the epc theory. basic notions of enterprise process...

Management and Production Engineering Review

Volume 1 • Number 3 • September 2010 • pp. 75–96

THE EPC THEORY.

BASIC NOTIONS OF ENTERPRISE PROCESS CONTROL

Mirosław Zaborowski

Academy of Business in Dąbrowa Górnicza, Department of IT, Poland

Corresponding author:

Mirosław Zaborowski

Academy of Business in Dąbrowa Górnicza

Department of IT

Cieplaka 1C, 41-300 Dąbrowa Górnicza, Poland

phone: +48 32 2622805

e-mail: [email protected]

Received: 25 August 2010 Abstract

Accepted: 13 September 2010 The essential part of the theory of Enterprise Process Control (the EPC theory) is a formaldescription of the framework EPC system. It is a universal reference model of integratedmanagement and process control systems for all enterprises, regardless of their trade andsize. Basic notions of the EPC theory have been presented in the paper. Certain defini-tions of broadly known terms (e.g. organizational system, process, resource, control unit,functional layer) are slightly different than the ones that are most often formulated. Thepurpose of these modifications is precise presentation of relationships between defined no-tions. Furthermore many new notions (functional subsystem, functional unit, transitionunit, information place, reengineering layer, readiness variant, organizational resources andthe like) have been introduced. They are necessary for presenting organizational and func-tional structure of the framework EPC system. The EPC theory has deductive nature andits notions are formulated on the basis of the more general, previously defined ones.

Keywords

management systems, multilevel systems, business processes, reference model, UML.

Scope and potential applications

of the EPC theory

The first reason to begin a research work for cre-ating a theory of enterprise process control (EPC)was a need of such a simulation system for integrat-ed planning and control in which it would be pos-sible to compare alternative decision making meth-ods (e.g. the MRP and the Kanban methods [1], ap-plied to the same production system). So the firstarea of the EPC theory is a formal description of theframework EPC system in which one can replaceindividual decision algorithms and other informationprocessing procedures without changing its structureas a whole.Later on it was noticed that if the elaborated

model is really universal, then it may be used asa universal kernel of real management and processcontrol systems. It is assumed here that there isa “1 to 1” relationship between the set of identifiers

of procedures (e.g. services of SOA (Service Orient-ed Architecture [2]) or stored procedures of relation-al databases [3]) in their external repositories andthe set of their numbers in the framework EPC sys-tem, from which they are called. Furthermore it isassumed that the “1 to 1” association exists also be-tween information elements of the framework EPCsystem and rows of tables of relational data struc-tures of real management and process control sys-tems in enterprises. These assumptions will be dis-cussed in the second and the third of planned pub-lications on the EPC theory from the series, whichencompasses the following items:

1. Basic notions of Enterprise Process Control.2. State and couplings between transitions in EPCsystems.

3. Data structure in EPC systems.4. Couplings between productive, preparatory andadministrative processes in EPC systems.

5. Direct control subsystems in EPC systems.

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Problems of IT solutions, which may be used forconnecting a framework EPC system with externalprocedure repositories and with a database of a us-er, are important for practical implementations butthey are not subjects of the EPC theory.

The framework EPC system is a universal ref-erence model of the integrated management andprocess control systems. However this model is es-sentially different than reference models delivered byvendors of ERP (Enterprise Resource Planning) soft-ware. First, this is not a branch model, but a univer-sal model. Second, it encompasses not only the ERPlevel, i.e. the management level in an enterprise, butalso the level of management in its organizationalcells and the level of control inside its workstations.Third, its description was not arise inductively, asdescription of functions of offered software in its for-mer applications, but deductively, as the system ofnotions and relationships between notions concern-ing information flow in enterprise management andprocess control systems. This description was namedthe EPC theory. Issues of analysis of mutual rela-tionships between its facts (which is a substance ofeach theory [4]), have been presented in the form ofsets of objects and relationships between them. Therelationships have been defined as subsets of Carte-sian products of the proper sets and as equivalentto them associations in class diagrams of the UMLlanguage [5, 6]. The side advantage by presentationof these diagrams is possibility of using them in thepreliminary design of the framework EPC system.

The early version of the EPC theory, published inthe 2008 year [7], was named the ERC theory (Enter-prise Resource Control), because EPC systems maybe considered to be extensions of well known ERPsystems. The ERC system (like the EPC system)is a multilevel, multilayer system [8] of enterpriseprocess control, but description of its structure isbased on Colored Petri Nets (CPN) [9, 10]. For thepresent version of the EPC theory the Unified Mod-eling Language (UML) [5, 6], which is better knownand easier to use than CPN, is a tool of modelingsystems. Data processing procedures in systems de-signed with the use of the UML may be written usingall popular programming languages, whereas “codesegments” of transitions in CPN simulation modelshave to be written in the SML language [9] (or in itsextensions, e.g. the CPN ML). For many languagesrecording and reading data from database tables,which are associated by relationships “1 to many”,may be performed with using simple embedded SQLinstructions. In the case of CPN ML it requires writ-ing special procedures for searching data in nestedlists of records, whose fields may be lists of records.

