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Designing adaptive information models for production management
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ProcediaProcedia CIRP 00CIRP (2017) 84000–000 (2019) 1088–1093 www.elsevier.com/locate/procedia
29th CIRP Design 2019 (CIRP Design 2019) 29th CIRP Design 2019 (CIRP Design 2019)
Designing information models for management 28th CIRP Design Conference, May 2018, Nantes, France management Designing adaptive adaptive information models for production production Vladimir Tsyganov*
Vladimir Tsyganov* and physical architecture of A new methodology to analyze the functional Institute of Control Sciences, 65 Profsoyuznaya, Moscow, 115035, Russia existing products for anof Control assembly orientedMoscow, product family identification Institute Sciences, 65 Profsoyuznaya, 115035, Russia * Corresponding author. Tel.: +7-495-334-9331; fax: +7-495-334-9340. E-mail address: [email protected] * Corresponding author. Tel.: +7-495-334-9331; fax: +7-495-334-9340. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
Abstract Abstract
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France
*ACorresponding Tel.:design +33 3 87 54 30; E-mail address:models [email protected] methodologyauthor. of open of 37 adaptive information for production management under uncertainty, based on a cognitive approach
A of open the design of adaptive for production management under uncertainty, based on cognitive approach andmethodology taking into account human factor, isinformation developed. models This methodology is based on the idea of designing a variety of aadaptive information and taking intoonaccount human factor, is developed. This of methodology is based on that the idea of designing a variety of used. adaptive information models based a singlethe basic model. In this case, a variety adaptation procedures are publicly available can be As an example, models basedmodels on a single model. In this case, a variety of adaptation are publicly can be As anparameters example, information basedbasic on self-learning procedures are considered. Theprocedures results of that the operation of available these models areused. adaptive information based on self-learning procedures considered. results of the operation these models are adaptive parameters Abstract (norms) and models production estimates. When designing sucharemodels, it can The be used many of the formal of self-learning procedures described in the (norms) models, it caninformation be used many of the self-learning procedures in the scientificand andproduction technical estimates. literature. When As an designing example, such the self-learning model for formal production management based described on a stochastic scientific and technical literature. As an example, the self-learning information model for production management based on a stochastic designed. Sufficient for its correctness are found, ensure the thetoproduction potentialthe taking Inapproximation today’s business environment, theconditions trend towards more product variety andwhich customization is unfolding unbroken. of Due this development, needinto of approximation designed. Sufficient conditions for self-learning its correctness arevarious found,products which is ensure the unfolding of To the design production potential taking into account human factor. The application the information model illustrated byfamilies. the example of wagon-repair production of agile and the reconfigurable production systemsofemerged to cope with and product and optimize production account thecorporation human factor. The application of the self-learning information model is illustrated by the example of wagon-repair production of large-scale Russian systems as well as to choose theRailways. optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to large-scale corporation Russian Railways. analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and © Authors. Published Published Elsevier B.V. nature ofThe components. This fact by impedes anB.V. efficient comparison and choice of appropriate product family combinations for the production © 2019 2019 The Authors. Elsevier © 2019 The Authors. Published by by Elsevier B.V. committee of the CIRP Design Conference 2019 Peer-review under responsibility of the scientific system. A newunder methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster Peer-review responsibility of the scientific Peer-review under responsibility of the scientific committee committee of of the the CIRP CIRP Design Design Conference Conference 2019. 2019 these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable Keywords: Design; production; information; model; adaptation; management assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and Keywords: Design; production; information; model; adaptation; management a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of 1. Introduction It is the base of management design for smart production thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. 1. Introduction It is the base of management design taking into account the human factor [4].for smart production © 2017 The Authors. Published by Elsevier B.V. taking into account the human factor [4]. The concept of a new industrial revolutionof the called Cognitive control2018. implies the development of a cognitive Peer-review under responsibility of the scientific committee 28th CIRP Design Conference
The concept new onindustrial revolution called INDUSTRIE 4.0 ofis abased the extensive design of INDUSTRIE 4.0 is based on the extensive design of Keywords: Assembly; Designwith method; Family identification information networks elements of artificial intelligence information networks with elements of artificial intelligence and cognitive control [1]. and cognitive control [1].
Cognitive control forecasting implies the and development of a based cognitive strategy, including management on strategy, including forecasting and management based on feedback. The cognitive approach implies the construction feedback. The cognitive approach implies the construction and analysis of a cognitive map — a graph, whose vertices and analysis ofto a cognitive — a graph,personnel whose vertices correspond objects map (production and correspond to objects (production personnel and management), and the arcs between vertices to relations 1. Introduction of the product range and arcs characteristics manufactured and/or management), and the between vertices to relations 1.1. Cognitive approach to the production management between these objects. A cognitive map includes a set of arcs assembled in this system. In this context, main challenge in 1.1. Cognitive approach to the production management between these objects. cognitive map the includes set of arcs connecting objects that A reflect the sequence of theira actions. Due to the fast development in the domain of modelling and analysis is nowthenot only toofcope with single connecting objects that reflect sequence their actions. Cognitive approach is the method of analysis and design Such cognitive map of production management in communication and an isongoing trendof of digitization and products, limited product or existing product families, Cognitive approach the method analysis and Such acognitive map isrange ofshown production in based on cognition, the search for interrelationships of design events conditions of uncertainty on Fig. management 1. At the upper digitalization, manufacturing enterprises are facing important but also to be able to analyzeisand to compare products to define based on cognition, the search for interrelationships of events conditions of uncertainty shown on Fig. 1. At the upper and phenomena. For example, the promising direction of the level of it is production management (Center), and at the challenges in today’s market environments: a continuing new product It can be observed that classical and phenomena. Forinexample, promising direction of the level it isfamilies. (Center), andexisting at the cognitive approach relation the to the manufacturing system lower oflevel - production production management personnel realizing technological tendency towards reduction of product development times and product families are regrouped in function of clients or features. cognitive approach in relation to the manufacturing system lower level production personnel realizing technological integration is based on a semiotic - the science of “signs” [2]. process with external input ξt and output yt, where t - time shortened product lifecycles. In addition, there is an increasing However, assembly oriented are hardlyt to- find. output integration is based on a semiotic [2]. process twith external input product ξt andthefamilies t, where Cognitive control can be - the usedscience for ofthe“signs” systemic period, = 0,1, ... Accordingly, core yprocedures oftime the demand of customization, being at used the same time in systemic a global On thet =product family level, products differ mainly in Cognitive control can be for the period, 0,1, ... Accordingly, the core procedures of two the coordination of different processes deals with production [3]. production management decision support system should be competition competitors all over thewith world. This trend, main characteristics: (i) thedecision number support of components (ii) the coordinationwith of different processes deals production [3]. production management system and should be which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). markets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the 2212-8271 © 2019 The Authors. Published by Elsevier B.V. 2212-8271 ©under 2019 Theaugmenting Authors. of Published by Elsevier To cope with this ascommittee wellB.V. asoftothebeCIRP ableDesign to Conference product 2019 structure on a physical level (components level) which Peer-review responsibility thevariety scientific Peer-review under responsibility of the scientific committee of the CIRP Design Conference 2019 identify possible optimization potentials in the existing causes difficulties regarding an efficient definition and production system, it is important to have a precise knowledge comparison of different product families. Addressing this 2212-8271©©2017 2019The The Authors. Published by Elsevier 2212-8271 Authors. Published by Elsevier B.V. B.V. Peer-review under responsibility of scientific the scientific committee theCIRP CIRP Design Conference 2019. Peer-review under responsibility of the committee of the of 28th Design Conference 2018. 10.1016/j.procir.2019.03.271
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Vladimir Tsyganov / Procedia CIRP 84 (2019) 1088–1093 Author name / Procedia CIRP 00 (2019) 000–000
forecasting (F), resource allocation (R), planning (P) and incentive (I) (see Fig. 1).
