Table Of ContentInternational Series in Operations
Research & Management Science
Volume 157
SeriesEditor:
FrederickS.Hillier
StanfordUniversity,CA,USA
SpecialEditorialConsultant:
CamilleC.Price
StephenF.Austin,StateUniversity,TX,USA
Forfurthervolumes:
http://www.springer.com/series/6161
Peter Bogetoft • Lars Otto
Benchmarking with DEA, SFA, and R
Peter Bogetoft Lars Otto
Department of Economics Institute of Food and Resource
Copenhagen Business School CBS Economics
Porcelaenshaven 16 A University of Copenhagen
2000 Frederiksberg Rolighedsvej 25
Denmark 1958 Frederiksberg C
p [email protected] Denmark
[email protected]
ISSN0884-8289
ISBN978-1-4419-7960-5 e-ISBN978-1-4419-7961-2
DOI10.1007/978-1-4419-7961-2
Springer New York Dordrecht Heidelberg London
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To
Victoria,Rasmus,Stina,andNete
MathiasandGerda
Preface
Subject
This book covers recent advances in efficiency evaluation, most notably the Data
EnvelopmentAnalysis (DEA) and Stochastic FrontierAnalysis (SFA) methods.It
introducestheunderlyingtheories,showshowtomaketherelevantcalculationsand
discusses some applications.The aim is to make the reader aware of the prosand
consofthe differentmethodsand to trainhim orheron theproperusage ofthese
methodsinbothstandardandnon-standardcases.
Severalsoftwarepackageshavebeendevelopedthatcanbeusedtosolvesome
ofthemostcommonDEAandSFAmodels.Inthisbook,however,werelyonR,a
freesoftwareenvironmentthatcanbeusedforoptimization,statisticalcomputing,
andgraphics.Thisprogramenablesthereadertosolvenotonlystandardproblems
but also many other problem variants. Using R, one can focus on understanding
thebusinesscaseanddevelopingagoodmodel.Oneisnotrestrictedtopredefined
modelsortotheuseofaone-size-fits-allapproach.
ThereareseveralRroutinesthatsupporttheuseofDEAandSFAmodels.While
writingthisbook,wehavealsodevelopedanR-packagenamedBenchmarkingthat
makesapplicationseasywithoutlimitingthevariationsin themodelsandcalcula-
tionsthatinnovativeresearchersandpractitionersseektouse.
Audience and style
Theintendedaudienceincludesgraduatestudents,advancedconsultantsandpracti-
tionerswithaninterestinquantitativeperformanceevaluation.
This book uses mathematical formulations of models, assumptions, etc. Un-
like original contributions on this subject, however, this book de-emphasizes for-
malproofs,partially by placingthem in appendicesor by referringto the original
vii
viii Preface
sources.Moreover,thisbookemphasizestheuseoftheoriesandinterpretationsof
themathematicalformulations.
Aseriesofsmallexamplesandgraphicalillustrationswillbepresented.Thistext
alsocombinesformalmodelswithlessformaleconomicandorganizationalthink-
ing. Moreover,it discusses numerousapplicationsbased on projects on which we
have worked. This includes some large projects with significant practical effects:
e.g.,thedesignofbenchmarking-basedregulationsforenergycompaniesindiffer-
entEuropeancountriesorthedevelopmentofmergerdecisionsupportsystemsfor
competitionauthorities.
Acknowledgements
The book covers material that we have used in several courses. We gratefully ac-
knowledgecommentsbystudentsatCopenhagenUniversityandCopenhagenBusi-
nessSchool,Denmark;UniversitatAuto`nomade Barcelona,Spain;the University
ofNewEngland,UNE,Australia;theHelsinkiSchoolofEconomicsandBusiness
Administration,Finland;andtheYaleSchoolofManagement,USA.
Inaddition,wehavebenefittedfromquestionsraisedbyparticipantsinaseries
of industrycoursesthatwe presentedin Denmark,Sweden,Germany,the Nether-
landsandCanadaduringthelastfiveyears.Wewouldalsoliketoacknowledgethe
influenceofa largenumberoffriends,coauthorsandcolleagueswhohavehelped
usto understandthe basicsof efficiencyevaluation.Atthe risk ofleaving outim-
portantindividuals,we would like to acknowledgethe contributionsof Professors
PerAgrell,MetteAsmild,RajivBanker,RobertChambers,TimCoelli,WilliamW.