From the EPC theory point of view this problembecame crucial, when it was noticed that the frame-work EPC system may be used in real managementand process control systems of enterprises, not onlyto modeling such systems.The EPC theory may be applied to describ-

ing control of every productive process in enterpris-es, including continuous and discrete manufacturingprocesses, service processes, as well as data process-ing for customer needs. The application area of theEPC theory also encompasses management of aux-iliary processes, such as overhauls, repairs, trainingsand the like, as well as all internal administrativeprocesses.The tentative thesis of the EPC theory is the

statement, that every management or process con-trol system, irrespective of size and branch of an en-terprise in which it is implemented, may be mapped,with all its functions and data, in the structure of theframework EPC system. The thesis is vital not on-ly because of declared universality of the frameworkEPC system but also for the reason of educationalusefulness of the EPC theory. Generality of the EPCtheory may not be formally proven, because it wouldrequire verification of all management and controlsystems, but it may be justified by demonstrating itsusefulness for analysing and designing real manage-ment and control systems, as well as by its compar-isons with standards concerning declared applicationareas. Therefore the second area of the EPC theory,beside description of the framework EPC system, isa research of its conformability• with existing methods of business process mod-elling, e.g. BPMN (Business Process Model andNotation [11]), EPC (Event Driven ProcessChain) of the ARIS Platform [12] (EPC diagramsshould not be confused with discussed here EPCsystems) etc.,

• with currently known standards of informationprocessing systems for management and controlin enterprises (MRP II [13], ISA-95 [14, 15], IEC61499 [16, 17], WFMC standard [18]),

• with descriptions of these systems from manualsand publications (the MRP method [19], the Kan-ban method [1], the Follow-up Production Controlmethod [7, 20], scheduling methods for discreteproduction processes [21], structure of productionmanagement systems [22], workflow managementmodels [23, 24], reference models of informationsystems for enterprises [25, 26], examples of man-agement engineering problems [27], classical struc-tures of automatic control systems [28, 29], ex-amples of control of continuous and discrete el-ementary processes inside workstations etc.), aswell as

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• with examples of practical applications of informa-tion processing systems to enterprise managementand to automatic control of industrial processes.

The main application field of the framework EPCsystem is a widely comprehended business processmanagement, which encompasses not only modelingand reengineering, but also executive managementand calling procedures, which are needed for it.

As is well known, initially business people wereconcentrated on allocation of resources to activities.Business processes were considered only as supe-rior structures for activities. Smith and Fingar inthe book “Business Process Management. The ThirdWave” [30] named this period, i.e. 1920–1990, thefirst wave of BPM. During the second wave, i.e.since 1990, attention has been directed to process-es, because their issues are important for customersand their structures have significant impact on en-terprise performance. Structural changes of businessprocesses are considerably frequent because of fre-quent changes of enterprise functioning conditionsand for the reason of needed improvements. Unfor-tunately, every change of business process structurerequired structural changes in information systemssupporting current management. These changes, outof necessity, were performed by IT systems devel-opers, which could hardly understand their businesspurposes. It caused significant losses resulting of un-satisfactory effects of the changes and too long timeof introducing them [30]. In opinion of Gartner (quot-ed in [2]) nowadays “processes managed in software”are not already “barriers to change”, but devel-opment of systems improving cooperation betweenbusiness people and IT people is still continued.

Smith and Fingar noticed that at the beginningof the third wave of BPM, i.e. around 2000, the lead-ing companies of the world economy started a devel-opment work, whose aim is that results of changes,introduced by business process designers with usingsimple graphic tools, are immediately visible in prac-tice of current business management, without need ofany corrections of existing software [30]. It requiresto unite systems of current management and con-trol with systems supporting business process reengi-neering. The motto of the book [30], endorsed bythe BPMI (Business Process Management Initiative)and WFMC (Workflow Management Coalition), is“Don’t bridge the business-IT divide, – obliterateit!”. In opinion of Smith and Fingar realization ofthe third wave of BPM demands requires elaborat-ing a new abstract data type describing businessprocesses and introducing the “business processes”to information systems as new building blocks of soft-ware.

The EPC theory suggests achieving the same goalby using the well known relational data model ina new way. Its essence is immediate and automatedcorrection of the structure of software, which is usedfor current business process management, as reactionto the changes of business processes structures, intro-duced by a process designer. The graphic tool sup-porting process designing is the add-on of the frame-work EPC system. One can build an entire EPC sys-tem connecting the framework EPC system, which isdescribed here, with external procedures repositoriesand with a relational database of a user.

On the question of integration of ERP, MES andSCADA-PLC systems [15] the EPC theory suggestsequally radical solutions. Instead of building inter-faces between these systems, e.g. such as describedby the ISA-95 standard [14], one can build an EPCsystem, whose functions encompass tasks of all orga-nizational levels of an enterprise, and in this way re-move the need of building these interfaces. Obvious-ly, it removes only structural problems of the inter-faces, but not technological problems of informationtransmission between computers and other technicaldevices which are included in an integrated system.

Organizational levels

and functional layers

The organizational system is a part of anEPC system, which is designed for executing a de-termined set of processes. Analogously, each organi-zational subsystem belonging to the given systemis designed to perform a determined set of activities,which are stage activities of processes located in thissystem. The organizational level, h∈H, is a set oforganizational systems situated in the same level ofthe enterprise hierarchy tree. Typically an EPC sys-tem has five organizational levels:h = 5 the system embracing the supervisory unit

over the primary organizational system,h = 4 the primary organizational system which en-

compasses the enterprise and its environ-ment: customers, suppliers, banks, naturalenvironment and the like,

h = 3 production plants which encompass their de-partments,

h = 2 organizational cells which encompass theirwork centers,

h = 1 workstations (elementary organizational sys-tems) which encompass their direct controlsubsystems or other elementary subsystems.

Apart from organizational subsystems there areworking subsystems in organizational systems.They are arrangements of parallel organizational

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subsystems with input or output products located incommon sets of border places. Organizational levelof working subsystems are not higher, but the sameas for their component organizational subsystems. Ina typical EPC system they are:

h = 3 enterprise, composed of one or many produc-tion plants,

h = 2 departments, composed of one or many or-ganizational cells,

h = 1 work centres, composed of one or many work-stations.

In small enterprises there are only 4 organization-al levels (there are no organizational cells from thelevel h = 2 and workstations belong directly to theplants). In very large enterprises (e.g. in great facto-ries of chemical industry) may be 6 of them (there isan additional level between plants and cells).

