Industry 4.0. Technique for ranking vector estimates when choosing business partners

. The fourth industrial revolution is affecting companies and leading to new strategic thinking. The changes brought about by the requirements of Industry 4.0 are forcing restructuring in many areas of management or building new business models.


Introduction
The fourth industrial revolution is a term that refers to the social, industrial and technological changes brought about by the digital transformation of industry.A characteristic feature of the Fourth Industrial Revolution is the knowledge of customer needs, which constitutes the competitive advantage of enterprises, allowing them to correctly identify their opportunities, challenges and problems, which, in turn, guarantees the conscious use of new market opportunities.
One of the subsets of the Fourth Industrial Revolution is the concept of Industry 4.0, which was adopted to denote the tasks of identifying and analyzing upcoming changes that are of strategic importance to the economy.In essence, Industry 4.0 is a trend towards automating data exchange in production systems, including cyber-physical systems, the Internet of things, cloud computing, cognitive computing and artificial intelligence, which is achieved by integrating intelligent machines and systems with business processes to improve production efficiency [1].With the introduction of the above technologies, through intelligent monitoring and decision making, companies and all their networks will be able to monitor and optimize their activities in near real time.Therefore, Industry 4.0 involves the introduction of modern IT solutions throughout the value chain, which allows you to create personalized products for a specific customer and related value chains.Advanced information and communication technologies make it possible to accurately adapt production to customer expectations while maintaining low costs, high quality and efficiency [2].Modern technological business models are accelerating the transformation of the industry, changing the structure of the market.This poses new challenges for many areas of management, which are forced to adapt to the architecture of the digital world.
Progressive globalization and networking of the economy necessitates the creation of new business concepts.Dynamic technological development and solutions implemented in modern companies lead to a change in management paradigms and the need to build new business models based on maintaining a balance between the development of intelligent technologies and the quality of life.As a rule, the company's business model is presented as a set of activities, methods and time frames and reflects the implementation of the strategy in terms of economic effects [3].The role of strategy in the model is most important, as current and future revenues are generated by the products offered to customers and the competitive approach to the market.This results in a revenue stream and return on investment through a combination of profits and an appropriate cost structure.Thus, the business model is a configuration of the strategy, taking into account the sources of income and profit.Innovation can be applied to all elements of a business model and is necessary to create value for the customer [4].Business models developed and implemented by companies determine their profitability and competitiveness.New strategic behavior is determined by the changes that can be observed in modern business.Nowadays, managers are required to use more and more sophisticated management methods and concepts.The analysis of the essence, structure and types of strategic models is an essential cognitive element in the sphere of development and operation.An important element of detailing business models are business processes, which, to some extent, are a way to realize value in the form of relationships with customers, in particular, providing them with products that meet specific needs [5].As a result, companies will have to redefine their strategies and business models in the coming years, not in relation to traditional market competitors, but in relation to emerging consumer ecosystems.Industry 4.0 technologies are creating new business opportunities by significantly facilitating open business models based on open innovation.These models are the strategic and operational basis for changing the configuration of products and processes in the enterprise, the basis of competitive market advantage, determined by the rules of the Industry 4.0 concept, where customers and business partners are directly involved in business processes and value creation.They also allow you to get more value by using key assets, resources or positions of the company not only in its own business, but also in the business of other companies [6].
Thus, companies with an open business model are actively looking for innovative ways to collaborate with all business partners: suppliers, customers or general partners, to expand their business, for example, through servitization [7].
In the process of implementing an open business model, the customer company is constantly faced with the need to evaluate its business partners.The assessment under consideration is multi-criteria (vector), while it should be noted that in the general case, the target function of the customer's company may not coincide with the target functions of partners who are also active participants in business processes seeking to realize their target functions.To formalize the description of the model for choosing business partners by the customer company, it is advisable to designate the latter as the Center, and partners as active systems for which vector estimates are generated.[8].Let the division of the set into classes have already been obtained.Therefore, it is known in advance to which class the presented vector estimate will be assigned.Thus, it is possible to determine the minimum number of questions to the Center required to build a given partition, if you use the previous procedure, but determine i Ô according to the formula i li Ô g = , where l - 4 number of the class to which the vector estimate belongs i y in this partition [9].This procedure was called <reference= (i.e., the best within the framework of the proposed approach), since at each step of the procedure a vector estimate is presented that determines in accordance with the ratio 0 P belonging to one of the classes of the maximum number of vector estimates.