1.2. Artificial intelligence and adaptation in production management “Intelligent means able to adapt, communicate and interact” [1]. So the first important element of artificial intelligence in a production deals with adaptation at changes. The design of production management with such elements of artificial intelligence as the ability to self-study and learning is becoming increasingly important [5]. Accordingly, procedure of forecasting (F) should be adaptive. To design this procedure a variety of adaptive algorithms described in the scientific and technical literature can be used [6]. For their implementation in decision support systems is created the basic adaptive information model (AIM), denoted as MB=(F,R,P,I) (see Fig. 1).
PRODUCTION MANAGEMENT (CENTER) MB=(F,R,P,I) RESOURCE (R)
PLAN (P)
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The logical architecture of production management in the era of intelligent networks is discussed in [9]. A feature of this architecture is the continuous management of the interaction of the elements of complex large-scale systems, such as the intelligent transport system of Russia [10]. The results of cognitive control can be used for system integration of elements of artificial intelligence [1]. This integration involves the coordination of various processes related to production and design of extensive information networks. An example of the optimal design of such information and telecommunication networks to support the management structure of a large railway company is considered in [11]. Long-term networking of intelligent production elements (creative industrial enterprises) ultimately leads to increased productivity and the cost of each [9]. Technologies of digital interaction of production systems are considered in [9]. Similar digital communication technologies are used in decision support systems for largescale production management [11]. For example, a decision support system developed on the basis of the above “reduced” AIM MO=(F,P,I) (see Fig. 2) is included in the information network of the innovation design cycle and their introduction into production at the corporation Russian Railways [7].
FORECAST (F) PRODUCTION OFFICER (CENTER)
INCENTIVE ( I )
MO=(F,P,I) FORECAST (F)
PRODUCTION PERSONNEL ξt
PLAN (P)
TECHNOLOGICAL PROCESS
INCENTIVE ( I )
yt Fig. 1. The basic AIM MB=(F,R,P,I) sovereign production manager.
AIM MB=(F,R,P,I) can be used as a base module to design other AIM in the face of uncertainty. In particular, in practice, the manager can perform only part of the above main functions F, R, P, and I. Therefore, it requires more simple AIM. For example, in [7] AIM MO=(F,P,I) investigated, designed to support a decision-making officer who does not have a resource allocation procedure (R) (Fig. 2). There, the production officer uses only the results of calculations of the forecast (F), planning (P) and incentives (I) from AIM MO=(F,P,I).
1.3. Intelligent networks with cognitive systems The other important elements of artificial intelligence in a manufacturing deal with communication and interaction. Production using intelligent networks with cognitive systems discussed in [3]. Cognitive semiotic framework for manufacturing systems integration deals with signs which could be linguistic or non-linguistic [8].
PRODUCTION PERSONNEL ξt
TECHNOLOGICAL PROCESS
yt
Fig. 2. The AIM MO=(F,P,I) for production officer.
In this article, we will look at the design of another important “reduced” AIM M C = ( F , I ) , which supports the decision making of a production clerk (who does not have the functions of regulatory planning P and resource allocation R). This model M C = ( f , I ) is self-learning by accumulating knowledge about production and forms adaptive norms, on the basis of which production can be estimated and personnel can be stimulated 2. Self-learning classification Many of the tasks of production management are reduced to the classification of observed situations and events. Examples include the early detection and prevention of
Vladimir Tsyganov / Procedia CIRP 84 (2019) 1088–1093 Author name / Procedia CIRP 00 (2019) 000–000
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disruptions or deficiencies in production due to random external interference ξt (see Fig. 1). The classification of the observed situations is carried out on the basis of the decision rule. Management is carried out depending on the result of this classification. With sufficient a priori information, the rules of the theory of statistical solutions are used. However, in a stochastic setting, a priori information is often not enough. There is a need to adapt the decision rule so as to minimize the loss of classification. This adaptation can be performed by observing the output of production using a self-learning procedure, for example, based on a stochastic approximation. Let p be a random variable characterizing production potential, p ∈ D ⊂ R1+ . Suppose that the Center can observe the random values of this variable. The task is to classify the production situation by assigning p it to one of the two domains that make up the set D. Incorrect classification leads to losses. 2.1. Density distribution of a random potential Suppose first that the Center knows the density distribution q(p) of a random variable p. Let us consider a partition of a set D into 2 domains D1 and D2, D1 ∪ D2 = D. In the classification, i.e. attributing the situation p to one of these domains, production management (the Center) makes a decision associated with some risk. The problem is in defining a partition that minimizes the average risk associated with the classification. For each unknown domain D1 and D2,, we introduce loss functions Lk ( c , p ), k = 1,2, , where c is an unknown parameter of the decision rule. Minimizes the average risk that evaluates the quality of the classification
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where the parameter of the decision rule (с) can be found as a solution to task (1) from condition (2). 2.2. Stochastic approximation of the decision rule parameter In practice, density distribution q(p) it is usually unknown. Therefore, it is not possible to directly determine the parameter c, solving the optimization task (1). So there is a need to adjust the parameter of the decision rule by observing the sequence pt , t=0,1,..., to minimize (1). Let use the method of stochastic approximation to solve (1). Taking into account (3) it is not difficult to show that
сt +1 = F (ct , pt ) t → c* = arg min J (c), →∞
(5)
if the procedure for forecasting of a decision rule parameter is
c + γ v if pt < (b + v)ct /(b + 1) сt +1 = F (ct , pt ) = t t , ct − γ t d if pt ≥ (b + v)ct /(b + 1) ∞
γ t > 0,
∑ γ t < ∞,
(6)
c0 = c 0 , t = 0,1,...
t =0
where γ t is adaptation coefficient. Because of (5), procedure F ( c , pt ) is called the optimal self-learning procedure. Note that to apply the procedure (6), Center must know the sequence of production potentials, pt, t=0,1,… However, in practice, production potential depends on external input ξ t (for example, interference) and other factors not always known to management. For actions in conditions of uncertainty, management needs to learn.
