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Collaborative Building of an Ontologyof Key Performance Indicators
Claudia Diamantini, Laura Genga,Domenico Potena, Emanuele Storti
DII, Universita Politecnica delle Marche, Ancona, Italy
CoopIS 2014, OTM 2014, Amantea, Italy, Oct 27-31
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 1 / 29
Outline
1 Introduction and Motivation2 Related Work3 Goal and Approach4 Methodology
Ontological model for KPIsReasoning over KPI formulasOntology editor
5 Experimentation6 Conclusion
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 2 / 29
Introduction
Scenario: performance measurement in collaborative environments(e.g., virtual organizations)
Problems:KPIs
complex data with an aggregate/compound naturebusiness view vs. technical view of KPIslack of shared understanding of the meaning of KPIs
shared library of KPIscollaborative managementmaintaining consistency of the repository
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 3 / 29
Motivation
Example: compare performances of two enterprises of a virtualenterprise
Requirements for the repository:compositional semantics for KPIs should be made explicitcollaboratively built: keep the repository consistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 4 / 29
Motivation
Example: compare performances of two enterprises of a virtualenterprise
Requirements for the repository:compositional semantics for KPIs should be made explicitcollaboratively built: keep the repository consistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 4 / 29
Motivation
Example: compare performances of two enterprises of a virtualenterprise
Requirements for the repository:compositional semantics for KPIs should be made explicitcollaboratively built: keep the repository consistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 4 / 29
Motivation
Example: compare performances of two enterprises of a virtualenterprise
Requirements for the repository:compositional semantics for KPIs should be made explicitcollaboratively built: keep the repository consistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 4 / 29
Motivation
Example: compare performances of two enterprises of a virtualenterprise
Requirements for the repository:compositional semantics for KPIs should be made explicitcollaboratively built: keep the repository consistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 4 / 29
Motivation
Example: compare performances of two enterprises of a virtualenterprise
Requirements for the repository:compositional semantics for KPIs should be made explicitcollaboratively built: keep the repository consistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 4 / 29
Related work
The complex nature of PI is not fully captured in existing models:semantic representations of the multidimensional model [Priebe et al2003, Niemi et al 2007, Neumar et al 2012]
to simplify and automatize design and analysis(non-logical) modeling of indicator formulas
to support calculation [Pedrinaci et al 2009],[Horkoff et al 2012]for interoperability [Golfarelli et al 2012]
Few work dealing with logical models for indicators:inference of dependencies among indicators [Popova et al 2010], [DelRıo Ortega et al 2010]
ontological representation of formulas [Kehlenbeck et al 2009]
Collaborative framework for management of KPIs:KPIshare, a social knowledge base [Resinas et al 2014]
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 5 / 29
Goal
Collaborative management of a shared, formal and valid referencemodel for KPIs providing support to:
introduction of new valid KPIs in the repositorysafe update/deletion of a KPIbrowsing and searching of KPIsconsensus management & versioning
Requirements:global view of KPIs and their formulasmapping of enterprise KPIs to global definitionsfunctionalities to manipulate and reason about KPIs
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 6 / 29
Goal
Collaborative management of a shared, formal and valid referencemodel for KPIs providing support to:
introduction of new valid KPIs in the repositorysafe update/deletion of a KPIbrowsing and searching of KPIsconsensus management & versioning
Requirements:global view of KPIs and their formulasmapping of enterprise KPIs to global definitionsfunctionalities to manipulate and reason about KPIs
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 6 / 29
Approach
Ontological representation of KPIsdescriptive and compositional semantics for KPIsgoal: annotation of local data with global definitions
