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A Conceptual Framework for Business Process Redesign George Koliadis Aditya K. Ghose Decision Systems Lab (DSL) School of Computer Science and Software Engineering University of Wollongong, Australia 10th Workshop on Business Process Modeling, Development and Support, 2009 Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 1 / 44

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A Conceptual Frameworkfor Business Process Redesign

George Koliadis Aditya K. Ghose

Decision Systems Lab (DSL)School of Computer Science and Software Engineering

University of Wollongong, Australia

10th Workshop on Business ProcessModeling, Development and Support, 2009

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 1 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 2 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 3 / 44

Example

Package Screening Process:

Current Context:I Route a package if held, otherwise only update status.I Routing prior to handling screen requests improves routing time.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 4 / 44

Example

Package Screening Process:

Revised Goals:I G u Performed(SO,Route,Package) ∧

Knows(SO,Package,Status,Clear) ∧Performed(SO,Update,PackageStatus)

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 5 / 44

Example

Package Screening Process:

Revised Business Rules:I R u G(Knows(RA,Package,Status,Held)⇒ ¬Performed(SO,Route,Package)W Knows(RA,Package,Status,Clear))

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 6 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 7 / 44

Some Relevant Milestones

Operational task decomposition and optimization.I The Principles of Scientific Management, 1911

(Cross) Organizational process decomposition and optimization.I Competitive Advantage: Creating and Sustaining Superior

Performance, 1985Enterprise architecture - multi-dimensional modeling.

I A Framework for Information Systems Architecture, 1987Enterprise governance, planning and execution reference.

I Value Chain Operational Reference (VCOR), 2005Zero Code Business Process Management System.

I Intalio|BPMS 4.2, 2006Challenge: Systematic Support for Governing and EngineeringDynamic Processes.

I Service-Oriented Computing: a Research Roadmap, 2008

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 8 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 9 / 44

Preliminary Evaluation

Business Process Redesign is an architectural activity.I Method and ProductI Effective / Repeatable ConstructionI Holistic / Context Sensitive (Milestones)

Enterprise Business Process Architecture [Koliadis et al., 2008]I Reference Models, Reference Frameworks (Structural, Functional)

F Value Chain-Based, BMM, HOBE, i*, e3 Value, TOVE

MethodI Literature Review: Proposal of a Functional Competence TheoryI Evaluate Frameworks with respect to Functional Competence

Preliminary ResultsI Highly Variable CoverageI Competencies: Actors, Goals, ProcessesI Deficiencies: Inter-relation, Strategy, Risk

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 10 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 11 / 44

Related Work

FrameworksI Planning and Configuration [Hendler et al., 1990]

[van der Aalst et al., 2005]I Dynamic Change [Rinderle et al., 2004]

Framework AspectsI Compliance Management [Ghose and Koliadis, 2007]

[Governatori et al., 2008]I Validation [Weber et al., 2008]I Variation Generation and Management [Lu and Sadiq, 2006]

[Ponnalagu and Narendra, 2008]I Change Impact Scope Analysis [Soffer, 2005]

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 12 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 13 / 44

Research Questions

1 What are the main drivers and business process redesign?2 How do we systematically react to these drivers?3 What should we consider when reacting to these drivers?4 How do we extend existing frameworks to support redesign?

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 14 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 15 / 44

Drivers of Redesign

Business Processes “Execute Strategy”[Smith and Fingar, 2003]Strategic / Regulatory View of Process Change[Regev and Wegmann, 2002] [Regev and Wegmann, 2004]

I Processes regulated by interrelationships with other systems (e.g.strategic management - competitive, technological e.t.c.).

I Process change occurs to maintain constancy (or “value” / utility) inthe context of these interrelationships.

Strategic vs Operational Change [Munive-Hernandez et al., 2004]I Operational influence (“emergent”) is also critical.

Regulation can occur by communicating change requests,representations - system products, or through observation.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 16 / 44

Considerations for Redesign

Identity (Intentionality: P |= G)I Satisfaction of the intent / operational goals of the process

[van Lamsweerde, 2001].I Permit innovation / flexibility [Wing, 1990].

