The article discusses methodological issues of creating network virtual enterprises and their management. Here, the network enterprise agent is represented as one of the network nodes that implements directed interactions with other nodes in order to produce and sell marketable products. A multiagent system (MAS) is a virtual enterprise (VE) that is created from various network enterprises on a contract basis. To create an effective VE, we must have a mathematical description of its structure and functions. In this paper, a three-level hierarchical system of diagnostics and performance management for network virtual enterprises is proposed. The functions of the proposed system are described at a formalized level. VE is presented in the form of a set of operators designed to diagnose crisis conditions and manage the effectiveness of its functioning. The main condition for the normal functioning of the VE is the absence of crisis states. Crisis states are manifested in a decrease in output and sales of products, and a deterioration in the financial condition of the VE. A method for diagnosing agents crisis states based on the evidence theory is proposed. It allows you to take into account both stochastic and content uncertainty. A numerical example of using this technique to identify a crisis situation in a certain VE is given. Based on the results obtained, control actions were proposed to remove the entire VE from the pre-crisis state by reengineering it.
The information technology development leads to a change in the paradigm [
database is available to other members as well as to firms involved in temporary participation. This makes it possible to form a general management system for VE and increase the efficiency of their activities. Another important advantage, in comparison with traditional economic structures, is the ability to dynamically change their structure by commuting the individual competencies of partners. Dynamism is showed in all spheres of activity, including the supplier-consumer relationship.
With the transition to the creation of network virtual enterprises, the issues of the
effectiveness of the functioning of such industries force us to reconsider the classical
methods of their construction. The solution to this problem is based on a
mathematical description of the structure and functions of a network enterprise [
This article proposes a new approach to building the VE model and managing the performance of virtual network enterprises, based on the use of methods of the theory of hierarchical systems. The issues of monitoring of crisis situations (CS) of the VE in uncertainty conditions are considered in detail, as the basis for managing their effectiveness.
The paper is developed with the financial support of RFBR (project № 20-0700199). 2
Mathematical description of the structure and functions of a network enterprise With the transition to computer-integrated (networked) enterprises, the issues of the effectiveness of the functioning of such industries force us to revise the classical methods of building enterprises. To solve this problem, it is necessary to have a mathematical description of the structure and functions of the network enterprise. All enterprises that are part of a network for the production of product are closely interconnected, so the ineffective work of one of them can lead to a crisis state of the other or to the collapse for the entire network of enterprises. The state of the entire network of enterprises is characterized by the values of economic indicators x1, ... , xi, ..., xn, where xi X is a set of economic indicators.. Imposing restrictions x and x on the indicators xi, ( i 1,...,n ),we determine the area of normal functioning for network enterprises ( x and x are the upper and lower boundaries of the i - th indicator). The crisis state shows the value of x going beyond the boundaries). The difference between the upper or lower value of the economic indicator border and its actual value will be denoted as a efficiency margin of xi ( i 1,...,n ), xi X ,where Х is a set of values characterizing the efficiency margin with help of operational values of economic indicators. The value of xi is calculated at a certain frequency during operation. These values predict the tendency of xi to zero and determine the control actions of y, y Y on the network enterprises. Control actions increase the efficiency margin, i.e. manage the efficiency of the network enterprise. Here Y is a set of control actions that allow to withdrawal enterprises from the pre-crisis state. Consider a network of enterprises A0, A1, A2, …, An, where A0 is the main enterprise. Assembly of the finished installation is performed on A1, А2, ..., An are network partners enterprises. They supply raw materials and components or consume a finished plant.
Enterprise A0 can be represented as a set of operators S0, ..., S3, designed to diagnose crisis states and manage the efficiency of network enterprises. As a result, we obtain a three-level hierarchical diagnostics and performance management of enterprise network systems (see Fig. 1).
Operator S1 is used to calculate the economic indicator Z1. Z1 is the profitability of the main enterprise A0 in conditions of significant uncertainty of the initial information.
Uncertainty arises due to the fact that the values X1i arrive at the enterprise A0 not with exact numerical values, but are determined in the form of probabilities by experts. Experts estimate the impact of the enterprise Ai on the profitability of Zi with a number in the range from 0 to 100. Let us describe the interaction between the operators shown in Figure 1 using the set mapping apparatus.
Operator S1 implements the function of determining the main enterprise profitability Z1 and is specified as mapping:
S1: X11 … X1i … X1n Z1 where Z1 is the set of the profitability indicator values of the enterprise A0; X1i is a set of values characterizing the efficiency margin for profitability of the enterprise Ai; X1i X.