Reasoning and manipulation services for KPIsfacts to represent KPIspredicates to formalize mathematical axioms for formulamanipulation and check of consistency
Ontology editorflexible management of the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 7 / 29
Approach
Ontological representation of KPIsdescriptive and compositional semantics for KPIsgoal: annotation of local data with global definitions
Reasoning and manipulation services for KPIsfacts to represent KPIspredicates to formalize mathematical axioms for formulamanipulation and check of consistency
Ontology editorflexible management of the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 7 / 29
Approach
Ontological representation of KPIsdescriptive and compositional semantics for KPIsgoal: annotation of local data with global definitions
Reasoning and manipulation services for KPIsfacts to represent KPIspredicates to formalize mathematical axioms for formulamanipulation and check of consistency
Ontology editorflexible management of the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 7 / 29
Approach
Ontological representation of KPIsdescriptive and compositional semantics for KPIsgoal: annotation of local data with global definitions
Reasoning and manipulation services for KPIsfacts to represent KPIspredicates to formalize mathematical axioms for formulamanipulation and check of consistency
Ontology editorflexible management of the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 7 / 29
KPI Ontology
Inspiring principles: VRM, SCOR, Six-Sigma, multidimensional models
Indicator ≡ ∀ hasDimension.Dimension u∀ hasFormula.Formula u (=1 hasFormula) u∀ hasUnitOfMeasure.UoM u (=1 hasUnitOfMeasure) u∀ hasBusObj.BusinessObject u (=1 hasBusObj) u∀ hasAggrFunction.AggrFun u (=1 hasAggrFunction)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 8 / 29
KPI Ontology
Dimension: coordinate along which an indicator can be computed(e.g., time, place and product for Total Costs)
Dimensions are organized in levels, e.g.:Time: Day�Week�Month�YearPlace: City�Region�Country
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 9 / 29
KPI Ontology
TBoxVE v OrganizationDimension
Enterprise v OrganizationDimension u ∀partOf.VE u(=1 partOf)
Department v OrganizationDimension u ∀partOf.Enterpriseu(=1 partOf)
ProjectTeam v OrganizationDimension u ∀partOf.Departmentu(=1 partOf)
ABoxVirEnt1:VE, ACME:Enterprise, R&D:Department, Team A:ProjectTeam
partOf(Team A,R&D),partOf(R&D,ACME), partOf(ACME,VirtEnt1)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 10 / 29
KPI Ontology
Formula: mathematical expression stating how an indicator iscomputed(e.g., PersonnelTrainingCost=HourlyCost*PersonnelTrainingTime)
Definition (Well-formed formula)Given a set {f1, ..., fn} of symbol of indicators and a set {op1, ...,opm} ofalgebraic operators,
fi is a well-formed formula;
opj(f1, ..., fk ) is a well-formed formula.
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 11 / 29
KPI Ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 12 / 29
KPI Ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 12 / 29
KPI Ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 12 / 29
KPI Ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 12 / 29
Approach
Ontological representation of KPIsdescriptive and compositional semantics for KPIsgoal: annotation of local data with global definitions
Reasoning and manipulation services for KPIsfacts to represent KPIspredicates to formalize mathematical axioms for formulamanipulation and check of consistency
Ontology editorflexible management of the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 13 / 29
Reasoning functionalities
Logic programming as unifying logic layer:representation of formulas as Prolog facts, e.g.:A = B + C → formula(A,B+C,’branch node’)
Prolog predicates for basic reasoning tasks:mathematical theory for formula manipulation (PRESS: PRologEquation Solving System)
basic math operationequation solving and formula rewriting
definition of specific predicates for KPI management
XSB as Prolog reasoner
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 14 / 29
Reasoning functionalities
Logic programming as unifying logic layer:representation of formulas as Prolog facts, e.g.:A = B + C → formula(A,B+C,’branch node’)
Prolog predicates for basic reasoning tasks:mathematical theory for formula manipulation (PRESS: PRologEquation Solving System)
basic math operationequation solving and formula rewriting
definition of specific predicates for KPI management
XSB as Prolog reasoner