Conformance (Realizability: R |= P and P |= C)I Consistent, complete, and minimal satisfaction w.r.t. resource,

operational and compliance constraints [van Lamsweerde, 2001].I Satisfy stakeholder requirements with available resources.

Direction (Optimality: P ′′ <O P ′)I Continual improvement [Harmon, 2003].I Balance quantitative (e.g. cost, time) and qualitative (e.g. quality,

learning and growth) [Kaplan and Norton, 1992] criteria.Degree (Minimality: P ′ <P P ′′)

I “Evolution” vs “revolution” [Smith and Fingar, 2003]I Minimize the degree of disruption and leverage existing assets.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 17 / 44

Process Context

Definition (Process Context)A process context is given by a tuple 〈P,R,C,G,O〉 where:

P is a process model;R is a resource model (or description);C is a set of constraints or business rules;G is a set of goals (or, without loss of generality, a singleconjunctive goal assertion);O is a set of objectives (or, objective functions),

such that P, R, C, G are mutually consistent.

Process contexts change in response to change requests andimprovement requests.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 18 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 19 / 44

Process Context DynamicsChange Requests

Process Constraint (e.g. add/remove/re-order task)I Implemented if P |= P ′ or P ′ v P (inclusion - graph morphism

[Ehrig et al., 2006]).Resource Constraint (e.g. add/remove resource)

I Implemented if R |= R′ or R′ ⊆ R (sentential inclusion).Compliance Constraint (e.g. add/remove business rule)

I Implemented if C |= C′ or C′ ⊆ C (sentential inclusion).Goal Constraint (e.g. add/remove goal)

I Implemented if G |= G′ or G′ ⊆ G (sentential inclusion).Objective Constraint (e.g. add/remove a preference)

I Implemented if O |= O′ (O’ asserts [non]membership).

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 20 / 44

Process Context DynamicsChange Requests

A revised process context 〈P ′,R′,C′,G′,O〉 is a minimalimplementation of a change request iff:

I 〈P ′,R′,C′,G′,O′〉 implements the change request in question;I there exists no P ′′ such that:

F P′′ ≺P P′ (minimal);F P′′ �P P′ and P′ <O P′′ (optimal); andF 〈P′′, R′, C′, G′, O〉 is a process context implementing the request;

I there exists no R′′ such that R′ ⊂ R′′ ⊆ R and 〈P ′,R′′,C′,G′,O〉 isa process context implementing the request;

I there exists no C′′ such that C′ ⊂ C′′ ⊆ C and 〈P ′,R′,C′′,G′,O〉 isa process context implementing the request;

I there exists no G′′ such that G′ ⊂ G′′ ⊆ G and 〈P ′,R′,C′,G′′,O〉 isa process context implementing the request.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 21 / 44

Process Context DynamicsImprovement Requests

Proximity Threshold dPe (e.g. cost or other comparison value)I Improvement if P ′ �P dPe and P <O P ′ (w.r.t. the objectives).

An improved process context 〈P ′,R′,C,G,O〉 is an optimalimprovement of an improvement request iff:

I 〈P ′,R′,C,G,O〉 is an improved process context;I there exists no P ′′ such that:

F P′′ �P dPe;F P′ <O P′′; andF 〈P′′, R′, C, G, O〉 is an improved process context;

I there exists no R′′ such that R′ ⊂ R′′ ⊆ R and 〈P ′,R′′,C,G,O〉 isan improved context.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 22 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 23 / 44

Model Extensions

Minimal analyst involvement [Jackson and Wing, 1996].Functional Effect Annotations

I Improves limited expression of functionality in high-level processmodels (including un-observable, compliance-related, side-effects).

I Can use free-form (NLP) or structured (CNL) natural languages.I Annotations in some service description languages.I Immediate effects are accumulated to produce a more complete

description of functionality achieved by the process (with referenceto some background knowledge).