2
J ( c ) = ∑ ∫ Lk ( c , p )q( p )dp → min c
(1)
3. Self-learning information model
k =1 Dk
The condition of minimum average risk (2) is:
2 1 if p ∈ Dk dL ( c , p ) M p ∑ Bk ( c , p ) k , (2) = 0, Bk ( c , p ) = dc 2 if p ∉ Dk k =1 where Mp is the expectation operator. The belonging p of a particular domain is determined by the sign of the decision rule g( c , p ) = L1( c , p ) − L2 ( c , p ) :
D if g( c , p ) < 0 p∈ 1 D2 if g (c , p ) ≥ 0
(3)
Let L1( c , p ) = p − vc, v < 1, L2 ( c , p ) = b( c − p ), vc ≤ p ≤ c. Substituting these expressions into (3), we obtain the decision rule for the classification in the form
D if p < ( b + v )c /( b + 1 ) y ∈ 1 , D2 if p ≥ ( b + v )c /( b + 1 )
In practice, staff is almost always more informed about production potential than management. In such cases, we talk about the asymmetric awareness of the parties [4]. Suppose that the potential pt is unknown to the Center. The potential pt becomes known to the staff at the beginning of the production period t, i.e. until the choice of output yt. So knowing pt, the staff can choose the indicator of production yt so as to provide themselves with the best estimates and incentives today and in the future. Of course, in any case, this output can not exceed the potential: yt ≤ pt . The Center only observes the output yt (which is not necessarily equal to the production potential, because of yt ≤ pt ). To support its decisions, the Center uses the selflearning AIM M C = ( F , I ) based on yt (see Fig. 3). In this AIM an adaptive assessment at +1 of the decision rule parameter сt +1 is formed, by using the optimal self-learning procedure (6):
a + γ v if yt < ( b + v )at /( b + 1 ) at +1 = F ( at , yt ) = t t at − γ t d if yt ≥ ( b + v )at /( b + 1 )
(7)
(4) In addition, a production evaluation et = I ( at , yt ) is formed in the self-learning AIM M C = ( F , I ) as a function of
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assessment at and output yt (Fig. 3). Depending on this evaluation et , the Center encourages staff.
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4.2. Management objectives
The main goal of management is using production potential pt. Thus the Center needs to design an AIM M C = ( F , I ) where staff is interested in unlocking production potential that is, fulfilling equality: yt = pt . In addition when yt ≠ pt , from (6) and (7) it follows that at ≠ ct . So generally speaking the adaptive assessment at does not converge to the optimal parameter c*. Therefore, the assessment obtained by using AIM M C = ( F , I ) may be far from optimal. Consequently, another important management goal is to design a correct AIM M C = ( F , I ) in which
PRODUCTION CLERC (CENTER) MC = ( F, I ) FORECAST WITH SELF-LEARNING at +1 = F ( at , yt )
INCENTIVE WITH PRODUCTION EVALUATION et = I ( at , yt )
at t → c*, a0 = a 0 , t = 0,1,... →∞
4.3. Disclosure of production potential and model correctness Suppose that the set of possible yt on which the maximum V ( at , yt ) is reached includes the point yt = pt . Then we will say that the hypothesis of benevolence of personnel with respect to the Center is valid if the personnel chooses an output equal to the potential: yt = pt (that is, uses the full potential of production). Theorem. For using the production potential and correctness AIM M C = ( F , I ) it is enough (7) and
PRODUCTION PERSONNEL ξt
(9)
TECHNOLOGICAL PROCESS yt Fig. 3. The AIM MC = ( F, I ) with self-learning.
1 if I ( at , yt ) = 0 if
4. Optimal design of a self-learning information model The Сenter is interested in using production potential pt unknown to it. However, the staff, knowing true potential pt, can choose the production indicator yt to provide the best incentives today and in the future. As a result of asymmetric awareness of a potential pt, a game of personnel and management arises. 4.1. Purpose and undesirable activities of production personnel Suppose that the potential pt becomes known to personnel before selecting an output yt in period t. Based on the fact that the output cannot exceed the potential: ( yt ≤ pt ), the farsighted personnel can choose yt so as to maximize own objective function t +T
V ( at , yt ) = ∑ ρ τ −t I ( aτ , yτ ),
(8)
τ =t
where ρ is the discount factor, 0 < ρ < 1, T is the staff foresight. In general, as a result of human factor - undesirable personnel activities aimed at maximizing the entire function (8), the output does not equal the production potential: yt ≠ pt .
yt ≥ at ( b + v ) /( b + 1 ) yt < at ( b + v ) /( b + 1 )
(10)
Proof. The objective function of the personnel V ( at , yt ) , determined according to (8), depends on both current and future evaluations eτ = I ( aτ , yτ ), τ = t ,t + T . By condition (10), as the indicator yt grows, the current evaluation et = I ( at , yt ) increases (does not decrease). Further, the Center uses the self-learning procedure (7), in which aτ decreases (does not increases) with growth yt when τ = t + 1,t + T . Consequently, according to (10), the future evaluation eτ = I ( aτ , yτ ) increases (do not decreases) with growth yt when τ = t + 1,t + T . So all terms on the right side (8) monotonically increase with growth yt . Thus the objective function of the personnel V ( at , yt ) , determined according to (8), monotonically increases with increases (do not decreases) with growth yt . Since yt ≤ pt , then the maximum V ( at , yt ) is at yt = pt . Consequently, by virtue of the benevolence hypothesis, the personnel choose an output yt equal to the potential: yt = pt . Thus personnel use of the potential of production. In addition, when yt = pt from (6) and (7) it follows (9). Then AIM M C = ( F , I ) is correct, QED. 4.4. Interpretation of the optimal design theorem Theorem admits a simple interpretation. Suppose that the higher the evaluation eτ = I ( aτ , yτ ) , the higher the staff incentives. The Center observes the value yt characterizing the efficiency of production in period t, wherein yt ≤ pt , and
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pt is the unknown (random) potential of production. So based on yt the Center adapts the decision rule parameter (7). Further, in accordance with the adopted decision rule (10), the Center classifies personnel according to the results of production. If yt < at ( b + v ) /( b + 1 )] then, the personnel belong to the class of dysfunctional (rank I ( at , yt ) = 0 ) and punished. If yt ≥ at ( b + v ) /( b + 1 )] then, the personnel belong to the class of successful (rank I ( at , yt ) = 1 ) and encouraged. Any of these decisions is associated with a certain risk for the Center. In the first case, losses L1( at , yt ) = yt − vat increase with a growth of the efficiency of production ( yt ) and an unjust punishment of personnel. In the second case, losses L2 ( at , yt ) = b( at − yt ) increase with the deterioration of the indicator yt (undeserved reward or bonus payments). So the classification norm xt = at ( b + v ) /( b + 1 ) is the lower limit of the production efficiency ( yt ) corresponding to satisfactory work of the staff. Note that, according to (6) - (8), the higher the indicator of production ( yt ), the lower the classification norm for the next period xt +1 = at +1( b + v ) /( b + 1 ). But, according to (10), this norm xt +1 plays the role of the threshold value of the indicator yt +1 , at which the staff will receives a promotion in the next period t+1. Consequently, it becomes easier for staff to get a promotion from the Center in the next period t+1, even with a smaller value of the random potential pt. In other words, with an increase of production efficiency ( yt ), personnel receives not only a higher reward. Also the threshold value for incentives in the future ( xt +1 ) is decreased. This further interest the personnel in the disclosure of the potential of production, i.e. in the selection yt = pt . In this case the adaptive procedure (7) ensures that assessment at is convergent to the optimal parameter of decision rule (c*).