For each level of the framework EPC system, ex-cept of the highest and the lowest level, there are 5functional layers:

j = 3 coordination of working subsystems in orga-nizational systems,

j = 2 allocation of working subsystems tasks to or-ganizational subsystems (in elementary sys-tems – direct control or elementary dataprocessing),

j = 1 reengineering (internal structure changes) fororganizational subsystems and their func-tional subsystems (in elementary systems –processing input signals into measuring sig-nals of basic control objects),

j = 0 data transfer between control units of orga-nizational systems and their administrativesubsystems,

j = 4 scheduling orders for executive subsystems(which are also organizational systems ofa lower level).

In practice certain functions of a given layer maybe executed by control units belonging to the high-er layers (which belong to the same or to the higherlevels). Then in corresponding implementation of theframework EPC system such a layer is neglected.

Each layer (h, j)∈HJF ⊂ H× JF has its own timescale, h∈H. Formally, the numbers of time scales andorganizational levels are equal, but a time scale isthe same only for four higher layers of a given level,whereas in a scheduling layer decisions and reportsare worked out with shorter time periods, which isproper for the lower level. Moreover, different timescales may have the same length of sampling period(for higher levels – planning period). They are for-mally distinguished in order to keep common num-bering of organizational levels and their time scales.For this reason in the framework EPC system it

would be possible that lengths of planning periodsfor coordination and scheduling layers of the sameorganizational level are equal. It is not a problem,if we consider a coordination layer and a schedul-ing layer from two different enterprises, for whichthe framework EPC system is a reference model, butfor the same enterprise it would be meaningless. Insuch cases either a scheduling layer or other layers ofa given level are neglected.

The specification of functional layers is presentedbelow, with exemplary planning periods, for a typical5-level EPC system:

• supervisory reengineering for the primary organi-zational system (month),

• data transfer for the supervisory administrativeoffice (month),

• supervisory scheduling for the primary organiza-tional system (month),

◦ coordination planning in the primary organiza-tional system (month),

◦ allocation planning for plants in the enterprise(month),

◦ reengineering for plants of the enterprise (month),◦ data transfer for the administrative office of theenterprise (month),

◦ master scheduling for plants of the enterprise (24hours),

• coordination planning for departments in a plant(24 hours),

• allocation planning for organizational cells in a de-partment (24 hours),

• reengineering for organizational cells (24 hours),• data transfer for the administrative office ofa plant (24 hours),

• executive scheduling for organizational cells(hour),

◦ coordination planning for work centers in an or-ganizational cell (hour),

◦ allocation planning for workstations in a work cen-ter (hour),

◦ reengineering for workstations (hour),◦ data transfer for the administrative workstation ofan organizational cell (hour),

◦ executive scheduling for workstations (second),• coordination control for elementary subsystems ina workstation (second),

• elementary data processing, especially dataprocessing for direct control of basic control ob-jects (second),

• receiving input signals and emitting measurementsignals of basic control objects (second).

The notions of organizational levels and func-tional layers are known since a long time [8]. Mul-tilevel organizational structure of enterprises is obvi-



ous and it does not require any comments. A workingsubsystem is a simple generalization of a work cen-tre [13]. Functional layers of coordination, allocationand scheduling, with the presented here order, ex-ist in many different management systems and it istaken into account in many methods of decision opti-mization [21]. Specificity of the EPC theory referringto these notions consists only in a statement thatthese layers exist in each organizational level exceptof the highest and the lowest ones. An assumptionof the same time scale for a coordination layer anda scheduling layer of the higher level is also specificto the EPC theory. The layers of reengineering andadministrative data transfer are absolutely new inmodels of management and process control systems.Presenting the sets of direct control units and di-rect control objects as the layers of elementary dataprocessing and basic control objects, defined in thesame way as other layers of an entire enterprise isalso a new idea.

Presenting reengineering as one of control func-tions of an organizational system means that the de-sign of the internal structures of its organizationalsubsystems (and its modifications) is made insidethis system, not in its environment, on the basis ofinformation which is available in it. The administra-

tive data transfer launches administrative processes(office processes), which replace these actions of busi-ness process control that require additional resourcesand/or consume more time than one planning peri-od. Introduction of the layer of basic control objectsresults from the assumption that systems of directcontrol belong to the set of organizational units of anenterprise. Wider discussion of these notions, as wellas many other terms which are introduced in this pa-per, requires separate publications. Herein structuralrelationships between discussed notions are present-ed. Then one can verify if these notions are consis-tent. Certain terms specific to the EPC theory werewider presented in the early monograph [7].

Organizational units

and control units

Organizational systems, working subsystems andorganizational subsystems, including preparativeand administrative subsystems, as well as elementarysubsystems (for direct control or elementary dataprocessing) are organizational units, s ∈ S. Func-tional layers are sets of such control units (s, j) ∈SJ ⊂ S × JF that have similar functions but concerndifferent organizational units.

Fig. 1. Object diagram for couplings between control units of the exemplary organizational system.



Fig. 2. Object diagram for couplings between control units of the exemplary organizational system and its reengi-neering control unit as well as its administrative functional unit.

Fig. 3. Class diagram for transition units and data processing phases.



Fig. 4. A conceptual component diagram for control of functional subsystems in the exemplary organizational system.



Fig. 5. Class diagram for functional subsystems in functional layers.

Relationships of dependency between controlunits in a simple exemplary organizational systemhave been presented by means of the object diagrams(Figs. 1, 2) and the component diagram (Fig. 4) ofthe UML language [5, 6]. The acronyms of classes,which are used in these diagrams, are explained inthe class diagram of functional subsystems (Fig. 5).The exemplary system consists of three working sub-systems. The first of them is composed of two organi-zational subsystems. The second and the third oneshave single organizational subsystems. The third oneis an administrative subsystem. Therefore it does notparticipate in processes of the system (Figs. 7, 8). Ac-tivities, which are located in such a subsystem, re-

place these procedures located in control units fromhigher layers (Figs. 1, 2, 4), which require separateresources and their execution times may not be ne-glected. Therefore between a control unit of adminis-trative data transfer and higher control units of a giv-en organizational system there are relationships ofrealization [5, 6], specifically – realization of controlprocedures by means of administrative activities.