Non-Functional AnnotationsI Based on an abstract preference structure [Bistarelli, 2001].I Generic scheme for representing non-functional objectives.I Recently generalized into bi-polar scheme [Pini et al., 2007].I Annotations available in service description languages.I Immediate descriptions are accumulated as per the definition of the

combination operators in the associated preference structure.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 24 / 44

Functional Annotations

Package Screening Process:

Effect:I Performed(SO,Handle,Package)

causes Knows(RA,Package,Status,Clear)

Background:I ∀a,∀o,∀p,∀v1, v2Knows(a,o,p, v1)∧¬equal(v1, v2)⇒ ¬Knows(a,o,p, v2)

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 25 / 44

Non-Functional Annotations

Definition (Constraint-Semiring [Bistarelli et al., 1999])A Constraint-Semiring is a 5-tuple S =〈A,⊕,⊗,0,1〉:

A is a set of abstract preference values and 0,1 ∈ A;⊕ and ⊗ are closed, commutative, associative binary operators.⊕ is a comparison operator;

I 0 is unit. 1 is absorbing. Idempotent.⊗ is a combination operator;

I 1 is unit. 0 is absorbing.

⊗ distributes over ⊕.The comparison operator induces a partial ordering ≤S such that foralla,b ∈ A a ≤S b iff a⊕ b = b. Both ⊕ and ⊗ are monotone on suchordering (negative preference structure).

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Non-Functional Annotations

Table: Package Screening Process

Activity OR OS OCTScan Package 0.98 128 20

Assess Package 0.96 128 30Route Package 0.94 64 600Handle Package 0.88 128 50Update Status 0.98 128 10

Success Rate: OR = 〈[0,1],max , ·, ·,0,1〉 (independence)Security: OS = 〈N+,max ,min,min,0,+∞〉Cycle Time: OCT = 〈R+,min,+,max ,+∞,0〉

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 27 / 44

Process Proximity

Structural Proximity (V or E)I Cardinality: P1 ≤P[V ]

P2 iff |V ∆V1| ≤ |V ∆V2|I Inclusion: P1 ≤P[V ]

P2 iff V ∆V1 ⊆ V ∆V2

Semantic ProximityI Final or Intermediate Scenarios (Final Preferred)I ∆E (P ′,P) = {e∆e′| |e∆e′| = min({|e1∆e′1|, . . . , |en∆e′m|})}I Cardinality: P1 ≤P[E ]

P2 iff Σ|δ1 ∈ ∆E (P1,P)| ≤ Σ|δ2 ∈ ∆E (P2,P)|I Inclusion: P1 ≤P[E ]

P2 iff ∀δ1 ∈ ∆E (P1,P) ∃δ2 ∈ ∆E (P2,P) δ1 ⊆ δ2

Proximity Metric (Combined)I d(P1,P2,P) = wV dV (P1,P2,P)/DV (P1,P2) + wE . . .+ wS . . .

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 28 / 44

Resolved Package Screening Process 1

Figure: Resolved Package Screening Process (R1)

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Resolved Package Screening Process 2

Figure: Resolved Package Screening Process (R2)

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 30 / 44

Functional and Non-Functional Analysis Analysis

First Resolution:I Node difference: 0.I Edge difference: 6 (not included).I End effects: identical.I Performance:

F 1 : OR = 0.76, OS = 64, OCT = 710F 2 : OR = 0.96, OS = 128, OCT = 30

Second Resolution:I Node difference: 0.I Edge difference: 4 (not included).I End effects: {{Performs(SO,Route,Package)}}.I Performance:

F 1 : OR = 0.76, OS = 64, OCT = 710F 2 : OR = 0.90, OS = 64, OCT = 630

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 31 / 44

Outline

1 MotivationExampleSome Relevant MilestonesCurrent State-of-the-ArtRelated WorkResearch Questions

2 ContributionsDrivers and ConsiderationsRedesign GuidanceModel Extensions

3 SummarySummary

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 32 / 44

Summary

ContributionsI Conceptual Framework for RedesignI Systematic [Non]Functional Analysis to Support RedesignI “Lightweight” Notational Extensions to Support Redesign

Future WorkI Role of other knowledge-related operators (e.g. postdiction).I Efficient implementation.I Experimental evaluation.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 33 / 44

Thankyou for Your Attention

Questions and Comments

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 34 / 44

For Further Reading I

Bistarelli, S. (2001).Soft Constraint Solving and Programming: a General Framework.PhD thesis, Computer Science Department, University of Pisa.

