Approach to Data-Driven Production Management Anton Romanov Aleksey Filippov Nadezhda Yarushkina Department of Information Systems Department of Information Systems Department of Information Systems Ulyanovsk State Technical University Ulyanovsk State Technical University Ulyanovsk State Technical University Ulyanovsk, Russia Ulyanovsk, Russia Ulyanovsk, Russia romanov73@gmail.com al.filippov@ulstu.ru jng@ulstu.ru ORCID: 0000-0001-5275-7628 ORCID: 0000-0003-0008-5035 ORCID: 0000-0002-5718-8732 Abstract—There are many methods and models for analyzing of production processes and the need for their adaptation to and managing complex systems. They differ in both the degree the changing nature of the problem area. of complexity and the degree of detail of the described objects. The industry-accepted standards of the industrial methodol- Mathematical models of business processes are very hard to implement. They do not consider multiple external and internal ogy are used to represent aircraft manufacturing and capacity influences o n t he p roduction, w hich m akes s uch m odels less management. The industrial methodology is formed based effective. on averaged indicators in the industry, which leads to the An alternative way to solve the production management following problems [4], [5]: problem is to introduce some parameterized algorithms as a simplified f orm o f m athematical m odels. S uch a lgorithms are 1) A large number of statistical factors and assumptions are usually expressed in the form of instructions, which are based on used for production control. the analyzed statistics. The disadvantage of this approach is the 2) Absence of methods for an objective evaluation of the significant averaging of the values of indicators and parameters of current state of production. the modeled objects. Methods are formulated for a whole range of similar industries, and they are unsuitable for the specific 3) Absence of methods for identifying problems and devi- conditions of each enterprise. ations in production processes. It is necessary to create data analysis methods and process 4) Automation of production processes does not imply an models that are adaptable to specific p roduction conditions. evaluation of the complex state of the enterprise leads Data from the information systems of various manufacturing to: enterprises can be analyzed to determine the states and con- ditions of production. The important knowledge for production • the complexity of forming an adaptable production management is extracted as a result of such analysis. model, The article describes a hybrid approach for analyzing the • frequent changes in methods for calculating evalu- dynamics of production indicators and forming linguistic rec- ation indicators, ommendations to increase the efficiency and quality of decision • the inability to identify hidden processes and sub- making. Hybridization means the usage of ontological engineer- ing methods to describe the characteristics of production in processes. the context of production indicators represented by time series Capacity management is the decision-making process for models. the choice of equipment used, planning and management of Keywords—data-driven decision making, type-2 fuzzy sets, the work schedule and working hours, materials and blanks, time series forecasting, ontology, inference units, and assemblies. The solution is based on an analysis of the data of the I. I NTRODUCTION enterprise information systems. The dynamic state of objects is modeled by a fuzzy time series. Existing formal models of production processes do not have the necessary capabilities for organizing data-driven In this case, the task is similar to the traditional problem of production management for modern complex industries, taking situational control of some object [1] (fig. 1). into account the dynamics of production [1]–[3]. Aircraft As you can see from figure 1, (n + r) inputs X and W manufacturing is used as an example of a manufacturing act on the controlled object. The value of the input xi can be enterprise in this study. determined at any time, but there is no such possibility for the Aircraft is a complex system with both quantitative and value of the input wj . The controlled object has m outputs Y . qualitative complexity. The quantitative complexity is deter- It is assumed that changes in the input values of X and W mined by the quantity of the components of the aircraft. The affect to the output values of Y , therefore exists some implicit qualitative complexity is determined by the complexity of function Y = f (X, W ). production processes and a high degree of uncertainty caused The output values of Y are usually critical in the decision- by the integral influence of many external and internal factors. making process for controlling an object. The decision-maker Modern aircraft enterprises produce a line of systems and (DM) needs to get certain values of the output parameters Y , their modifications. T his f act d etermines t he d ynamic nature while the DM cannot modify the input values of X and W . Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) Data Science Obtaining the necessary values of Y is possible by changing Trend analysis in production processes is carried out using the values of U , so the function Y = F (X, U, W ) exists. It the proposed models and methods for analyzing time series is necessary to find such values of U to get the output values based on type 2 fuzzy sets. The results of modeling the time of Y that satisfy the decision-maker with known input values series of production indicators are input data for the subsystem of X and unknown input values of W . Thus, the function to for generating recommendations for the modification of pro- control an object is U = Φ(X, Y ). duction. This allows to expand the output vector Y . Estimated and forecasted values of indicators and recommendations for production modification allow discarding some parameters of the vector W . These models and the analyzed indicators will be included in the control system U = Φ(X, Y ). III. T IME SERIES MODEL BASED ON TYPE -2 FUZZY SETS Type-2 fuzzy sets are making it possible to model uncer- tainty of higher degree in the process of time series modeling [7], [8]. It is suggested to use the triangular shape of fuzzy sets. The triangular shape of fuzzy sets has low computational complexity on time-series modeling. Type 2 fuzzy sets à in the universum U can be defined using type 2 membership function. Type 2 fuzzy sets can be represented as: à = ((x, u), µÃ (x, u))|∀x ∈ U, ∀u ∈ Jx ⊆ [0, 1] Fig. 1. An example of situational control of an object. where x ∈ U and u ∈ Jx ⊆ [0, 1] in which 0 ≤ µÃ (x, u) ≤ 1. The main membership function is in the range from 0 to 1, II. THE TASK OF DATA-DRIVEN PRODUCTION so the appearance of the fuzzy set is expressed as: Z Z MANAGEMENT à = µÃ (x, u)/(x, u)Jx ⊆ [0, 1] The main goal of the study is to reduce the degree of x∈U u∈Jx uncertainty in the capacity management process of complex where the operator RR denotes the union over all incoming production. Each production has various characteristics. Also, x and u. complex production is an unconventional object of manage- Time series modeling needs to define interval fuzzy sets and ment in the concept of the situational control theory [1]. their shape. The fig. 2 shows the appearance of the sets. The capacity management includes next steps: • developing technical passport of the enterprise; • calculation of capacities for each production unit and the enterprise as a whole; • development of shortage control strategy; • generation of a consolidated report with the forecast for the implementation of the product program; • calculation of consolidated capacity balance. The input parameter vector W from situational control in- cludes such indicators as the fund of working time, equipment usage, the useful annual fund of equipment time, and others. These indicators have a great influence on the evaluation of total production productivity. The inability of the DM to set the values of these indicators severely limits the efficiency of decisions. Fig. 2. The shape of the upper and lower membership functions. Thus, the following research objectives must be solved: Triangular fuzzy sets are defined as follows: • data collection of production state through integration with enterprise information systems (data consolidation, Ãi = (ÃU L u u u U i , Ãi ) = ((ai1 , ai2 , ai3 , h(Ãi )), ETL) [6], (ali1 , ali2 , ali3 , h(Ãli ))). • trend analysis of process performance (time-series anal- ysis and modeling), where ÃU L i and Ãi is a triangular type 1 fuzzy sets; • developing recommendation for the DM to manufacture ai1 , ai2 , ai3 , ai1 , ali2 , ali3 , is reference points of type 2 interval u u u l upgrade in terms of balancing production capacities. fuzzy set Ãi , h is the value of the membership function of the VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 