production - excellent (4), good (3), satisfactory (2), and bad (1). To do this classification, the management forms the following 2 procedures for determining the adaptive assessments of the parameters of the decision rule, designing them from the basic optimal procedure (7) satisfying the conditions of the Theorem. 1. If the current production indicator is non-negative ( yt ≥ 0 ), then the corresponding adaptive assessment at++1 used to assign production to class (rank) 3 or 4 is recalculated:
a + + γ t v if yt < at+ (b + v) /(b + 1) at++1 = F + (at++1, yt ) = +t at − γ t d if yt ≥ at+ (b + v) /(b + 1)
5.1. The optimal self-learning procedure The wagon-repair production is classified weekly. In order to make the results of classification more visual, the corporative management determines 4 classes (ranks) of this
(11)
Then the value xt+ = at+ (b + v) /(b + 1) is called the upper classification norm. 2. If the current production indicator is negative ( yt < 0 ), then the corresponding adaptive assessment at−+1 used to assign the production to 1 or 2 class is recalculated:
a − + γ t v if yt < at− (b + v) /(b + 1) at−+1 = F − (at−+1, yt ) = −t at − γ t d if yt ≥ at− (b + v) /(b + 1)
(12)
The value xt− = at− ( b + v ) /( b + 1 ) is called the lower classification norm. Figure 4 shows the graphs of weekly indicators of production yt , as well as the upper norm xt+ and lower norm xt− , t = 1,52. As can be seen from Fig. 4, adaptive procedures (11) and (12) ensure fast convergence of the upper and lower norms to their stationary values. yt , xt+ , x t− xt+
5. Example: railway wagon-repair production Self-learning AIM M C = ( F , I ) applications that satisfy the conditions of the Theorem are aimed at using the production potential and obtaining correct assessments. Moreover, the Center can design some rules of decision making with appropriate adaptive assessments based on procedure (7) and the conditions of the Theorem. We illustrate such applications on the example of a self-learning AIM M C = ( F , I ) supporting the wagon-repair production of corporation Russian Railways. The management of this corporation weekly observes the actual volume of this production - the number of wagons released after an overhaul. This volume is matched with the weekly production plan (which is derived from the annual production plan, by dividing it by 52, that is, by the number of weeks in a year). The indicator yt , characterizing the efficiency of production in period t, is calculated as the deviation of actual weekly volume of production from the weekly production plan.
5
xt− yt
Fig. 4. Weekly indicators and norms obtained from self-learning AIM.
5.2. Production evaluations and ranking Based on weekly indicators and norms obtained from selflearning AIM M C = ( F , I ) (see Fig. 4), the management determines production rank (rt) in accordance with the decision rule:
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Vladimir Tsyganov / Procedia CIRP 84 (2019) 1088–1093 Author name / Procedia CIRP 00 (2019) 000–000
rt =
4 3 2 1
if if if if
yt ≥ xt+ = at+ (b + v) /(b + 1) 0 ≤ yt < xt+ = at+ (b + v) /(b + 1) t = 1,52 (13) xt− = at− (b + v) /(b + 1) ≤ yt < 0 yt < xt− = at− (b + v) /(b + 1)
So the upper classification norm xt+ = at+ ( b + v ) /( b + 1 ) is the lower limit of the production efficiency ( yt ) corresponding to excellent work of the staff. The lower classification norm xt− = at− ( b + v ) /( b + 1 ) is the lower limit of the production efficiency ( yt ) corresponding to satisfactory work of the staff. If the indicator yt is below this norm xt− , then management intervention in the work of production personnel is required. Figure 5 shows a graph of weekly production ranks rt calculated by the formula (13), t = 1,52. rt
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making in a large corporation production under conditions of uncertainty. In practice, managers in such a corporation perform various combinations of the above basic functions F,R,P, and I. Thus, combining obtained AIM M C = ( F , I ) for production clerk (Fig. 3) with AIM MB=(F,R,P,I) for sovereign manager (Fig. 1), and AIM MO=(F,P,I) for production officer (Fig. 2), it is possible to design more and more complex decision support systems in production management. Accordingly, future research in this area is related to the design of complex adaptive information models as effective innovative tools for processing big data about production in large corporations. Acknowledgements This work is partially sponsored by grant № 17-20-05216 given by Russian Foundation for Basic Research and corporation Russian Railways.
4 References
3 2 1 Fig. 5. Weekly production ranks obtained from self-learning AIM.
5.3. Stimulation of wagon-repair production The incentive system of wagon-repair production in the corporation is structured in such a way that the higher the production rank, the higher the rewards for the staff. Taking into account (13), we find that the higher the production indicators yt , the higher the staff incentives. In addition, according to (11) and (12), the higher the indicator yt , the lower the norms of ranking for the next period. Thus, with an increase in the indicator yt , the personnel receives not only higher rewards, but also “reward bars” for him in the future goes down. This further interests the personnel in the disclosure of the potential of production. In this case the adaptive procedures (11) and (12) ensure that corresponding assessments convergent to the optimal parameters of decision rule (9). Remember that the indicator yt , is calculated as the deviation of actual weekly volume of production from its plan. Thus self-learning AIM M C = ( F , I ) with procedures (11)-(13) satisfying the conditions of the Theorem is correct, and ensures the maximum volume of production. 6. Conclusions The proved theorem and the considered practical example show that the designed self-learning information model M C = ( F , I ) can be an effective tool to support the decision
[1] Blanchet M, Rinn T, Thaden G, Thieulloy G. INDUSTRIE 4.0 - the new industrial revolution. How Europe will succeed. München: Roland Berger Strategy Consultants GMBH; 2014. [2] Putnik GD. Semiotics-based manufacturing system integration. Int J of Computer Integrated Manufacturing 2010; 23: 8, 687-690. [3] Lödding H, Kersten W, Koller H. Industrie 4.0 wie intelligente vernetzung und kognitive systeme unsere arbeit verändern. Berlin: GITO; 2014. [4] Burkov V, Gubko M, Kondratiev V, Korgin N, Novikov D. Mechanism design and management. Mathematical methods for smart organizations. New York: NOVA Publishers; 2013. [5] Tsyganov V. Regulation of decentralized active system development and intelligent control mechanisms. IFAC-PapersOnline 2010; 9: 94-98. [6] Saridis G. Self-organazing control of stochastic systems. New York: Marsel Dekker, Inc; 1977. [7] Tsyganov V. Learning mechanisms in digital control of large-scale industrial systems. In: Global smart industry conf. Chelyabinsk: IEEE; 2018. doi: 10,0509/GloSIC.2018.8570093. [8] Putnik GD, Putnik Z. A semiotic framework for manufacturing systems integration - Part I: Generative integration model. Int J of Computer Integrated Manufacturing 2010; 23: 8, 691-709. [9] Bauernhansl T, Hompel M, Vogel-Heuser B. Industrie 4.0 in produktion, automatisierung und logistik - anwendung, technologie, migration. Wiesbaden: Springer; 2014. [10] Malygin I, Komashinsky V, Tsyganov V. International experience and multimodal intelligent transportation system of Russia. In: Proceedings of conf. on large-scale system development management. Moscow: IEEE; 2017. doi: 10.1109/MLSD.2017. 8109658. [11] Enaleev A, Tsyganov V. Service support structure optimization of a large-scale rail company. CEUR Workshop Proceedings 2018; 2098: 396406.