The control in any control unit must take into ac-count the internal structure of subsystems submittedto this unit. This structure is designed in a corre-sponding control unit of reengineering. Therefore allcontrol units (s, j) ∈ SJ of a given organizational sys-tem (sn, 3) ∈ S × {3} have direct relationships of de-



pendency with the reengineering unit, which is supe-rior in relation to this organizational system (Fig. 2).

Transition units

and data processing phases

Each control unit (s, j) ∈ SJ ⊂ S × JF is com-posed of two system transition units (Fig. 3),(s, j) ∈ TJ ⊂ S × J. The transition unit is a set oftransitions which are sites of data processing pro-cedures in control units. Each transition correspondsto exactly one transition procedure f ∈ F, but thesame procedure from the transition procedure repos-itory may be called by different transitions. Thustransition procedures are not permanently bound upwith transitions, what assures the proper flexibilityof an EPC system. Transitions belonging to the de-cision transition unit (s, j) ∈ TJD ⊂ TJ processdecisions from higher layers and information fromlower layers into decisions concerning lower layers.Transitions belonging to the information transi-tion unit (s, j) ∈ TJI ⊂ TJ process informationfrom lower layers into information for higher layers.

In the framework EPC system succession of ini-tiating actions of transition units at beginning timesof planning periods is precisely determined. The da-ta processing phase is a set of transition unitswhose actions are initiated by the same synchroniz-ing pulse. In the EPC system with 21 layers, likein the above-presented example, there are 42 dataprocessing phases. Each of them is identified by thetime scale number and by the phase number for a giv-en time scale, (h, j) ∈ HJ ⊂ H × J (Fig. 3). Eachsystem transition unit (s, j) ∈ TJ⊂ S × J is identifiedby the organizational unit number and by the phasenumber. The number of the time scale h(s, j)∈H isnot required because it univocally depends on thenumbers of the phase and the organizational unit.

For information transition units (s, ji) ∈ TJI ⊂TJ the numbers of data processing phases ji ∈ {0, 1,2, 3, 4} are the same as the numbers of correspondingfunctional layers. For decision transition units (s, jd)∈ TJD ⊂ TJ they are numbers jd ∈ {5, 6, 7, 8, 9},which in a given functional layer satisfy a condition:jd + ji = 9. In conclusion, the functional layer, whichwas previously defined as a set of control units, maybe also interpreted as a set of transition units, whichis subdivided into two subsets: information and de-cision data processing phases.

In the set of data processing phases (h, j)∈HJ ofthe same time scale „h” the order of phases, i.e. thesuccession of actions of belonging to them transitionunits at a given beginning time t∈T of the samplingperiod (h, t) ∈ H × T, is compatible with their num-

bering. It means that in a given sampling period theinformation transition units act before the decisionones, in the set of the information ones – the unitsfrom lower layers before the ones from higher lay-ers and in the set of decision units – the units fromlower layers after the ones from higher layers. At spe-cial beginning times of sampling periods that belongto different time scales (e.g. at the beginning of theday, which is also the beginning of its first hour andthe beginning of its first second) after the informa-tion phase of scheduling executive orders (j = 4) theEPC system pass to the higher information phaseof administrative data transfer (j = 0) which beginactions with a longer time scale. At the beginningtimes of all other sampling periods after the infor-mation phase of scheduling (j = 4) the correspondingdecision phase (j = 5) occurs.

Functional subsystems

The control unit of coordination planning con-trols its organizational system and, at the same time,it is a main gate for communication between this sys-tem and control units belonging to higher layers ofthe EPC system. For those control units the orga-nizational system is a functional system, which exe-cutes orders coming from them and send to them cor-responding reports. Each of those control units (ex-cept of reengineering units), is in contact only withcoordinative control unit of the controlled organiza-tional system and “does not see” the inside of thissystem. Thus, from the point of view of control units,which control a given organizational system and be-long to the higher functional layers, the coordinativecontrol unit is a functional unit, which receives deci-sions and send information.

Analogous conclusions may be formulated also forother control units in the EPC system. Each con-trol unit is also a functional unit correspondingto exactly one functional subsystem. This sim-ple observation is one of the main issues of the EPCtheory. Precise connection of basic notions from fourdifferent areas – management engineering, produc-tion engineering, software engineering and modelingdiscrete in time control systems for control objectswith continuous or discrete state – is possible owingto this observation together with presenting controlunits as pairs composed of decision and informationcontrol units.

In higher organizational levels (h > 1) successivefunctional layers correspond to the following func-tional subsystems (Fig. 4):

j = 3 organizational systems (which are also ex-ecutive subsystems of higher level),



j = 2 working subsystems,j = 1 structural subsystems,j = 0 administrative subsystems,j = 4 organizational subsystems.

In the first organizational level (h = 1):

j = 2 elementary subsystems (for elementary da-ta processing or for direct control of basicobjects),

j = 1 basic control objects (which contain onlyfunctional units and have no other compo-nents)

are functional subsystems of elementary organiza-tional systems (j = 3).

In conclusion, the set of all functional subsystemsin the EPC system may be subdivided into subsets ofexecutive, working, structural, administrative, orga-nizational, elementary and basic subsystems SJ = SK∪ SL ∪ SX ∪ SD ∪ SH ∪ SE ∪ SB (Fig. 5). Moreover,the executive subsystems (s, j) ∈ SK are also orga-nizational systems of the lower organizational levels,SN = SK.