Operator S2 implements the function for calculating the cost of the final product Z2, manufactured by the enterprise A0, and is described by the mapping:
S2: X21 … X2i … X2n Z2 where Z2 is the set of values of the indicator of the cost of finished products for the enterprise A0; X2i is a set of values characterizing the efficiency margin for the cost of raw materials, components or finished products of network acceptance Ai; Operator S0 monitors the crisis conditions of network enterprises. The implementation of the function S0 is associated with significant uncertainty; therefore, the output of S0 should not be exact, but probabilistic characteristics. S0 maps:
X2i X.
S0: Z2 Z2 P(Ai) where P(Ai) is a set of values of probabilities that determine the crisis state of enterprisesA1, А2, ..., An.
Operator S2 implements the function for performance management of enterprise network:
S3: P(Ai) V L Y where Y is the set of control actions that allow to bring enterprises out of the pre-crisis state, Y = Y1 ... Yi, ... Yn (Yi - a set of control actions for A); V is the volume of products supplied or consumed by network enterprises, V = V1 ... Vi, ... Vn (Vi is the volume of products supplied or consumed Ai); L - cost of products supplied or consumed by network enterprises, L = L1...Li,...Ln (Li- the cost of products delivered or consumed by the Ai enterprise).
The functioning of the i - th network enterprise is mapping by the operator Ai, which implements four functions.
The first function Ai1 determines the margin of efficiency in terms of profitability: Ai1: Vi Si X1i,
Ai2: Vi X2i.
Ai3: Yi X1i Vi. where is a set of external disturbances.
The second function Ai2 determines the efficiency margin at cost: The third function Ai3 forms the volume of products supplied or consumed: The fourth function Ai4 determines the cost of the supplied or consumed product:
Ai4: X2i Si
The presented formulation of the problem of building a computer-integrated
enterprise is difficult to implement in practice due to the lack of reliable operational
information. However, the use of modern computer technology allows us to solve this
problem. The considered approach was partially used in the development of an expert
control system for the evolution of continuous multistage processes [
Monitoring of VE crisis states on the basis of the
DempsterSchafer evidence theory
Monitoring of the CS (crisis states) of the VE consists in the analysis of the financial
and economic activities of network enterprises of multi-agent systems. Crisis states of
agents cause a decrease in the efficiency of the functioning of the entire VE [
According to [
Based on the probability distribution, a number of additional characteristics can be calculated to evaluate the results of diagnostic procedures.
The confidence degree in a crisis state for an agent of the subset m(Ci ) [0;1]
Bel (Ci ) m(C j ) C j Ci
Bel () 0 ; Bel (C j ) [
The plausible reasoning degree for a crisis state of an agent in the subset Ci A
Ci A Pl(Ci ) 1 Dou(Ci ) 1 Bel (Ci ) 1 m(C j ) ; Ci C j .
To combine different frame of discernment it is necessary to calculate the orthogonal
sums of the base probabilities defined for each of the evidence. For this purpose, the
Dempster rule [
* m1(Y ) * m2 (Z ) , 1 m() Y Z A where Y and Z are two focal elements distributed on the frame of discernment, generated by different evidence. The probability measure corresponding to an empty set has the form m
Y Z
m1( Y )*m2( Z ) .
The Dempster’s rule is associative and commutative. It allows a lot of evidence to be combined in this way. 4
The example of the implementation of the method for recognizing crisis states of agents for VE
- aviation enterprises Ca; - other enterprises Cb.
The structure of consumer agents is shown in Figure 3. The integrated structure of the virtual enterprise is shown in Figure 4. Consider the structure and composition of a virtual enterprise (VP) for the production of SCP in the formulation of multi-agent systems (MAS).
In the fig. 4, vertex 1 denotes the main enterprise. All the work from design to assembly of the UPPF-ZMK unities carried out by main enterprise.
To the left of vertex 1 are the agents-suppliers of raw materials (S1 - stainless metal rolling; S2 - black rolled metal) and components (E1 - vacuum technology; E2 - electronics products; E3 - wires; E4 - other components). To the right of the vertex 1 are the agents-consumers of the produced UPPF-ZMK installations: Ca, Cb. In 2014, there was a favorable economic situation: the aviation industry was in dire need of such installations, and agents-suppliers of raw materials and purchased products offered their products at relatively low prices. Let us consider the reasons for the economic recession in the VE activities by the end of 2015. We use the method for diagnosing the crisis conditions of network enterprises.