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 14 / 29
Reasoning functionalities
Logic programming as unifying logic layer:representation of formulas as Prolog facts, e.g.:A = B + C → formula(A,B+C,’branch node’)
Prolog predicates for basic reasoning tasks:mathematical theory for formula manipulation (PRESS: PRologEquation Solving System)
basic math operationequation solving and formula rewriting
definition of specific predicates for KPI management
XSB as Prolog reasoner
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 14 / 29
Reasoning functionalities
Logic programming as unifying logic layer:representation of formulas as Prolog facts, e.g.:A = B + C → formula(A,B+C,’branch node’)
Prolog predicates for basic reasoning tasks:mathematical theory for formula manipulation (PRESS: PRologEquation Solving System)
basic math operationequation solving and formula rewriting
definition of specific predicates for KPI management
XSB as Prolog reasoner
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 14 / 29
Reasoning: mathematical predicates
Mathematical functions for rewriting:
solve equation for resolution of equations:Costs = TravelCosts+PersonnelCostsPersonnelCosts= Costs − TravelCosts
simplify solution (simplification and substitution):
ROI IG = ExpectedMarketImpactTravelCosts+PersonnelCosts
ROI IG = ExpectedMarketImpactCosts
Note: useful to infer new formulas not explicitly written in the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 15 / 29
Reasoning: mathematical predicates
Mathematical functions for rewriting:
solve equation for resolution of equations:Costs = TravelCosts+PersonnelCostsPersonnelCosts= Costs − TravelCosts
simplify solution (simplification and substitution):
ROI IG = ExpectedMarketImpactTravelCosts+PersonnelCosts
ROI IG = ExpectedMarketImpactCosts
Note: useful to infer new formulas not explicitly written in the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 15 / 29
Case study
KPIs chosen for monitoring of a Virtual Enterprise:
InvestmentInEmplDevelopment = PersonnelTrainingCosts + TeachCost
PersonnelTrainingCosts = HourlyCost ∗ PersonnelTrainingTime
TeachCosts = PersonnelTrainingTime ∗ HourRate
PersonnelCosts = NumHours ∗ HourlyCost ∗ (Overhead + 1)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 16 / 29
Case study
KPIs chosen for monitoring of a Virtual Enterprise:
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 16 / 29
Reasoning: consistency check
Let KB be a repository of KPIs, a new indicator with formula fnew isconsistent with KB iif:
@fi ∈ KB/fi = fnew(no formula is identical to fnew )
KB 1 fnew(no formula is mathematically equivalent to fnew )
KB ∪ {fnew} 1 ⊥(the formula is coherent with the others in the KB)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 17 / 29
Reasoning: consistency check
Let KB be a repository of KPIs, a new indicator with formula fnew isconsistent with KB iif:
@fi ∈ KB/fi = fnew(no formula is identical to fnew )→ identical
KB 1 fnew(no formula is mathematically equivalent to fnew )
KB ∪ {fnew} 1 ⊥(the formula is coherent with the others in the KB)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 17 / 29
Reasoning: consistency check
Let KB be a repository of KPIs, a new indicator with formula fnew isconsistent with KB iif:
@fi ∈ KB/fi = fnew(no formula is identical to fnew )→ identical
KB 1 fnew(no formula is mathematically equivalent to fnew )→ equivalence
KB ∪ {fnew} 1 ⊥(the formula is coherent with the others in the KB)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 17 / 29
Reasoning: consistency check
Let KB be a repository of KPIs, a new indicator with formula fnew isconsistent with KB iif:
@fi ∈ KB/fi = fnew(no formula is identical to fnew )→ identical
KB 1 fnew(no formula is mathematically equivalent to fnew )→ equivalence
KB ∪ {fnew} 1 ⊥(the formula is coherent with the others in the KB)→ incoherence
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 17 / 29
Reasoning: consistency check
Evaluation of equivalent formulas:
equivalence(F): given a formula G of the ontology, a formula F isequivalent to G if can be rewritten as G (by rewriting functionalities)
Policies:remove the duplicatekeep duplicates and declare that the corresponding KPIs are thesame indicator
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 18 / 29
Reasoning: consistency check
Scenario: insertion of a new indicatorTotCostEmpTrain = TeachCosts+PersonnelTrainingTime ∗HourlyCost
Result: equivalent to InvestmentInEmployeeDevelopment
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 19 / 29
Reasoning: consistency check