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ProcediaProcedia CIRP 00CIRP (2017) 84000–000 (2019) 1088–1093 www.elsevier.com/locate/procedia
29th CIRP Design 2019 (CIRP Design 2019) 29th CIRP Design 2019 (CIRP Design 2019)
Designing information models for management 28th CIRP Design Conference, May 2018, Nantes, France management Designing adaptive adaptive information models for production production Vladimir Tsyganov*
Vladimir Tsyganov* and physical architecture of A new methodology to analyze the functional Institute of Control Sciences, 65 Profsoyuznaya, Moscow, 115035, Russia existing products for anof Control assembly orientedMoscow, product family identification Institute Sciences, 65 Profsoyuznaya, 115035, Russia * Corresponding author. Tel.: +7-495-334-9331; fax: +7-495-334-9340. E-mail address: [email protected] * Corresponding author. Tel.: +7-495-334-9331; fax: +7-495-334-9340. E-mail address: [email protected]
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat
Abstract Abstract
École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France
*ACorresponding Tel.:design +33 3 87 54 30; E-mail address:models [email protected] methodologyauthor. of open of 37 adaptive information for production management under uncertainty, based on a cognitive approach
A of open the design of adaptive for production management under uncertainty, based on cognitive approach andmethodology taking into account human factor, isinformation developed. models This methodology is based on the idea of designing a variety of aadaptive information and taking intoonaccount human factor, is developed. This of methodology is based on that the idea of designing a variety of used. adaptive information models based a singlethe basic model. In this case, a variety adaptation procedures are publicly available can be As an example, models basedmodels on a single model. In this case, a variety of adaptation are publicly can be As anparameters example, information basedbasic on self-learning procedures are considered. Theprocedures results of that the operation of available these models areused. adaptive information based on self-learning procedures considered. results of the operation these models are adaptive parameters Abstract (norms) and models production estimates. When designing sucharemodels, it can The be used many of the formal of self-learning procedures described in the (norms) models, it caninformation be used many of the self-learning procedures in the scientificand andproduction technical estimates. literature. When As an designing example, such the self-learning model for formal production management based described on a stochastic scientific and technical literature. As an example, the self-learning information model for production management based on a stochastic designed. Sufficient for its correctness are found, ensure the thetoproduction potentialthe taking Inapproximation today’s business environment, theconditions trend towards more product variety andwhich customization is unfolding unbroken. of Due this development, needinto of approximation designed. Sufficient conditions for self-learning its correctness arevarious found,products which is ensure the unfolding of To the design production potential taking into account human factor. The application the information model illustrated byfamilies. the example of wagon-repair production of agile and the reconfigurable production systemsofemerged to cope with and product and optimize production account thecorporation human factor. The application of the self-learning information model is illustrated by the example of wagon-repair production of large-scale Russian systems as well as to choose theRailways. optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to large-scale corporation Russian Railways. analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and © Authors. Published Published Elsevier B.V. nature ofThe components. This fact by impedes anB.V. efficient comparison and choice of appropriate product family combinations for the production © 2019 2019 The Authors. Elsevier © 2019 The Authors. Published by by Elsevier B.V. committee of the CIRP Design Conference 2019 Peer-review under responsibility of the scientific system. A newunder methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster Peer-review responsibility of the scientific Peer-review under responsibility of the scientific committee committee of of the the CIRP CIRP Design Design Conference Conference 2019. 2019 these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable Keywords: Design; production; information; model; adaptation; management assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and Keywords: Design; production; information; model; adaptation; management a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of 1. Introduction It is the base of management design for smart production thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. 1. Introduction It is the base of management design taking into account the human factor [4].for smart production © 2017 The Authors. Published by Elsevier B.V. taking into account the human factor [4]. The concept of a new industrial revolutionof the called Cognitive control2018. implies the development of a cognitive Peer-review under responsibility of the scientific committee 28th CIRP Design Conference
The concept new onindustrial revolution called INDUSTRIE 4.0 ofis abased the extensive design of INDUSTRIE 4.0 is based on the extensive design of Keywords: Assembly; Designwith method; Family identification information networks elements of artificial intelligence information networks with elements of artificial intelligence and cognitive control [1]. and cognitive control [1].
Cognitive control forecasting implies the and development of a based cognitive strategy, including management on strategy, including forecasting and management based on feedback. The cognitive approach implies the construction feedback. The cognitive approach implies the construction and analysis of a cognitive map — a graph, whose vertices and analysis ofto a cognitive — a graph,personnel whose vertices correspond objects map (production and correspond to objects (production personnel and management), and the arcs between vertices to relations 1. Introduction of the product range and arcs characteristics manufactured and/or management), and the between vertices to relations 1.1. Cognitive approach to the production management between these objects. A cognitive map includes a set of arcs assembled in this system. In this context, main challenge in 1.1. Cognitive approach to the production management between these objects. cognitive map the includes set of arcs connecting objects that A reflect the sequence of theira actions. Due to the fast development in the domain of modelling and analysis is nowthenot only toofcope with single connecting objects that reflect sequence their actions. Cognitive approach is the method of analysis and design Such cognitive map of production management in communication and an isongoing trendof of digitization and products, limited product or existing product families, Cognitive approach the method analysis and Such acognitive map isrange ofshown production in based on cognition, the search for interrelationships of design events conditions of uncertainty on Fig. management 1. At the upper digitalization, manufacturing enterprises are facing important but also to be able to analyzeisand to compare products to define based on cognition, the search for interrelationships of events conditions of uncertainty shown on Fig. 1. At the upper and phenomena. For example, the promising direction of the level of it is production management (Center), and at the challenges in today’s market environments: a continuing new product It can be observed that classical and phenomena. Forinexample, promising direction of the level it isfamilies. (Center), andexisting at the cognitive approach relation the to the manufacturing system lower oflevel - production production management personnel realizing technological tendency towards reduction of product development times and product families are regrouped in function of clients or features. cognitive approach in relation to the manufacturing system lower level production personnel realizing technological integration is based on a semiotic - the science of “signs” [2]. process with external input ξt and output yt, where t - time shortened product lifecycles. In addition, there is an increasing However, assembly oriented are hardlyt to- find. output integration is based on a semiotic [2]. process twith external input product ξt andthefamilies t, where Cognitive control can be - the usedscience for ofthe“signs” systemic period, = 0,1, ... Accordingly, core yprocedures oftime the demand of customization, being at used the same time in systemic a global On thet =product family level, products differ mainly in Cognitive control can be for the period, 0,1, ... Accordingly, the core procedures of two the coordination of different processes deals with production [3]. production management decision support system should be competition competitors all over thewith world. This trend, main characteristics: (i) thedecision number support of components (ii) the coordinationwith of different processes deals production [3]. production management system and should be which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). markets, results in diminished lot sizes due to augmenting Classical methodologies considering mainly single products product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the 2212-8271 © 2019 The Authors. Published by Elsevier B.V. 2212-8271 ©under 2019 Theaugmenting Authors. of Published by Elsevier To cope with this ascommittee wellB.V. asoftothebeCIRP ableDesign to Conference product 2019 structure on a physical level (components level) which Peer-review responsibility thevariety scientific Peer-review under responsibility of the scientific committee of the CIRP Design Conference 2019 identify possible optimization potentials in the existing causes difficulties regarding an efficient definition and production system, it is important to have a precise knowledge comparison of different product families. Addressing this 2212-8271©©2017 2019The The Authors. Published by Elsevier 2212-8271 Authors. Published by Elsevier B.V. B.V. Peer-review under responsibility of scientific the scientific committee theCIRP CIRP Design Conference 2019. Peer-review under responsibility of the committee of the of 28th Design Conference 2018. 10.1016/j.procir.2019.03.271
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Vladimir Tsyganov / Procedia CIRP 84 (2019) 1088–1093 Author name / Procedia CIRP 00 (2019) 000–000
forecasting (F), resource allocation (R), planning (P) and incentive (I) (see Fig. 1).