Cooper, Philippe Van den Eeckaut, Rolf Fa¨re, Finn Førsund, Shawna Grosskopf,
Harold Fried, Emili Griffle-Tatje, Arne Henningsen, Pekka Korhonen, Jens Leth
Hougaard, Knox Lovell, Ole Olsen, Niels Chr. Petersen, Leopold Simar, Jørgen
Tind,HenryTulkens,andPaulWilson.
Copenhagen, PeterBogetoft
September2010 LarsOtto
Contents
1 IntroductiontoBenchmarking................................... 1
1.1 Whybenchmark ........................................... 1
1.1.1 Learning ........................................... 2
1.1.2 Coordination........................................ 3
1.1.3 Motivation.......................................... 5
1.2 Idealevaluations ........................................... 6
1.3 KeyPerformanceIndicatorsandRatios ........................ 8
1.4 Technologyandefficiency ................................... 11
1.5 Manyinputsandoutputs..................................... 13
1.6 Fromeffectivenesstoefficiency .............................. 15
1.7 Frontiermodels ............................................ 17
1.7.1 Asimpletaxonomy .................................. 17
1.7.2 Prosandcons ....................................... 18
1.8 Software.................................................. 20
1.9 Summary ................................................. 20
1.10 Bibliographicnotes......................................... 21
2 EfficiencyMeasures ............................................ 23
2.1 Introduction ............................................... 23
2.2 Setting ................................................... 23
2.3 Efficientproduction......................................... 24
2.4 Farrellefficiency ........................................... 26
2.4.1 Non-discretionaryinputsandoutputs.................... 29
2.4.2 UsingFarrelltorankfirms ............................ 29
2.4.3 FarrellandShepharddistancefunctions ................. 30
2.5 Directionalefficiencymeasures............................... 31
2.6 Efficiencymeasureswithprices............................... 35
2.6.1 Costandinputallocativeefficiency ..................... 36
2.6.2 Revenueandoutputallocativeefficiency................. 39
2.6.3 Profitefficiency...................................... 41
2.7 Dynamicefficiency......................................... 41
ix
x Contents
2.8 Structuralandnetworkefficiency ............................. 45
2.9 Choicebetweenefficiencymeasures........................... 48
2.10 Summary ................................................. 50
2.11 Bibliographicnotes......................................... 50
2.12 Appendix:Moreadvancedmaterialonefficiencymeasures........ 51
2.12.1 Therationaleofefficiency............................. 52
2.12.2 Axiomaticcharacterizationofefficiencymeasures......... 53
3 ProductionModelsandTechnology .............................. 57
3.1 Introduction ............................................... 57
3.2 Setting ................................................... 57
3.3 Thetechnologyset ......................................... 59
3.4 Freedisposabilityofinputandoutput.......................... 60
3.5 Convexity................................................. 64
3.6 Freedisposalandconvex .................................... 68
3.7 Scalingandadditivity ....................................... 70
3.8 Alternativedescriptionsofthetechnology...................... 74
3.9 Summary ................................................. 77
3.10 Bibliographicnotes......................................... 78
3.11 Appendix:Distancefunctionsandduality ...................... 78
4 DataEnvelopmentAnalysisDEA ................................ 81
4.1 Introduction ............................................... 81
4.2 Setting ................................................... 82
4.3 Minimalextrapolation....................................... 82
4.4 DEAtechnologies.......................................... 85
4.5 DEAprograms............................................. 90
4.6 Peerunits ................................................. 93
4.6.1 NumericalexampleinR .............................. 95
4.7 DEAasactivityanalysis .................................... 98
4.8 Scaleandallocativeefficiency................................ 99
4.8.1 ScaleefficiencyinDEA............................... 99
4.8.2 AllocativeefficiencyinDEA ..........................102
4.9 Summary .................................................104
4.10 Bibliographicnotes.........................................105
4.11 Appendix:MoretechnicalmaterialonDEAmodels..............106
4.11.1 WhytheT(cid:2).(cid:2)/setswork .............................106
4.11.2 Linearprogramming .................................107
4.11.3 DEA“cost”andproductionfunctions ...................109
5 AdditionalTopicsinDEA .......................................115
5.1 Introduction ...............................................115
5.2 Super-efficiency............................................115
5.3 Non-discretionaryvariables ..................................118
5.4 Directionalefficiencymeasures...............................121