184 Data Science element ai (for the upper and lower membership functions, ontology is used to get linguistic summarization of the time respectively). series forecast [10], [11]: An operation of combining type 2 fuzzy sets is required in O = hI, E, S, A, R, F i, (1) the process of working with a rule base build on the values of a time series. The combining operation defined as follows: where I = {I1 , I2 , . . . , In } is a set of indicators that determine the state of the production capacities at some point Ã1 ⊕ Ã2 = (ÃU L U L 1 , Ã1 ) ⊕ (Ã2 , Ã2 ) = in time; = ((au11 + au21 , au12 + au22 , au13 + au23 ; E = {Bad, Good, High, M iddle, Low} is a set of linguistic min(h1 (ÃU U U U U 1 ), h1 (Ã2 )Ã1 )), min(h2 (Ã1 ), h2 (Ã2 )), ); labels for linguistic summarization of the values of production (al11 + al21 , al12 + al22 , al13 + al23 ; indicators; S = {StateHigh, StateM iddle, StateLow} is a set of min(h1 (ÃL L L L 1 ), h1 (Ã2 )), min(h2 (Ã1 ), h2 (Ã2 ))); textual representations of linguistic labels from the set E; The proposed algorithm for smoothing and forecasting of A = {hI1 , Badi, hI1 , Goodi, hI2 , Badi, hI2 , Goodi, . . . , time series based on type 2 fuzzy sets can be represented as hIn , Badi, hIn , Goodi} is a set of textual representations of a sequence of the following steps: recommendations for each production indicator that depends on various evaluation of its condition: Good (within the 1) Determination of the universe of observations. U = norm) and Bad (deviation from the norm); [Umin , Umax ], where Umin and Umax are minimal and R is a set of ontology relationships: maximal values of a time series respectively. 2) Definition of membership functions for a time series R = {RE S, RE A, RI E}, M = {µ1 , . . . , µl }, l  n, where l is the number of where RE S is a set of relationships between a linguistic label membership functions of fuzzy sets, n is the length of a and its textual representation; time series. The number of membership functions and, RE A is a set of relationships between a linguistic label and a accordingly, the number of fuzzy sets is chosen relatively textual representation of a recommendation; small. The motivation for this solution is the multi-level RI E is a set of relationships between a value of production approach to modeling a time series. To decrease the indicator and its linguistic label. This type of relationship is dimension of the set of relations it is necessary to reduce formed in the process of linguistic summarization of the values the number of fuzzy sets at each level. Obliviously, of production indicators using the reasoner and the set of rules this approach decrease the approximation accuracy of in the SWRL language [12]; a time series. However, creating the set of membership F is interpretation function that forms the set of relations RI E functions at the second and higher levels increase the defined by the set of rules in SWRL. approximation accuracy with an increase in the number The ALCHF(D) [13]–[15] extension of the descriptive of levels. logic is used for the logical presentation of the ontology O 3) Definition of fuzzy sets for a time series. The su- (eq. 1) for linguistic summarization of the time series forecast. perscript defines the type of fuzzy sets in that case. With using the description logic ALCHF(D) the ontology O A1 = {A11 , . . . , A1l }, A2 = {A21 , . . . , A2m }, where l is can be represented as: the number of type 1 fuzzy sets, m is the number of type 2 fuzzy sets. O = T Box ∪ ABox, 4) Fuzzification of a time series by type 1 sets. ∀xi ỹi = F uzzy(xi ) where T Box is the terminological box; 5) Fuzzification a time series by type 2 sets. ABox is the assertional box. 6) Creation of relations. The rules for the creation of rela- The T Box contains statements describing concept hier- tions are represented in the form of pairs of fuzzy sets archies and relations between them. The ABox contains in terms of antecedents and consequents, for example: axioms defined as a set of individuals and relations between A11 A21 . . . −→ A12 A2 1. individuals and concepts. 