1.2. Artificial intelligence and adaptation in production management “Intelligent means able to adapt, communicate and interact” [1]. So the first important element of artificial intelligence in a production deals with adaptation at changes. The design of production management with such elements of artificial intelligence as the ability to self-study and learning is becoming increasingly important [5]. Accordingly, procedure of forecasting (F) should be adaptive. To design this procedure a variety of adaptive algorithms described in the scientific and technical literature can be used [6]. For their implementation in decision support systems is created the basic adaptive information model (AIM), denoted as MB=(F,R,P,I) (see Fig. 1).
PRODUCTION MANAGEMENT (CENTER) MB=(F,R,P,I) RESOURCE (R)
PLAN (P)
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The logical architecture of production management in the era of intelligent networks is discussed in [9]. A feature of this architecture is the continuous management of the interaction of the elements of complex large-scale systems, such as the intelligent transport system of Russia [10]. The results of cognitive control can be used for system integration of elements of artificial intelligence [1]. This integration involves the coordination of various processes related to production and design of extensive information networks. An example of the optimal design of such information and telecommunication networks to support the management structure of a large railway company is considered in [11]. Long-term networking of intelligent production elements (creative industrial enterprises) ultimately leads to increased productivity and the cost of each [9]. Technologies of digital interaction of production systems are considered in [9]. Similar digital communication technologies are used in decision support systems for largescale production management [11]. For example, a decision support system developed on the basis of the above “reduced” AIM MO=(F,P,I) (see Fig. 2) is included in the information network of the innovation design cycle and their introduction into production at the corporation Russian Railways [7].
FORECAST (F) PRODUCTION OFFICER (CENTER)
INCENTIVE ( I )
MO=(F,P,I) FORECAST (F)
PRODUCTION PERSONNEL ξt
PLAN (P)
TECHNOLOGICAL PROCESS
INCENTIVE ( I )
yt Fig. 1. The basic AIM MB=(F,R,P,I) sovereign production manager.
AIM MB=(F,R,P,I) can be used as a base module to design other AIM in the face of uncertainty. In particular, in practice, the manager can perform only part of the above main functions F, R, P, and I. Therefore, it requires more simple AIM. For example, in [7] AIM MO=(F,P,I) investigated, designed to support a decision-making officer who does not have a resource allocation procedure (R) (Fig. 2). There, the production officer uses only the results of calculations of the forecast (F), planning (P) and incentives (I) from AIM MO=(F,P,I).
1.3. Intelligent networks with cognitive systems The other important elements of artificial intelligence in a manufacturing deal with communication and interaction. Production using intelligent networks with cognitive systems discussed in [3]. Cognitive semiotic framework for manufacturing systems integration deals with signs which could be linguistic or non-linguistic [8].
PRODUCTION PERSONNEL ξt
TECHNOLOGICAL PROCESS
yt
Fig. 2. The AIM MO=(F,P,I) for production officer.
In this article, we will look at the design of another important “reduced” AIM M C = ( F , I ) , which supports the decision making of a production clerk (who does not have the functions of regulatory planning P and resource allocation R). This model M C = ( f , I ) is self-learning by accumulating knowledge about production and forms adaptive norms, on the basis of which production can be estimated and personnel can be stimulated 2. Self-learning classification Many of the tasks of production management are reduced to the classification of observed situations and events. Examples include the early detection and prevention of
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disruptions or deficiencies in production due to random external interference ξt (see Fig. 1). The classification of the observed situations is carried out on the basis of the decision rule. Management is carried out depending on the result of this classification. With sufficient a priori information, the rules of the theory of statistical solutions are used. However, in a stochastic setting, a priori information is often not enough. There is a need to adapt the decision rule so as to minimize the loss of classification. This adaptation can be performed by observing the output of production using a self-learning procedure, for example, based on a stochastic approximation. Let p be a random variable characterizing production potential, p ∈ D ⊂ R1+ . Suppose that the Center can observe the random values of this variable. The task is to classify the production situation by assigning p it to one of the two domains that make up the set D. Incorrect classification leads to losses. 2.1. Density distribution of a random potential Suppose first that the Center knows the density distribution q(p) of a random variable p. Let us consider a partition of a set D into 2 domains D1 and D2, D1 ∪ D2 = D. In the classification, i.e. attributing the situation p to one of these domains, production management (the Center) makes a decision associated with some risk. The problem is in defining a partition that minimizes the average risk associated with the classification. For each unknown domain D1 and D2,, we introduce loss functions Lk ( c , p ), k = 1,2, , where c is an unknown parameter of the decision rule. Minimizes the average risk that evaluates the quality of the classification
3
where the parameter of the decision rule (с) can be found as a solution to task (1) from condition (2). 2.2. Stochastic approximation of the decision rule parameter In practice, density distribution q(p) it is usually unknown. Therefore, it is not possible to directly determine the parameter c, solving the optimization task (1). So there is a need to adjust the parameter of the decision rule by observing the sequence pt , t=0,1,..., to minimize (1). Let use the method of stochastic approximation to solve (1). Taking into account (3) it is not difficult to show that
сt +1 = F (ct , pt ) t → c* = arg min J (c), →∞
(5)
if the procedure for forecasting of a decision rule parameter is
c + γ v if pt < (b + v)ct /(b + 1) сt +1 = F (ct , pt ) = t t , ct − γ t d if pt ≥ (b + v)ct /(b + 1) ∞
γ t > 0,
∑ γ t < ∞,
(6)
c0 = c 0 , t = 0,1,...
t =0
where γ t is adaptation coefficient. Because of (5), procedure F ( c , pt ) is called the optimal self-learning procedure. Note that to apply the procedure (6), Center must know the sequence of production potentials, pt, t=0,1,… However, in practice, production potential depends on external input ξ t (for example, interference) and other factors not always known to management. For actions in conditions of uncertainty, management needs to learn.