The working subsystem and the organizationalsubsystem, which belongs to it, are different func-tional subsystems of the same organizational unit ifand only if the working subsystem does not containany other organizational subsystems. However, if theworking subsystem is composed of many organiza-tional subsystems, then all of them, as well as theworking subsystem itself, are considered to be differ-ent organizational unit. The organizational subsys-tem and the organizational system of the lower levelare different functional subsystems corresponding tothe same organizational unit. It refers also to the ad-ministrative organizational unit. Analogously, for theorganizational unit of a direct control system, whichbelongs to an elementary organizational system,there are two functional subsystems: the control sys-tem itself, which is an elementary subsystem and thebasic control object, which is a basic subsystem. Ifthe elementary subsystem of an elementary organiza-tional system is an organizational unit of elementarydata processing, then it have no basic subsystems.

The functional subsystems are identified just ascorresponding functional units, i.e. by pairs (s, j) ∈SJ ⊂ S × JF, in which s∈S and j∈JF are correspond-ingly the numbers of organizational units and func-tional layers. The system couplings of controlunits, that is the relationships of association (s, j,u, y) ∈ SJY ⊂ SJ × SY, may occur between a givenfunctional unit (s, j)∈SJ and the control units (u, y)∈ SY ⊂ S × JF belonging to any higher functionallayer (h, j) ∈ HJF from the same or higher organiza-tional level (Fig. 1, 2, 4). Thus in the framework EPCsystem one can apply any known method of planning

and control in spite of their structural constraints (inthe diagram of Fig. 4 most of couplings between thelayers that are not adjacent have been hidden for sim-plicity). The only condition refers to the couplingsbetween control units belonging to different orga-nizational levels. In such cases the functional unitshould be a coordinative unit (because it is a func-tional unit of an organizational system) or should be-long to the layer, which is lower than the layer of thesuperior control unit in its own organizational level.

Information places

and information layers

Data structure of the EPC systems is like in re-lational databases [7]. Such data recording, in tablesor in single records, is quite common in practice. Itrefers to relational databases [3], which are appliedto most of management systems and to databases oflower level control systems, as well as to memory ofdirect control devices. The relational database of theEPC system stores not only current information anddecisions which are processed in the system but al-so the structure of the system itself. E.g. the list ofenterprise customers is a part of the specification ofall organizational units of the EPC system. The oth-er example is a list of associations of activities withresources, which are required to execute these activ-ities. Thus functioning of couplings between reengi-neering control units and subordinate to them func-tional units (Fig. 2) relies on updating (appendingor deleting rows) those segments of the database ta-bles describing the EPC system structure which areneeded for particular functional units.

In the EPC theory it is assumed that the set of allrows of all tables of the EPC database may be sub-divided into separable subsets called informationplaces, m ∈ M [31]. The specified row of a given ta-ble belongs to the information place “mx”, if there issuch a unique index for this table that the informa-tion place number “m” is one of its attributes andm = mx for this row. Analogously, the specified rowof a given table belongs to the information clus-ter determined by the tuple (x1, x2 . . . xk), if thereis such a unique index for this table that containsattributes a1, a2 . . . ak and a1 = x1, a2 = x2 . . . ak= xk for this row.

The information places are classified into the sys-tem places m ∈ MS, i.e. places of information con-cerning functional subsystems, the resource placesm ∈ MR, i.e. places of information concerning locat-ed resources, the synchronizing places m ∈ MJ,i.e. places of information concerning data process-ing phases and the structural knowledge places



m ∈ MW, i.e. places of information concerning kindsof activities and kinds of resources, as well as theirparameters and relationships between them. Placesof information concerning the transition proceduresand the kinds of administrative information, whichare discussed hereunder, also belong to the structuralknowledge places.In the EPC system all information places m ∈ M

= MS ∪ MR ∪ MJ ∪ MW have common number-ing. Apart from this numbering, information placeswithin specified subsets may be identified just as en-tities, which are described by information containedin these places. E.g. system places may be identifiedby pairs (s, j) ∈ SJ, which are identifiers of functionalsubsystems. One can say that dependencies MS(SJ)and SJ(MS) are mutually univocal (Fig. 5).As is well known, rows of tables (more formal-

ly: tuples of relations) in relational databases corre-spond to objects of classes in object-oriented datamodel [3]. In the EPC theory the tables of the data-base of the framework EPC system, which are notsubclasses of other tables, are called “kinds of ad-ministrative information” or shortly: informationkinds, i ∈ I. In other words, each table of the data-base of the EPC system is an information kind ora subclass of certain information kind. Then for eachsuch a table its primary key or one of its unique in-dexes is a primary key of certain information kind.Furthermore, each row of each table of any EPC sys-tem corresponds to one and only one row of certaininformation kind. It is important for practical imple-mentations, because the number of all informationkinds is relatively small. The complete specificationof the tables of the information kinds, together withtheir key attributes, will be presented in the thirdof planned papers on the EPC theory. There willbe also presented the list of all 27 key attributes ofthese tables, which are named structural attribut-es. Considering declared universality of the frame-work EPC system the total number of structural at-tributes seems to be very small.Rows in tables of information kinds are called in-

formation elements (i, d) ∈ DI ⊂ I × D. For eachinformation element the number of the informationplace, m(i, d) ∈ M, containing this element, is oneof its attributes. The located information (m, i) ∈IM ⊂ M × I is a set of those information elements ofthe kind i ∈ I, which belong to the information placem ∈ M.Among information clusters one should distin-

guish activity information clusters (m, a) ∈AM ⊂ MS × A, for which a ∈ A are activitykinds numbers, and resource information clus-ters (m, r) ∈ XRM ⊂ MR × R, for which r ∈ Rare resource kinds (Fig. 6). System and resource

