

Fig. 2. The graphic model of the simple target operation
We will determine the parameters ( ) RE,T,PE as target signatures.

Multisystem process
We will consider the system operations which are carried out by different systems within a certain interval of time as a multisystem process.
Definition 11.Two MSTO 1 x and of 2 x of one class will be called parallel if: ( ) ( ) ( ) ( ) ( )  .Total (general, cumulative) added value of parallel MSTO within one time interval of research will be defined as the "multisystem added value ( ) )) MSTO in which r1 r2 t t ... = = and p1 p2 t t ... = = , will be defined as the simple target operations synchronized in time or as synchronized operations from a nonempty set of '  M , a set subset of M.
( ) ( )  (Fig. 3).Comparison of efficiency of synchronized MSTO by comparison of their added value, generally, can be carried out if expert estimates of input products are equal.
Theorem 1.Any MSTO x can be presented in the form of two or more synchronized with this operation, MSTO 1 2 y ,y so that ( ) ( ) ( )

Testing of relative indicators which can be used for identification of efficiency of simple target operations
As an example, we consider testing of three indicators which in various sources are defined as performance indicators.It is the coefficient of the value added (profitability) (ER) [2], the growth rate of the value added (EC) [10] and the indicator (EL) [11]: ( ) The results of comparison of efficiency of the operations x and of y with the use of the developed method for 6 classes are given in Table 2. 3 operations of these classes were evaluated in Table 3 with the use of the tested indicators.
The comparative analysis has been carried out for couples of AME + indicators (Table 2) and couples of indicators ER, EC and EL (Table 3).
In the column ( ) 1/ 0 , directly following the criterion indicators, the reliability of its assessment is shown.The 1 level corresponds to logical "True", the 0 levelto logical "False".So, for example, the indicator ER isn't suitable for an assessment of 2 and of 8 STO classes.The indicator EC estimates the classes 5 and 8 inadequately.The indicator EL provides an adequate efficiency assessment of all classes of STO given in Table 2 without restriction.

Discussion of the results of the research that is connected with testing of identification indicators of simple target operations
The researches carried out within this work have shown a basic possibility of verification of indicators with the use of reference operations, which efficiency is calculated by the use of methods and indicators of the developed theory.
It should be noted that the research results of were limited to a set of models of simple target operations.At the same time, the received results don`t cover all classes of these models, and in two cases subclasses of classes as well.
It means that subjects of further investigations in this direction will concern the expansion of classes and subclasses of MSTO within which sets of reference MSTO can be received.It causes practical interest of expansion of a set of reference couples or sets of operations for the entire class of target operations.
The offered method of verification of indicators of identification of target operations provides the objective choice of the criterion of efficiency according to the requirement of the practical solution of optimization problems.At the same time, the solution of the problems of the eighth class with the specified restriction is possible only in that case when parameters of affiliated MSTO are well known.
The results of the research can be used by experts who are engaged in the development of the theory of estimation, Table 3 Results of testing of three indicators ER, EC, EL regarding a possibility of an assessment of classes of operations (Table 1) The work is a continuation of earlier research [11,12].
12. Conclusions 1. Bases of the theory of estimation of models of target operations and the processes generated by them have been designed.It is proved that any MSTO can be transformed into two or more synchronized MSTO of one class.At the same time, it is proved that at equality of coefficients of the value added, the initial and the transformed MSTO are equally effective.The technique of creation of the generated MSTO of processes is offered.A feature of the generated processes is their comparability according to the values of the indicator of efficiency.Within the theory, the absolute predictive value added measure of the developing process is formulated.
2. The method of calculation of efficiency of simple target operations is developed.The essence of the method is that, in case of need, the initial MSTO in the beginning should be transformed into equally efficient MSTO with equal input expert estimates of MSTO.Then, if necessary, the synchronization of the process duration of short MSTO with MSTO, having a greater duration is made.In case of duration synchronization, the affiliated operation from the first short process operation is formed at the last stage.By means of the developed absolute predictive measure AME + , the comparative assessment of efficiency of the processes generated from initial operations is made.Based on the received assessment, the judgment of the relation of initial operations efficiency is expressed.
3. Eight classes of MSTO are defined, the MSTO couples of which can be used for testing of the indicators that are offered as criteria for efficiency evaluation of MSTO.Restrictions for creation of couples of reference MSTO within each class are defined.
4. Testing of three known indicators regarding the possibility of their use as the efficiency criterion is held.It is shown that only one of the three indicators adequately estimates couples of all classes of reference MSTO within which such standards can be created for today.
"cybernetic operation is target operation"; ( ) S x -"cybernetic operation is simple target operation"; ( ) B x -"the moment of beginning of the operation x is defined"; ( ) C x -"the moment of the end of the operation x is defined"; ( ) D x, c -"the product c of operation x has quantitative definition";( ) R x, r -"the product r is an input technological product of x operation";( ) P x, p -"the product p is an output technological product of x operation"; ( ) ' R x, r -"the product r is an input exchange product of x operation"; p -"the product p is an output exchange product of x operation";( ) RQ x, r -"the operation product r at the beginning of x operation has a quantitative estimation";( ) PQ x, p -"the operation product p at the end of x operation has a quantitative estimation";( ) RE x, r -"the operation product r at the beginning of x operation has an expert estimation"; p -"the operation product p at the end of x operation has an expert estimation"; class of operations generated by system;

Definition 5 .Definition 6 . 7 . 8 .
System target operation, the input products of which are defined in the form of total expert assessment of input products of operation (RE ), and output products are defined in the form of total expert assessment of output products of operation (PE), we will determine by the concept "model of simple target operation (MSTO) Time of the beginning of the simple target operation ( ) r t is defined by the moment of registration of its input product in the form of a total expert assessment RE.Definition The end time of simple target operation ( ) p t is defined by the moment of registration of its output product in the form of a total expert assessment PE.Definition The target product of the operation ( ) ' AOE is a part of an exchange product ' RE the value of which is numerically equal to the added operation value ( ) values in which are equivalent.

1 . 6 )
For MSTO x, it is possible to define PE RE AOE AME − Conclusion about the efficiency of the compared STO, on the basis of comparison of AME + .As

Table 2
Set of the STO models that can be used as efficiency assessment standardsClass RE(x) T(x) PE(x) RE(y) T(y) PE(y) AME + (x) AME + (y)