2
J ( c ) = ∑ ∫ Lk ( c , p )q( p )dp → min c
(1)
3. Self-learning information model
k =1 Dk
The condition of minimum average risk (2) is:
2 1 if p ∈ Dk dL ( c , p ) M p ∑ Bk ( c , p ) k , (2) = 0, Bk ( c , p ) = dc 2 if p ∉ Dk k =1 where Mp is the expectation operator. The belonging p of a particular domain is determined by the sign of the decision rule g( c , p ) = L1( c , p ) − L2 ( c , p ) :
D if g( c , p ) < 0 p∈ 1 D2 if g (c , p ) ≥ 0
(3)
Let L1( c , p ) = p − vc, v < 1, L2 ( c , p ) = b( c − p ), vc ≤ p ≤ c. Substituting these expressions into (3), we obtain the decision rule for the classification in the form
D if p < ( b + v )c /( b + 1 ) y ∈ 1 , D2 if p ≥ ( b + v )c /( b + 1 )
In practice, staff is almost always more informed about production potential than management. In such cases, we talk about the asymmetric awareness of the parties [4]. Suppose that the potential pt is unknown to the Center. The potential pt becomes known to the staff at the beginning of the production period t, i.e. until the choice of output yt. So knowing pt, the staff can choose the indicator of production yt so as to provide themselves with the best estimates and incentives today and in the future. Of course, in any case, this output can not exceed the potential: yt ≤ pt . The Center only observes the output yt (which is not necessarily equal to the production potential, because of yt ≤ pt ). To support its decisions, the Center uses the selflearning AIM M C = ( F , I ) based on yt (see Fig. 3). In this AIM an adaptive assessment at +1 of the decision rule parameter сt +1 is formed, by using the optimal self-learning procedure (6):
a + γ v if yt < ( b + v )at /( b + 1 ) at +1 = F ( at , yt ) = t t at − γ t d if yt ≥ ( b + v )at /( b + 1 )
(7)
(4) In addition, a production evaluation et = I ( at , yt ) is formed in the self-learning AIM M C = ( F , I ) as a function of
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assessment at and output yt (Fig. 3). Depending on this evaluation et , the Center encourages staff.
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4.2. Management objectives
The main goal of management is using production potential pt. Thus the Center needs to design an AIM M C = ( F , I ) where staff is interested in unlocking production potential that is, fulfilling equality: yt = pt . In addition when yt ≠ pt , from (6) and (7) it follows that at ≠ ct . So generally speaking the adaptive assessment at does not converge to the optimal parameter c*. Therefore, the assessment obtained by using AIM M C = ( F , I ) may be far from optimal. Consequently, another important management goal is to design a correct AIM M C = ( F , I ) in which
PRODUCTION CLERC (CENTER) MC = ( F, I ) FORECAST WITH SELF-LEARNING at +1 = F ( at , yt )
INCENTIVE WITH PRODUCTION EVALUATION et = I ( at , yt )
at t → c*, a0 = a 0 , t = 0,1,... →∞
4.3. Disclosure of production potential and model correctness Suppose that the set of possible yt on which the maximum V ( at , yt ) is reached includes the point yt = pt . Then we will say that the hypothesis of benevolence of personnel with respect to the Center is valid if the personnel chooses an output equal to the potential: yt = pt (that is, uses the full potential of production). Theorem. For using the production potential and correctness AIM M C = ( F , I ) it is enough (7) and
PRODUCTION PERSONNEL ξt
(9)
TECHNOLOGICAL PROCESS yt Fig. 3. The AIM MC = ( F, I ) with self-learning.
1 if I ( at , yt ) = 0 if
4. Optimal design of a self-learning information model The Сenter is interested in using production potential pt unknown to it. However, the staff, knowing true potential pt, can choose the production indicator yt to provide the best incentives today and in the future. As a result of asymmetric awareness of a potential pt, a game of personnel and management arises. 4.1. Purpose and undesirable activities of production personnel Suppose that the potential pt becomes known to personnel before selecting an output yt in period t. Based on the fact that the output cannot exceed the potential: ( yt ≤ pt ), the farsighted personnel can choose yt so as to maximize own objective function t +T
V ( at , yt ) = ∑ ρ τ −t I ( aτ , yτ ),
(8)
τ =t
where ρ is the discount factor, 0 < ρ < 1, T is the staff foresight. In general, as a result of human factor - undesirable personnel activities aimed at maximizing the entire function (8), the output does not equal the production potential: yt ≠ pt .
yt ≥ at ( b + v ) /( b + 1 ) yt < at ( b + v ) /( b + 1 )
(10)
Proof. The objective function of the personnel V ( at , yt ) , determined according to (8), depends on both current and future evaluations eτ = I ( aτ , yτ ), τ = t ,t + T . By condition (10), as the indicator yt grows, the current evaluation et = I ( at , yt ) increases (does not decrease). Further, the Center uses the self-learning procedure (7), in which aτ decreases (does not increases) with growth yt when τ = t + 1,t + T . Consequently, according to (10), the future evaluation eτ = I ( aτ , yτ ) increases (do not decreases) with growth yt when τ = t + 1,t + T . So all terms on the right side (8) monotonically increase with growth yt . Thus the objective function of the personnel V ( at , yt ) , determined according to (8), monotonically increases with increases (do not decreases) with growth yt . Since yt ≤ pt , then the maximum V ( at , yt ) is at yt = pt . Consequently, by virtue of the benevolence hypothesis, the personnel choose an output yt equal to the potential: yt = pt . Thus personnel use of the potential of production. In addition, when yt = pt from (6) and (7) it follows (9). Then AIM M C = ( F , I ) is correct, QED. 4.4. Interpretation of the optimal design theorem Theorem admits a simple interpretation. Suppose that the higher the evaluation eτ = I ( aτ , yτ ) , the higher the staff incentives. The Center observes the value yt characterizing the efficiency of production in period t, wherein yt ≤ pt , and
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pt is the unknown (random) potential of production. So based on yt the Center adapts the decision rule parameter (7). Further, in accordance with the adopted decision rule (10), the Center classifies personnel according to the results of production. If yt < at ( b + v ) /( b + 1 )] then, the personnel belong to the class of dysfunctional (rank I ( at , yt ) = 0 ) and punished. If yt ≥ at ( b + v ) /( b + 1 )] then, the personnel belong to the class of successful (rank I ( at , yt ) = 1 ) and encouraged. Any of these decisions is associated with a certain risk for the Center. In the first case, losses L1( at , yt ) = yt − vat increase with a growth of the efficiency of production ( yt ) and an unjust punishment of personnel. In the second case, losses L2 ( at , yt ) = b( at − yt ) increase with the deterioration of the indicator yt (undeserved reward or bonus payments). So the classification norm xt = at ( b + v ) /( b + 1 ) is the lower limit of the production efficiency ( yt ) corresponding to satisfactory work of the staff. Note that, according to (6) - (8), the higher the indicator of production ( yt ), the lower the classification norm for the next period xt +1 = at +1( b + v ) /( b + 1 ). But, according to (10), this norm xt +1 plays the role of the threshold value of the indicator yt +1 , at which the staff will receives a promotion in the next period t+1. Consequently, it becomes easier for staff to get a promotion from the Center in the next period t+1, even with a smaller value of the random potential pt. In other words, with an increase of production efficiency ( yt ), personnel receives not only a higher reward. Also the threshold value for incentives in the future ( xt +1 ) is decreased. This further interest the personnel in the disclosure of the potential of production, i.e. in the selection yt = pt . In this case the adaptive procedure (7) ensures that assessment at is convergent to the optimal parameter of decision rule (c*).