Materials and methods
To generate the initial partition of the set of alternatives into decision classes, the following procedure is proposed.The researcher sets the number of criteria Q, the number of gradations on the scale of each criterion number of classes N. A set of alternatives (vector estimates) is formed Y representing all possible combinations of assessments on criteria scales.It is known that a vector score that has the first scores on the scales of all criteria belongs to the first class, and a vector score that has the last scores on the scales of all criteria belongs to N -mu class.Then, in accordance with the proposed survey procedure, the Center determines the vector estimate i y Y  , which must be presented to the Center in order for it to be assigned to one of the classes [10].The answer of the Center is modeled using a pseudo-random number generator: the coefficients of proximity of a given vector estimate to different classes, determined in accordance with the procedure, are considered as the probabilities of attributing the presented vector estimate y i to the corresponding class.By the value of the next pseudo-random number R, the number of the class to which the presented vector assessment will be assigned is determined: where 0 0 i P = After that, in accordance with the dominance relation, the sets of numbers are corrected j G for each vector estimate j y Y  , belonging to a certain class has not yet been determined.Next, the coordinates of the centers of the classes are recalculated, and the procedure is repeated until the belonging to one of the classes of each vector estimate of the set Y [11].The number of calls to the pseudo-random number generator characterizes the number of questions to the Center for constructing this partition based on the proposed rational procedure for polling the Center.

Research and results
The scheme of statistical testing of the behavior of the proposed algorithm consists of the following stages.I. Generation of the Center's answers using a random number generator and determination of the initial partition of the set of alternatives into decision classes.

II. Determination of a <reference= sequence of questions to the Center (in this case, the
Center is a partition of the set of alternatives generated at stage I) to split the initial set of alternatives into classes.
III.Multiple repetition of stages I-II and comparison of results.
Steps I and II are carried out in accordance with the described procedures.Stage III consists of repeated repetition of stages I and II for a different number of criteria Q, gradations on the scales of criteria w and decision classes N. The data obtained at each stage on the number of vector assessments presented are averaged, and the value of this indicator obtained at the stage is compared I (N0) and II ( ý N ).This ratio characterizes the effectiveness of the proposed rational procedure for polling the Center [12].
For each variant of the number of criteria, gradations on the scales of criteria and the number of decision classes, about 500 implementations of procedures were carried out, on each of which an estimate was determined for the number of presentations of vector estimates, when the partition is known in advance and when it is not known.
The average values of these estimates are given in Table .1 for the case of four and five criteria with three and four gradations according to their scales and two, three and four classes of solutions [13].The given data show that the proposed procedure requires the presentation of no more than 2.8 times more vector estimates than the reference algorithm.Moreover, this ratio decreases with the growth of the number of classes of solutions.The absolute values of the number of presented vector estimates are much less than the power Y , which indicates the expediency of using the proposed procedure for surveying the Center [14].
Note that the proposed algorithm for determining the vector estimates that should be presented to the Center ensures the construction of a partition of the set Y into decision classes for a relatively small number of calls to the Center.At the same time, its use significantly reduces the possibility of checking the correctness of the Center's answers based on the ratio 0 P , so for the case N=2 when applying the algorithm, the possibility of contradictions in the partition is completely excluded Y .On the one hand, this is a positive phenomenon, since we need to construct a consistent partition.On the other hand, a random error of the Center when assigning the presented vector assessment to one of the classes can lead to a split that does not meet the real preferences of the Center [15].
A practical decision-making method should provide the possibility of verifying the information received [16].In this case, the requirement is put forward that each vector estimate of the set not presented to the Center Y was evaluated directly or indirectly (based on the relationship 0 P ) at least two times.Therefore, after constructing a partition using the proposed algorithm, an additional presentation of a part of vector estimates for which this condition was not satisfied is provided [17,18].
The following procedure for additional polling of the Center is proposed.To a subset Z Y  vector estimates are distinguished, the belonging of which to a certain class of solutions was determined on the basis of the relation with the help of the proposed algorithm was assigned to the class l Y ) [19].
Thus, the number of vector estimates presented to the Center for constructing a partition of the set Z into classes of solutions will not exceed the number of vector estimates presented in Table .1 for the corresponding values of the parameters Q,  и N.
In the resulting partitioning of the set Y into classes of solutions, the vector estimates of the set Z refer to the classes in which they fell when partitioned into classes of the set Z [20].
The division of the set Y into classes of solutions constructed in this way, even for N = 2, does not guarantee the asymmetry of the relation * P .In this regard, one should use Y the procedure for reducing the resulting partition of the set to a consistent form [21].

Conclusions
Thus, the proposed method of ranking vector estimates allows you to determine the class of business partners and make decisions about further interaction within the framework of an open business model.In addition, the proposed methodology can be used as the basis for automating business processes associated with the need to rank active systems, which is consistent with the basic requirements for open business models characteristic of Industry 4.0.
just one time.For this subset, a <reference= procedure is used to determine the sequence of presented vector estimates, i.e., 0 P