collaborative building of an ontology of key performance ......collaborative building of an ontology...

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

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

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

Motivation

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]

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

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

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

Approach

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)

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

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)

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.

KPI Ontology

Approach

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

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

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

Case study

KPIs chosen for monitoring of a Virtual Enterprise:

InvestmentInEmplDevelopment = PersonnelTrainingCosts + TeachCost

PersonnelTrainingCosts = HourlyCost ∗ PersonnelTrainingTime

TeachCosts = PersonnelTrainingTime ∗ HourRate

PersonnelCosts = NumHours ∗ HourlyCost ∗ (Overhead + 1)

Case study

KPIs chosen for monitoring of a Virtual Enterprise:

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)

@fi ∈ KB/fi = fnew(no formula is identical to fnew )→ identical

KB 1 fnew(no formula is mathematically equivalent to fnew )

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

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

Scenario: insertion of a new indicatorTotCostEmpTrain = TeachCosts+PersonnelTrainingTime ∗HourlyCost

Result: equivalent to InvestmentInEmployeeDevelopment

Scenario: insertion of a new indicatorTotCostEmpTrain = TeachCosts+PersonnelTrainingTime ∗HourlyCost

Result: equivalent to InvestmentInEmployeeDevelopment

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

Scenario: update of an indicatorPersonnelTrainingTime = PersonnelTrainingCosts + HourlyCost

Result: incoherent with PersonnelTrainingCost

Scenario: update of an indicatorPersonnelTrainingTime = PersonnelTrainingCosts + HourlyCost

Result: incoherent with PersonnelTrainingCost

Approach

Ontology editor

Creation of a new indicator

Ontology editor

Search/Browse indicators

Ontology editor

Creation of a new member

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

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

Experimentation: results

Average execution time[ms]identical 4 (±1.1)

equivalence 197 (±11.5)incoherence 201 (±10.5)

Experimentation: results

Experiments with a set of synthetic ontologies with increasing sizeoperands:2..4, levels:2..5 = 12 ontologies73980 unique tests

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

Conclusion

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)

collaborative building of an ontology of key performance ......collaborative building of an ontology...

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