information places m ∈ MS, m ∈ MR (Fig. 7), aswell as contained in them activity information clus-ters and resource information clusters (Fig. 8) forminformation layers, which are located betweenfunctional layers. Subsets of information places sets,as well as subsets of information clusters sets, whichcorrespond to particular information layers (Fig. 6)are separable subsets: MS = MK ∪ MX ∪ MA ∪ML ∪ MH ∪ ME ∪ MB, AM = AMK ∪ AMX ∪AMA ∪ AML ∪ AMH ∪ AME ∪ AMB, MR = MRK∪ MRL ∪ MRH ∪ MRE ∪ MRB, XRM = XRMK∪ XRML ∪ XRMH ∪ XRME ∪ XRMB. Each in-formation layer has the same number as the func-tional layer which is placed immediately below it:j = 2 coordinating information of working sub-

systems,j = 1 reengineering information of structural

subsystems,j = 0 administrative orders,j = 4 allocating information of organizational

subsystems,j = 3 executive information of executive subsys-

tems (organizational systems of lower lev-el).

It also concerns the allocating information lay-er, but its number (j = 4) is not less by 1 than thenumber of allocation planning (j = 2). It is neitherthe number j = 1, nor j = 0, because these function-al layers do not participate in functional processesof a given organizational system (Fig. 7, 8). There-fore in corresponding information layers there are noresource places (and no corresponding resource clus-ters). In the reengineering information layer (j = 1)instead of resource places m ∈ MR there are struc-tural knowledge places m ∈ MW. Resources, whichare processed in administrative subsystems (j = 0),are information elements, so they already have gottheir own places in the structure of organizationalsystems.

Process structure

After APICS, the business process is a set of log-ically related tasks or activities performed to achievea defined business outcome [32]. In the EPC theorythis definition is similar but different – the businessprocess is a functional process, i.e. an ordered setof functional activities and separating them locatedresources. The purpose of a given business processor the purpose of the business process which is su-perior in relation to a given process is to satisfycustomer needs. The exemplary structures of func-tional processes are shown in the object diagram(Fig. 8) for above-presented simple organizationalsystem (Fig. 1, 2, 4, 7).



Fig. 6. Class diagram for information places and information clusters.



Fig. 7. Object diagram for the exemplary organizational system structure.



Fig. 8. Object diagram for functional processes of the exemplary organizational system.



The functional activity (s, j, a) ∈ SJA ⊂ SJ× A is determined by the activity kind, a ∈ A,and the functional subsystem, (s, j) ∈ SJ ⊂ S × J,in which this activity is performed (Fig. 9), whereasthe functional process (sn, 3, p) ∈ SJP ⊂ SJ × P –by the process kind, p∈P⊂ A and the organizationalsystem, (sn, 3) ∈ S × {3}. The process is an activityof the higher level, (sn, 3, p) ∈ SJP ⊂ SJA (Fig. 10).The located resource (m, r) ∈ RM ⊂ MR × Ris determined by the resource kind, r ∈ R and bythe resource place, m ∈ MR ⊂ M. The functionalactivity may also be defined as a located activity(s, a) ∈ SA ⊂ S × A that is performed in the orga-nizational unit s ∈ S and observed at the functionallayer (h(s, j), j) ∈ HJ.Functional subsystems from successive layers

correspond to the following functional activities(Fig. 10):j = 3 processes (which are also executive activi-

ties of the higher level),j = 2 working activities (in the lowest level – ele-

mentary activities),j = 1 basic activities (only in the lowest level),j = 0 administrative activities,j = 4 allocated activities (allocated to organiza-

tional subsystems).Thus the set of all functional activities may be

subdivided into subsets of executive, working, struc-

tural, administrative, allocated, elementary and ba-sic activities SJA = SKA ∪ SLA ∪ SXA ∪ SDA∪ SHA ∪ SEA ∪ SBA (Fig. 10). Moreover, execu-tive activities (s, j, a) ∈ SKA are as well functionalprocesses, SJP = SKA, which are located in organi-zational systems of the lower levels, SN = SK. Thelocated resources, which separate functional activi-ties in processes, are classified into analogous sepa-rable subsystems: RM = RMK ∪ RML ∪ RMH ∪RME ∪ RMB.Functional activities, like functional subsystems,

correspond to activity functional units, which areactivity control units from the view point of lowerlayers. Activity control units are contained in corre-sponding system control units and – analogously tothem – participate in system couplings of activi-ty control units between the functional layers (s, j,a, u, y, c) ∈ SJAC ⊂ SJA × SYC (Fig. 9). Moreover,(s, j, a) ∈ SJA identify functional units, whereas con-trol units are identified by (u, y, c) ∈ SYC ⊂ SJA.The activity functional unit corresponding to the

functional process is a common control unit for func-tional activities belonging to this process (Fig. 8).Thus relationships between functional activities (s, j,a) ∈ SJA belonging to the functional process (sn(s),3, p) ∈ SJP and this process itself are special casesof couplings between activity control units (s, j, a,sn(s), 3, p) ∈ SJAP ⊂ SJAC (Fig. 10).

Fig. 9. Class diagram for functional activities.



Fig. 10. Class diagram for activities of functional processes.

The functional process may be:j = 2 a working process (in the lowest level – an

elementary process),j = 1 a basic process (only in the lowest level),j = 4 an allocated process orj = 3 an executive process.It depends on the layer, to which the component ac-tivities of the process belong (Fig. 8, 10). However,in each case the functional process in a given orga-nizational system is identified by the same controlunit, which belongs to the coordination layer (j = 3)in this system.

Information flow between coupled system controlunits relies on recording and reading data in systeminformation places m ∈MS and resource information

places m ∈ MR (Fig. 7). Analogously, activity infor-mation clusters (m, a) ∈ AM ⊂MS × A and resourceinformation clusters (m, r) ∈ XRM ⊂ MR × R par-ticipate in couplings between activity control units(Fig. 8). In particular, it refers to couplings betweenthe control unit of a process and its component func-tional activities. Moreover, between system placesand functional subsystems, as well as between activ-ity clusters and functional activities, there are mu-tually univocal dependencies. In the class diagrams(Fig. 5, 9) alternative primary keys are shown – (s, j)∈ SJ for the system place table MS and (s, j, a) ∈SJA for the activity cluster table AM – because theyare more often used to searching in an EPC databasefor information.



Fig. 11. Class diagram for resource inputs and outputs of functional subsystems and activities.



The assumption of separating activities by re-sources is crucial for formal description of the processstructure. Output resources of a given activity areinput resources for other activities. In this way theorder of activities in the functional process is definedby resource inputs and outputs of functionalactivities. They are formally determined by associ-ations between functional activities and located re-sources, ((s, j, a), (m, r)) ∈ SJA × RM, which arerecorded as the fives of numbers of organizationalunits, functional layers, activity kinds, resource in-formation places and resource kinds: for inputs (s, j,a, m, r) ∈ URSJA, whereas for outputs (s, j, a, m, r)∈ YRSJA (Fig. 11). Tables of inputs and outputs oflocated resources to/from functional activities cor-respond to analogous specifications of resource in-puts and outputs of activity kinds (a, r) ∈ URA,(a, r) ∈ YRA (Fig. 11), resource inputs and out-puts of functional subsystems (s, j, m) ∈ USJ,(s, j, m) ∈ YSJ (Fig. 7, 11) and generic resourceinputs and outputs of functional subsystems

(s, j, m, r) ∈ URSJ, (s, j, m, r) ∈ YRSJ (Fig. 11).Information elements of resource inputs and out-

puts, which are recorded in presented above tablesof USJ, URSJ, URSJA, YSJ, YRSJ, YRSJA, aredistributed among resource information places m ∈MR, and more narrowly – among resource informa-

tion clusters, identified by corresponding located re-sources (m, r) ∈ RM. Analogous information con-cerning input and output couplings of systemcontrol units (s, j, m, u, y) ∈USJY ⊂USJ× SY, (s,j, m, u, y) ∈ YSJY ⊂ YSJ × SY (through input andoutput resource information places of functional sub-systems), as well as input and output couplingsof activity control units (s, j, a, m, r, u, y, c) ∈URSJAC ⊂ URSJA × SYC, (s, j, a, m, r, u, y, c)∈ YRSJAC ⊂ YRSJA × SYC (through input andoutput located resources of functional activities), isrecorded in the same resource places and resourceclusters (Fig. 11).

Classification of activities

and resources

Enterprise processes may be classified by theirnature into:

• manufacturing processes, whose products are newmaterial goods,

• service processes, whose outcome (product) is sat-isfaction of needs, that are other than the need ofpossessing material goods, and

• data processing processes, whose products are in-formation items.

Fig. 12. Class diagram for classification of activity and resource kinds.



For functional processes classification by theirrole in the EPC systems is more important. Strictlyspeaking, the question concerns the role of processesin organizational systems of the higher level, wherethese processes are activities. In the EPC theory ac-tivity kinds are subdivided into:• productive activities (of various nature),• preparatory activities (tooling setups, repairs,overhauls and the like) and

• administrative activities (performed in adminis-trative subsystems and initiated by those tran-sition procedures of organizational systems thatrequire additional time and resources).

This classification reminds the one from [23, 24],which specifies production, support and managerialprocesses, but it not exactly the same.In the case of service processes and data process-

ing processes the postulate of separating their com-ponent activities by resources may seem to be wrong.However, it is possible owing to properly wide defini-tion of resources. In the EPC theory the classificationof resource kinds includes (Fig. 12):• reusable resources,• consumable resources,• financial resources,• information resources,• organizational resources and• administrative resources.It is important that the same resource specimen indifferent circumstances may be an element of differ-ent categories.Information resources mean not only data

processed for customers but also products of serviceactivities, e.g. the messages of service activity termi-nations which, in turn, are used to the next activitiesof a given service process. The products of servicesare not material but information of these productsreally exists. One should notice that also in the caseof manufacturing processes the systems of manage-ment and control have no disposal material goods,which are manufactured in these processes, but on-ly information concerning these goods, just as in thecase of service processes. Administrative resourcesare information elements, which are inputs or out-puts of mentioned above administrative activities.Organizational resources are products of presentedhereunder preparatory activities.

Aggregation of activities,

resources, organizational units

and information places

Different resource categories, activitygroups and statistical groups of organization-

al units are widely used in management practice.Examples of such groups are the fixed assets, com-prising among others various kinds of machines andthe resource roles (particularly – workers special-ties), meant as groups of activities which requirethese resources, as well as the statistical groups ofcustomer organizational units, which may be classi-fied by size, trade, geographic location and the like.Inclusions of a resource kind r ∈ R in the categoryv ∈ V, an activity kind a ∈ A in the group g ∈ Gand an organizational unit s ∈ S in the statisticalgroup w ∈ W are determined correspondingly withassociations (r, v) ∈ VR ⊂ R × V, (a, g) ∈ GA ⊂ A× G, (s, w) ∈ WS ⊂ S × W (Fig. 12).

In the EPC theory resource categories are formal-ly numbered among resource kinds, V ⊂ R, activitygroups among activity kinds, G ⊂ A, and groups oforganizational units among the set of organizationalunits, W ⊂ S. Owing to this one can avoid troubleswith multilevel classification. E. g. “lathes”, whichform a category of various kinds of lathes, are alsoconsidered to be a resource kind belonging to the cat-egory “machine tools”, which, in turn, is a resourcekind belonging to the category “fixed assets”.