7) Forecasting for the first and second levels based on a A. Terminological box T Box set of rules. The forecast is calculated by the centroid method, first on type 1 fuzzy sets A1 = {A11 , . . . , A1l }, Ev> Bad v E Good v E then on type 2 fuzzy sets. High v E M iddle v E Low v E 8) Errors evaluation. High v ¬Low High v ¬M iddle M iddle v ¬Low Bad v ¬Good IV. O NTOLOGY- BASED LINGUISTIC SUMMARIZATION OF A Recommendation v > A v Recommendation TIME SERIES FORECAST S v Recommendation Linguistic Summarization of the time series forecast allows StateHigh v S StateM iddle v S the decision-maker to react to changes in the production state StateLow v S more operatively. The rule base in the form of the following StateHigh v ¬StateM iddle VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 185 Data Science StateHigh v ¬StateLow ˆ swrlb:greaterThan(?val, 2000) StateLow v ¬StateM iddle ˆ swrlb:lessThanOrEqual(?val, 4000) Iv> −> Middle(?ind) I ≡ > u ∃hasResume.A u ∃hasState.S u EP(?ind) ˆ hasValue(?ind, ?val) u∃hasV alue.Double ˆ swrlb:greaterThan(?val, 4000) Recommendation ≡ > u ∃hasDescription.String u −> High(?ind) u∀hasDescription.String TP(?ind) ˆ hasValue(?ind, ?val) where E is a concept representing a linguistic label of ontol- ˆ swrlb:lessThanOrEqual(?val, 1000) ogy; −> Low(?ind) Bad, Good, High, M iddle, Low are concepts representing TP(?ind) ˆ hasValue(?ind, ?val) linguistic labels for linguistic summarization of values of ˆ swrlb:greaterThan(?val, 1000) production indicators; ˆ swrlb:lessThanOrEqual(?val, 3000) I is a concept representing a production indicator; −> Middle(?ind) S is a concept representing a linguistic label; TP(?ind) ˆ hasValue(?ind, ?val) A is a concept representing ontology recommendations; ˆ swrlb:greaterThan(?val, 3000) StateHigh, StateM iddle, StateLow are concepts represent- −> High(?ind) ing the state of production capacities; Recommendation is a concept representing linguistic labels Each production indicator is associated with a specific and recommendations in textual form; linguistic label after the implementation of these rules: v is the concept inclusion axiom; EP : M iddle T P : M iddle hasResume is a role to set the correspondence between the recommendation and the production indicator; A predefined set of SWRL rules is used to map a linguistic hasState is a role to set the correspondence between a label to its textual representation: linguistic label and a production indicator; hasV alue is a role to set a value (in Double) of production Low(?ind) ˆ StateLow(?state) indicator; −> hasState(?ind, ?state) hasDescription is a functional role to specify a textual Middle(?ind) ˆ StateMiddle(?state) description (in String) of a linguistic label or recommendation. −> hasState(?ind, ?state) B. Assertional box ABox High(?ind) ˆ StateHigh(?state) −> hasState(?ind, ?state) i1 : I i1 : High Following axioms are added in ABox after executing the s1 : StateHigh a1 : A set of SWRL rules presented above: (i1 , value1 : Double) : hasV alue (i1 , s1 ) : hasState (EP, StateM iddle) : hasState (a1 , value2 : String) : hasDescription (T P, StateM iddle) : hasState (i1 , a1 ) : hasResume The following rule in SQWRL language [16] is used to C. Linguistic summarization of production indicators produce the linguistic summarization of production indicators Suppose that at some enterprise two indicators of production based on the content of ABox: capacities are used: hasState(?ind, ?state) 1) Power in man-hours per 1 month (EP ). ˆ hasDescription(?state, ?descr) 2) Power in machine hours per 1 month (T P ). −> sqwrl:select(?ind, ?descr) Production indicator values must be specified based on Executing a query in the SQWRL language presented above forecast values in the form of following ABox axioms: produces the following result: EP : I TP : I TP The value of the production indicator is average (EP, 3610) : hasV alue EP The value of the production indicator is average (T P, 2700) : hasV alue Linguistic labels are used to forming recommendations for The expert is forming the following set of SWRL-rules balancing the production capacities of an enterprise. to produce a linguistic summarization for each production indicator: D. Generation of linguistic recommendations for production EP(?ind) ˆ hasValue(?ind, ?val) management ˆ swrlb:lessThanOrEqual(?val, 2000) The following set of SWRL rules set by the expert is used −> Low(?ind) to generate recommendations for balancing the production EP(?ind) ˆ hasValue(?ind, ?val) capacities: VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 186 Data Science EP(?ep) ˆ Low(?ep) −> Bad(?ep) EP(? ep) ˆ Middle(?ep) −> Bad(?ep) EP(?ep) ˆ TP TP Bad ”Capacity in machine hours per 1 month is High(?ep) −> Good(?ep) not enough to execute the production program. Additional equipment is required.” TP(?ep) ˆ Low(?ep) −> Bad(?ep) TP(? ep) ˆ Middle(?ep) −> Bad(?ep) TP(?ep) ˆ EP EP TP Bad ”Capacity in man−hours and machine High(?ep) −> Good(?ep) hours per 1 month is not enough to execute the The SWRL rules presented above are based on linguistic production program. The following steps must be taken: labels assigned by the linguistic summarization algorithm and buy additional equipment, hire additional personnel.” generate the following ABox axioms: TP EP TP Bad ”Capacity in man−hours and machine EP : Bad T P : Bad hours per 1 month is not enough to execute the The following SWRL rules are used to generate textual production program. The following steps must be taken: recommendations for balancing production capacities based buy additional equipment, hire additional personnel.” on the attached linguistic labels of production indicators: Recommendations generated for different indicators (EP EP(?ep) ˆ Bad(?ep) ˆEP Bad(?res) and T P ) and received after the implementation of the same −> hasResume(?ep, ?res) rule (recommendation EP TP Bad) are displayed only once. EP(?ep) ˆ Good(?ep) ˆ EP Good(?res) Recommendations formed by more complex (compound) rules −> hasResume(?ep, ?res) (recommendation EP TP Bad) overlap recommendations of more simplistic rules (recommendations EP Bad, TP Bad). TP(?tp) ˆ Bad(?tp) ˆ TP Bad(?res) Thus, the user has received the following information as −> hasResume(?tp, ?res) recommendations for balancing the production capacities of TP(?tp) ˆ Good(?tp) ˆ TP Good(?res) the enterprise: −> hasResume(?tp, ?res) Capacity in man−hours and machine hours per 1 month is not enough to execute the production program. The EP(?ep) ˆ Bad(?ep) ˆ TP(?tp) ˆ Bad(?tp) following steps must be taken: buy additional ˆ EP TP Bad(?res) equipment, hire additional personnel. −> hasResume(?ep, ?res) ˆ hasResume(?tp, ?res) V. C ONCLUSION EP(?ep) ˆ Good(?ep) ˆ TP(?tp) ˆ Good(?tp) ˆ EP TP Good(?res) Data-driven production management is a relevant area of −> hasResume(?ep, ?res) ˆ hasResume(?tp, ?res) research. The growth of data-driven production management is promoted by both the existing automation systems at enter- Recommendations for balancing production capacities prises and the volumes of data accumulated in such systems. (EP Bad, EP Good, TP Bad, TP Good, EP TP Bad, This article has proposed an approach to the analysis of EP TP Good) set by the expert and contains some textual the dynamics of production indicators based on time series representation. models. Type 2 fuzzy sets are used for time series modeling. ABox is contained the following axioms after the execution Type 2 fuzzy sets allow modeling objects with a higher degree of SWRL rules presented above: of uncertainty. (EP, EP BAD) : hasResume The proposed approach allows to increase the efficiency of (EP, EP TP BAD) : hasResume decision-making on production management. The proposed (T P, TP BAD) : hasResume approach in contrast to the decision-making process based (T P, EP TP BAD) : hasResume on an industrial methodology operates not with average pro- duction indicators, but with values of production indicators The following rule in SQWRL language is used to develop extracted from the information systems of an enterprise. recommendations for balancing production capacities of en- The proposed approach to the formation of linguistic rec- terprise based on the content of ABox: ommendations allows decision-makers to gain a deeper un- hasResume(?ind, ?rule) derstanding of the current state of production and respond to ˆ hasDescription(?rule, ?descr) changes in production indicators more operatively. The process −> sqwrl:selectDistinct(?ind, ?rule, ?descr) of forming linguistic recommendations is based on a set of The following result will be obtained as a result of executing fuzzy and SWRL-rules. the SQWRL rule presented above: ACKNOWLEDGMENT EP EP Bad ”Capacity in man−hours per 1 month is The reported study was funded by RFBR and Ulyanovsk not enough to execute the production program. region, projects numbers 18-47-732016, 18-47-730022, 19-47- Additional personnel is required.” 730005, 19-07-00999. VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 187 Data Science R EFERENCES [1] D.A. Pospelov, Situational control: theory and practice, Moscow: Nauka Publishers, 1986. [2] C. Liu, J.B. Wang and X.J. Zhang, "Digital Manufacturing System of Aircraft Wing Integral Panel," Advanced Materials Research, vol. 97, pp. 2732-2735, 2010. [3] H. Wang, G. Zhao, W. Wang and C. 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