Scenario: insertion of a new indicatorTotCostEmpTrain = TeachCosts+PersonnelTrainingTime ∗HourlyCost
Result: equivalent to InvestmentInEmployeeDevelopment
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 19 / 29
Reasoning: consistency check
Predicate to maintain a consistent ontology:
incoherence(F): given a new formula F = expression
for each formula G in KB containing a reference to F
solve G for F, obtaining F = expression2if {indicators in expression} ⊆ {indicators in expression2} then F isinconsistent
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 20 / 29
Reasoning: consistency check
Scenario: update of an indicatorPersonnelTrainingTime = PersonnelTrainingCosts + HourlyCost
Result: incoherent with PersonnelTrainingCost
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 21 / 29
Reasoning: consistency check
Scenario: update of an indicatorPersonnelTrainingTime = PersonnelTrainingCosts + HourlyCost
Result: incoherent with PersonnelTrainingCost
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 21 / 29
Approach
Ontological representation of KPIsdescriptive and compositional semantics for KPIsgoal: annotation of local data with global definitions
Reasoning and manipulation services for KPIsfacts to represent KPIspredicates to formalize mathematical axioms for formulamanipulation and check of consistency
Ontology editorflexible management of the ontology
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 22 / 29
Ontology editor
Creation of a new indicator
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 23 / 29
Ontology editor
Search/Browse indicators
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 24 / 29
Ontology editor
Creation of a new member
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 25 / 29
Experimentation
BIVEE ontology:356 production and innovation KPIs (281 connected, 75disconnected)lattices: 3.14 levels and 2.67 operands per indicator
Experimental procedure (for identical, equivalence, incoherence):
for each connected indicator
compute execution time (x10 times)average results
average on all indicators
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 26 / 29
Experimentation
BIVEE ontology:356 production and innovation KPIs (281 connected, 75disconnected)lattices: 3.14 levels and 2.67 operands per indicator
Experimental procedure (for identical, equivalence, incoherence):
for each connected indicator
compute execution time (x10 times)average results
average on all indicators
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 26 / 29
Experimentation: results
Average execution time[ms]identical 4 (±1.1)
equivalence 197 (±11.5)incoherence 201 (±10.5)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 27 / 29
Experimentation: results
Experiments with a set of synthetic ontologies with increasing sizeoperands:2..4, levels:2..5 = 12 ontologies73980 unique tests
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 27 / 29
Conclusion
Collaborative building of a ontology of Key Performance Indicatorslogical model for indicators (KPIOnto)reasoning services (mathematical model + set of predicates)
Current status of the workmanagement of KPIOnto in BIVEE projectonly linear equations (not a limitation)
Future workreason with both descriptive properties and formulasrecognition of similar (not equivalent) formulas
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 28 / 29
Conclusion
Collaborative building of a ontology of Key Performance Indicatorslogical model for indicators (KPIOnto)reasoning services (mathematical model + set of predicates)
Current status of the workmanagement of KPIOnto in BIVEE projectonly linear equations (not a limitation)
Future workreason with both descriptive properties and formulasrecognition of similar (not equivalent) formulas
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 28 / 29
Conclusion
Collaborative building of a ontology of Key Performance Indicatorslogical model for indicators (KPIOnto)reasoning services (mathematical model + set of predicates)
Current status of the workmanagement of KPIOnto in BIVEE projectonly linear equations (not a limitation)
Future workreason with both descriptive properties and formulasrecognition of similar (not equivalent) formulas
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 28 / 29
Acknowledgements
This work has been partly funded by the EC through the ICT ProjectBIVEE: Business Innovation and Virtual Enterprise Environment(FoF-ICT-2011.7.3-285746)
Emanuele Storti (UNIVPM) Building of an Ontology of KPIs CoopIS 2014 29 / 29