Analogous formal description is used to aggrega-tion of information places m ∈ M. The aggregationaccounts, i.e. accounts of aggregation of informa-tion places, belong to the set of information places,b ∈ B ⊂ M, and relationships between them are de-termined with associations (m, b) ∈ BM ⊂ M × B.The costs or revenues accounts as well as the bal-ance accounts from the enterprise accounting system[33] are important examples of aggregation accounts.In the EPC theory it is assumed that for each re-source place m ∈ MR there is its balance accountb∈MCR and for each system place m ∈ MS (thenalso for each functional subsystem (s, j) ∈ SJ) thereis its costs or revenues account b∈MCS. In practiceone account b ∈ MC = MCR ∪ MCS ⊂ MR ∪ MS⊂ M aggregates information from many resource orsystem places, but it does not exclude existence ofmany subaccounts for one information place.

Among activity groups the organizational ac-tivity groups g ∈ GG ⊂ G ⊂ A are especiallyimportant for the EPC theory. Each organizationalor working subsystem, i.e. each organizational units ∈ S except of elementary subsystems, has at leastone organizational activity group, which may be con-sidered to be the type of this unit. It is the set ofall activities, which potentially may be performedwith this unit. Other organizational activity groupsare its subsets. If the organizational unit is some-times set up to enable performing different activitygroups, then corresponding groups of functional ac-



tivities (s, j, a) ∈ SJA are called readiness vari-ants [10] of functional subsystems (s, j, g) ∈ SJG ⊂S × J × GG (Fig. 12). Like organizational activitygroups, which formally belong to the set of all ac-tivity kinds, the readiness variants belong to the setof functional activities, SJG ⊂ SJA. Each organiza-tional activity group has its main product, which isthe family of main products of activities belongingto this group.

Among input resource kinds of a given organiza-tional activity group one should distinguish the or-ganizational resource kind ro(g) ∈ RO ⊂ R, whichcorresponds to it. Its zero-one attribute is the readi-ness state of functional subsystems which can per-form this activity group. It demonstrates readinessof a given functional subsystem (s, j) ∈ SJ to per-form activities belonging to corresponding readinessvariant (s, j, g) ∈ SJG. The organizational resource,like reusable resources, is returned to its rest place(i.e. to the corresponding information place) after ex-ecuting activities from a given group. On the otherhand, the organizational resource is a main prod-uct of the preparatory activity a ∈ AO ⊂ A,which prepares organizational units to correspond-ing readiness variant. The dependencies between or-ganizational activity groups, organizational resourcekinds and preparatory activity kinds are mutuallyunivocal (Fig. 12).

If preparations refer to the change of produc-tion profile of an organizational system, then their“product” is readiness to the new overall activitygroup. If the preparatory activity is the repair af-ter a break-down, then its “product” is the readinessstate of repaired organizational unit, which in gen-eral is the same as before the break-down. It shouldbe stressed that preparatory activities are performedwith proper preparatory organizational units, notwith the units which are their objects. Furthermore,one execution of the preparatory activity preparesthe organizational unit to one ore many executions ofone or many kinds of productive activities. Thus thepresented here model better reflects practical casesthan commonly used simple operation description, inwhich the execution time is subdivided to the setuptime and the run time.

Separation of preparatory activities, as well as in-troduction of organizational resources and organiza-tional activity groups, facilitates unified descriptionof internal structure of productive and preparatoryorganizational units. What is more, owing to this itis possible to work out a precise model of interactionbetween management systems for production and forpreparations to production. In this model, obviously,production is planned with regard to constraints re-

sulting from decisions concerning maintenance, over-hauls and the like, but on the other hand it is possibleto adapt these decisions (in the permissible scope) tothe current production decisions.

Conclusions

The theory of Enterprise Process Control (theEPC theory) is structured by way of deduction. Frommore general notions, namely from the notions oforganizational level, functional layer, organizationalunit, activity kind, resource kind, information place,information kind, other basic notions of the EPCtheory are deduced. Among them one should noticethe notions of organizational system, functional sub-system, control unit, functional unit, transition unit,transition, functional activity, functional process, lo-cated resource, inputs and outputs of functional sub-systems and functional activities, information clusterand the like. Successive notions are defined by wayof presentation of their relationships with previous-ly defined notions. Using diagrams of the UML lan-guage [5, 6] to describe these relationships assuresprecision of the definitions and, on the other hand,demonstrates that the framework EPC system maybe used in practice.

From basic notions of the EPC theory one candeduce more detailed notions, such as transactions,orders, plans, reports, their parameters and the like.Among many new detailed notions there are alsosuch as reengineering units, administrative resources,organizational resources, readiness variants of func-tional subsystems and the others, which are intro-duced to remove structural barriers on the way toprecise modeling problems of reengineering organiza-tional systems in all organizational levels, problemsof data transfer between productive and administra-tive processes, problems of interaction between pro-ductive and preparatory process management sys-tems etc.

The meaning of notions, presented herein andin the following publications on the EPC theory, isunivocal, but their names may be an object of dis-cussion. As a result of this discussion those namesshould be recommended, which properly associatewith the sense of these notions for experts of fourdifferent special fields – management engineering,production engineering, software engineering and au-tomation. In certain cases not only names, but alsothe sense of definitions may seem to be disputable.E.g. it refers to the definition of a business process, inwhich resources separating activities are mentioned,and the definition of a resource, which does not en-compass organizational units. Resources are always



passive beings, whereas an organizational unit is anactive being and in addition contains internal controlunits.

Deductive nature of the EPC theory facilitatesverification of its consistence, that should induce toaccept the thesis of its generality. This, in turn, jus-tifies advisability of a research into the EPC theoryusefulness to modeling practical problems of man-agement and process control, as well as advisabilityof starting work on the prototype of the frameworkEPC system.

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