Bistarelli, S., Montanari, U., Rossi, F., Schiex, T., Verfaillie, G., andFargier, H. (1999).Semiring-based csps and valued csps: Frameworks, properties,and comparison.Constraints, 4(3):199–240.

Ehrig, H., Ehrig, K., Prange, U., and Taentzer, G. (2006).Fundamentals of Algebraic Graph Transformation (Monographs inTheoretical Computer Science. An EATCS Series).Springer.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 35 / 44

For Further Reading II

Ghose, A. K. and Koliadis, G. (2007).Auditing business process compliance.In Proc. of the International Conference on Service-OrientedComputing (ICSOC’07).

Governatori, G., Hoffmann, J., Sadiq, S., and Weber, I. (2008).Detecting regulatory compliance of business process modelsthrough semantic annotations.In Proceedings of the 4th International Workshop on BusinessProcess Design.

Harmon, P. (2003).Business Process Change.Morgan Kaufmann.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 36 / 44

For Further Reading III

Hendler, J., Tate, A., and Drummond, M. (1990).Ai planning: Systems and techniques.AI Magazine, 11(2):61–77.

Jackson, D. and Wing, J. (1996).Lightweight formal methods.IEEE Computer, pages 21–22.

Kaplan, R. S. and Norton, D. P. (1992).The balanced scorecard - measures that drive performance.Harvard Business Review.

Koliadis, G., Ghose, A. K., and Padmanabhuni, S. (2008).Towards an enterprise business process architecture standard.In Proceeeding of the 2008 IEEE International Conference onServices Computing (SCC’08).

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 37 / 44

For Further Reading IV

Lu, R. and Sadiq, S. (2006).Managing process variants as and information resource.In Proceedings of the Fourth International Conference onBusiness Process Management (BPM’06).

Munive-Hernandez, E. J., Dewhurst, F. W., Pritchard, M., andBarber, K. (2004).Modelling the strategy management process - an initial bpmapproach.Business Process Management Journal, 10(6):691–711.

Pini, M. S., Rossi, F., Venable, K. B., and Bistarelli, S. (2007).Bipolar preference problems: Framework, properties and solvingtechniques.In Proceedings of the 2006 ERCIM Workshop on Constraints,Springer LNAI 4561.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 38 / 44

For Further Reading V

Ponnalagu, K. and Narendra, N. C. (2008).Deriving service variants from business process specifications.In Proceedings of the 1st Bangalore annual Compute conference(COMPUTE’08), pages 1–9, New York, NY, USA. ACM.

Regev, G. and Wegmann, A. (2002).Regulation based linking of strategic goals and businessprocesses.In Proceedings of the 3rd BPMDS Workshop on Goal-OrientedBusiness Process Modeling (GBPM’02).

Regev, G. and Wegmann, A. (2004).Remaining fit: On the creation and maintenance of fit.In Proceedings of the 5th BPMDS Workshop on Creating andMaintaining the Fit between Business Processes and SupportSystems (BPMDS’04).

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 39 / 44

For Further Reading VI

Rinderle, S., Reichert, M., and Dadam, P. (2004).Correctness criteria for dynamic changes in workflow systems - asurvey.Data and Knowledge Engineering, 50:9–34.

Smith, H. and Fingar, P. (2003).Business Process Management: The Third Wave.Meghan-Kiffer Press, Tampa, FL.

Soffer, P. (2005).Scope analysis: identifying the impact of changes in businessprocess models.Software Process: Improvement and Practice, 10(4):393–402.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 40 / 44

For Further Reading VII

van der Aalst, W., Dreiling, A., Rosemann, M., and Jansen-Vullers,M. H. (2005).Configurable process models as a basis for reference modelling.In Proceedings of the Workshop on Business Process ReferenceModels (BPRM’05).

van Lamsweerde, A. (2001).Goal-oriented requirements engineering: A guided tour.In Proceedings of the International Joint Conference onRequirements Engineering, pages 249–263. Toronto, IEEE.