A quantitative and qualitative analysis showed that the reason for the economic downturn in the activities of the virtual enterprise was the deterioration of the economic indicators (DEI) of the agents-suppliers of raw materials and components. In the second half of 2015, the VE general manager was forced to continuously monitor the economic state of the VE in two indicators: profitability - Z1 and actual cost - Z2. The monitoring was carried out under conditions of significant uncertainty; therefore the calculations were performed using the methods of the interval analysis theory. The monitoring showed information about DEI at profitability of 0.1÷ 0.25% and an actual cost of 24.1÷ 34.0 million rubles. As a result of the examination, the specialists-managers received expert assessments for the agents-suppliers, which may be in pre-crisis or crisis (CS) states in the current economic conditions. The results of the examination are presented in Table 1. Based on the data shown in Table1, we define two fuzzy sets of agent-suppliers, suspected of having a CS but each of the DEI: Z1 - profitability, Z2 – cost price.
СZ1 {(S1.1;0,15), (S1.2;0,2), (E3;0,1), (E4;0,25)} СZ 2 {(S 2;0,2), (E1;0,25), (E2;0,2), (E3;0,3), (E4;0,15)} Next, the normalized probability distribution for the indicator Z1 (profitability) is calculated mZ1(S1.1)
As a result of normalization, the probability distribution for the disturbed diagnostic variables will be as follows:
mZ1 S1.1; S1.2; E3; E4 0,21;0,28;0,14;0,36 ; mZ 2 (S 2, E2); E1; E3; E4 0,22;0,28;0,33;0,17 .
Taking into account the interval values of the diagnostic variables Z1 and Z2, as well as the acceptable deviation intervals d Z1 and d Z1 , we calculate the probability of occurrence of CS PZ1 and PZ2. The value of the Z2 index on the observation interval is within the limits of [24.1; 34.0] million rubles. With the regulatory limits of 20.04 25.0 million rubles, the probability of CS
PZ2 = (34.0 - 25.0) / (34.0 - 24.1) = 0.91.
The doubt degree in CS: UZ2 = 1 - PZ2 = 0.09 Using the calculated probabilities of CS occurrence, we refine the obtained probability distributions mZl and mZ2: mZ1' S1.1; S1.2; E3; E4;C 0,14;0,19;0,09;0,24;0,33 ; m'Z 2 (S 2, E2); E1; E3; E4;C 0,2;0,25;0,3;0,16,0;09 .
Calculations for combining different evidence about the probability distribution in favor of a single hypothesis are shown in table 2. The probability measure for hypotheses about the CS of supplier agents is calculated as follows m(S1.1) 0,013 / 0,465 0,028 ; m(S1.2) 0,017 / 0,465 0,037 ; m(S 2 E2) 0,066 / 0,465 0,14 m(E1) 0,083 / 0,465 0,178
m(E3) (0,027 0,099 0,008) / 0,465 0,288 ; m(E4) (0,038 0,053 0,022) / 0,465 0,243 ; m(C) 0,03 / 0,465 0,065 m(C) 0,03 / 0,465 0,065 .
m S1.1; S1.2; (S 2, E2); E1; E3; E4; C 0,028;0,037;0,14;0,178;0,288;0,243;0,065
S1.1[0,028;0,093], S1.2[0,037;0,102], S 2[0,14;0,205], E1[0,178;0,243] ; № 1 2 3 4 5 6 7
Thus, an analysis of the situation based on the theory of evidence leads to the diagnosis shown in table 3. It can be seen from the table that S1.1 and SI.2 have the highest probability of CS. As a result of the analysis, the VE managers identified a crisis state with the supply of stainless metal rolling for the production of the UPPF-ZMK installation.To liquidate this CS, another agent-supplier of stainless metal rolling products was urgently involved - S1.3 and the production plan for the UPPF-ZMK installations in 2016 was fulfilled, but profitability the last fourth install was only 1.8%. 5
Conclusions The proposed new approach to modeling and designing network enterprises based on a three-level hierarchical interaction system allows creating new information models for diagnosing and managing the efficiency of virtual enterprises using digital communication networks.
The presented method of monitoring the crisis States of a virtual enterprise, taking into account the uncertainty of data, allows: - to provide a consistent and continuous analysis of the state of a virtual enterprise with localization of the source of the crisis state; - use interval diagnostic variables in its structure to account for both stochastic and content uncertainty and combine the results of analytical and expert analysis of the virtual enterprise state; - - analyze inefficiently operating structural units of a virtual enterprise with minimal time and resources for conducting diagnostic procedures.
- analyze inefficiently functioning structural units of a virtual enterprise with minimal time and resources for conducting diagnostic procedures..