production - excellent (4), good (3), satisfactory (2), and bad (1). To do this classification, the management forms the following 2 procedures for determining the adaptive assessments of the parameters of the decision rule, designing them from the basic optimal procedure (7) satisfying the conditions of the Theorem. 1. If the current production indicator is non-negative ( yt ≥ 0 ), then the corresponding adaptive assessment at++1 used to assign production to class (rank) 3 or 4 is recalculated:
a + + γ t v if yt < at+ (b + v) /(b + 1) at++1 = F + (at++1, yt ) = +t at − γ t d if yt ≥ at+ (b + v) /(b + 1)
5.1. The optimal self-learning procedure The wagon-repair production is classified weekly. In order to make the results of classification more visual, the corporative management determines 4 classes (ranks) of this
(11)
Then the value xt+ = at+ (b + v) /(b + 1) is called the upper classification norm. 2. If the current production indicator is negative ( yt < 0 ), then the corresponding adaptive assessment at−+1 used to assign the production to 1 or 2 class is recalculated:
a − + γ t v if yt < at− (b + v) /(b + 1) at−+1 = F − (at−+1, yt ) = −t at − γ t d if yt ≥ at− (b + v) /(b + 1)
(12)
The value xt− = at− ( b + v ) /( b + 1 ) is called the lower classification norm. Figure 4 shows the graphs of weekly indicators of production yt , as well as the upper norm xt+ and lower norm xt− , t = 1,52. As can be seen from Fig. 4, adaptive procedures (11) and (12) ensure fast convergence of the upper and lower norms to their stationary values. yt , xt+ , x t− xt+
5. Example: railway wagon-repair production Self-learning AIM M C = ( F , I ) applications that satisfy the conditions of the Theorem are aimed at using the production potential and obtaining correct assessments. Moreover, the Center can design some rules of decision making with appropriate adaptive assessments based on procedure (7) and the conditions of the Theorem. We illustrate such applications on the example of a self-learning AIM M C = ( F , I ) supporting the wagon-repair production of corporation Russian Railways. The management of this corporation weekly observes the actual volume of this production - the number of wagons released after an overhaul. This volume is matched with the weekly production plan (which is derived from the annual production plan, by dividing it by 52, that is, by the number of weeks in a year). The indicator yt , characterizing the efficiency of production in period t, is calculated as the deviation of actual weekly volume of production from the weekly production plan.
5
xt− yt
Fig. 4. Weekly indicators and norms obtained from self-learning AIM.
5.2. Production evaluations and ranking Based on weekly indicators and norms obtained from selflearning AIM M C = ( F , I ) (see Fig. 4), the management determines production rank (rt) in accordance with the decision rule:
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rt =
4 3 2 1
if if if if
yt ≥ xt+ = at+ (b + v) /(b + 1) 0 ≤ yt < xt+ = at+ (b + v) /(b + 1) t = 1,52 (13) xt− = at− (b + v) /(b + 1) ≤ yt < 0 yt < xt− = at− (b + v) /(b + 1)
So the upper classification norm xt+ = at+ ( b + v ) /( b + 1 ) is the lower limit of the production efficiency ( yt ) corresponding to excellent work of the staff. The lower classification norm xt− = at− ( b + v ) /( b + 1 ) is the lower limit of the production efficiency ( yt ) corresponding to satisfactory work of the staff. If the indicator yt is below this norm xt− , then management intervention in the work of production personnel is required. Figure 5 shows a graph of weekly production ranks rt calculated by the formula (13), t = 1,52. rt
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making in a large corporation production under conditions of uncertainty. In practice, managers in such a corporation perform various combinations of the above basic functions F,R,P, and I. Thus, combining obtained AIM M C = ( F , I ) for production clerk (Fig. 3) with AIM MB=(F,R,P,I) for sovereign manager (Fig. 1), and AIM MO=(F,P,I) for production officer (Fig. 2), it is possible to design more and more complex decision support systems in production management. Accordingly, future research in this area is related to the design of complex adaptive information models as effective innovative tools for processing big data about production in large corporations. Acknowledgements This work is partially sponsored by grant № 17-20-05216 given by Russian Foundation for Basic Research and corporation Russian Railways.
4 References
3 2 1 Fig. 5. Weekly production ranks obtained from self-learning AIM.
5.3. Stimulation of wagon-repair production The incentive system of wagon-repair production in the corporation is structured in such a way that the higher the production rank, the higher the rewards for the staff. Taking into account (13), we find that the higher the production indicators yt , the higher the staff incentives. In addition, according to (11) and (12), the higher the indicator yt , the lower the norms of ranking for the next period. Thus, with an increase in the indicator yt , the personnel receives not only higher rewards, but also “reward bars” for him in the future goes down. This further interests the personnel in the disclosure of the potential of production. In this case the adaptive procedures (11) and (12) ensure that corresponding assessments convergent to the optimal parameters of decision rule (9). Remember that the indicator yt , is calculated as the deviation of actual weekly volume of production from its plan. Thus self-learning AIM M C = ( F , I ) with procedures (11)-(13) satisfying the conditions of the Theorem is correct, and ensures the maximum volume of production. 6. Conclusions The proved theorem and the considered practical example show that the designed self-learning information model M C = ( F , I ) can be an effective tool to support the decision
[1] Blanchet M, Rinn T, Thaden G, Thieulloy G. INDUSTRIE 4.0 - the new industrial revolution. How Europe will succeed. München: Roland Berger Strategy Consultants GMBH; 2014. [2] Putnik GD. Semiotics-based manufacturing system integration. Int J of Computer Integrated Manufacturing 2010; 23: 8, 687-690. [3] Lödding H, Kersten W, Koller H. Industrie 4.0 wie intelligente vernetzung und kognitive systeme unsere arbeit verändern. Berlin: GITO; 2014. [4] Burkov V, Gubko M, Kondratiev V, Korgin N, Novikov D. Mechanism design and management. Mathematical methods for smart organizations. New York: NOVA Publishers; 2013. [5] Tsyganov V. Regulation of decentralized active system development and intelligent control mechanisms. IFAC-PapersOnline 2010; 9: 94-98. [6] Saridis G. Self-organazing control of stochastic systems. New York: Marsel Dekker, Inc; 1977. [7] Tsyganov V. Learning mechanisms in digital control of large-scale industrial systems. In: Global smart industry conf. Chelyabinsk: IEEE; 2018. doi: 10,0509/GloSIC.2018.8570093. [8] Putnik GD, Putnik Z. A semiotic framework for manufacturing systems integration - Part I: Generative integration model. Int J of Computer Integrated Manufacturing 2010; 23: 8, 691-709. [9] Bauernhansl T, Hompel M, Vogel-Heuser B. Industrie 4.0 in produktion, automatisierung und logistik - anwendung, technologie, migration. Wiesbaden: Springer; 2014. [10] Malygin I, Komashinsky V, Tsyganov V. International experience and multimodal intelligent transportation system of Russia. In: Proceedings of conf. on large-scale system development management. Moscow: IEEE; 2017. doi: 10.1109/MLSD.2017. 8109658. [11] Enaleev A, Tsyganov V. Service support structure optimization of a large-scale rail company. CEUR Workshop Proceedings 2018; 2098: 396406.