Weber, I., Hoffman, J., and Mendling, J. (2008).Semantic business process validation.In Proceedings of the 3rd International Workshop on SemanticBusiness Process Management.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 41 / 44

For Further Reading VIII

Wing, J. M. (1990).A specifier’s introduction to formal methods.IEEE Computer, 23(9):8–24.

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Similarities with Soft Constraint Problems

Solution uncertainty.Non-traditional valuation structures (“soft” constraints).

I FuzzyI ProbabilisticI Weighted

Table: C1

X def (x)

〈0〉 0.25〈1〉 1

Table: C2

X def (x)

〈0〉 0.5〈1〉 0.4

Table: C1 ⊗ C2

X def (x)

〈0〉 0.25〈1〉 0.4

An algebraic generalization of constraint valuation.I The constraint-semiring structure [Bistarelli et al., 1999].

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Examples of Constraint-Semirings

Constraints LiteratureI Classical = 〈{0,1},∨,∧,0,1〉I Fuzzy = 〈[0 . . . 1],max ,min,0,1〉I Probabilistic = 〈[0 . . . 1],max ,×,0,1〉I Weighted = 〈R−,max ,+,−∞,0〉

Process-RelatedI Cost = 〈R+,min,+,+∞,0〉I Quality = 〈{1,2,3,4,5},max ,min,1,5〉I Security1 = 〈N0,max ,min,0,+∞〉I Security2 = 〈N0,min,+,+∞,0〉 (+ is problematic)I Security3 = 〈2U,⊂,∪,U, ∅〉I Security4 = 〈{L,M,H}, cpS4 , cbS4 ,L,H〉I Risk = 〈R+,min,+,+∞,0〉I Vulnerability = 〈2A,⊂,∪,A, ∅〉

Constraint-Semirings can be combined.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 44 / 44

Examples of Constraint-Semirings

Constraints LiteratureI Classical = 〈{0,1},∨,∧,0,1〉I Fuzzy = 〈[0 . . . 1],max ,min,0,1〉I Probabilistic = 〈[0 . . . 1],max ,×,0,1〉I Weighted = 〈R−,max ,+,−∞,0〉

Process-RelatedI Cost = 〈R+,min,+,+∞,0〉I Quality = 〈{1,2,3,4,5},max ,min,1,5〉I Security1 = 〈N0,max ,min,0,+∞〉I Security2 = 〈N0,min,+,+∞,0〉 (+ is problematic)I Security3 = 〈2U,⊂,∪,U, ∅〉I Security4 = 〈{L,M,H}, cpS4 , cbS4 ,L,H〉I Risk = 〈R+,min,+,+∞,0〉I Vulnerability = 〈2A,⊂,∪,A, ∅〉

Constraint-Semirings can be combined.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 44 / 44

Examples of Constraint-Semirings

Constraints LiteratureI Classical = 〈{0,1},∨,∧,0,1〉I Fuzzy = 〈[0 . . . 1],max ,min,0,1〉I Probabilistic = 〈[0 . . . 1],max ,×,0,1〉I Weighted = 〈R−,max ,+,−∞,0〉

Process-RelatedI Cost = 〈R+,min,+,+∞,0〉I Quality = 〈{1,2,3,4,5},max ,min,1,5〉I Security1 = 〈N0,max ,min,0,+∞〉I Security2 = 〈N0,min,+,+∞,0〉 (+ is problematic)I Security3 = 〈2U,⊂,∪,U, ∅〉I Security4 = 〈{L,M,H}, cpS4 , cbS4 ,L,H〉I Risk = 〈R+,min,+,+∞,0〉I Vulnerability = 〈2A,⊂,∪,A, ∅〉

Constraint-Semirings can be combined.

Koliadis, Ghose (Decision Systems Lab) Framework for Business Process Redesign BPMDS 2009 44 / 44