Paper 3: DEA Weights (Mar Molinero & Portillo)

3rd International Workshop on Innovation3rd International Workshop on Innovationand Performance Managementand Performance Management

University of Kent, UKUniversity of Kent, UK1-4 July 20101-4 July 2010

WHY DEA WEIGHTS ARE OFTEN WHY DEA WEIGHTS ARE OFTEN WRONGLY CALCULATED AND WHAT WRONGLY CALCULATED AND WHAT

CAN BE DONE ABOUT ITCAN BE DONE ABOUT IT

Cecilio Mar MolineroCecilio Mar Molinero, , Kent Business School, UKKent Business School, UK

Fabiola PortilloFabiola Portillo, , University of La Rioja, SpainUniversity of La Rioja, Spain

3rd International Workshop on Innovation and Performance Management, University of Kent, UK, 1-4 July 2010 2

SummarySummary Production and frontier functions Properties of efficient points The Linear Programming formulation Degeneracy and its graphical interpretation Proposed solution An example Models for non-homogeneous organisations


IsoquantsIsoquants

Production and frontier functionsProduction and frontier functions


Budget functionsBudget functions



Production possibility frontierProduction possibility frontier



Returns lineReturns line



DEA-CCR ModelDEA-CCR Model

The Linear Programming formulationThe Linear Programming formulation

R......,1 0

J......,1 0

N......,1 1

1

1

1

1

1

1

1

1

1

,ru

,j v

,i

xu

yv

xu

yv

yv:a.s

xu

yv

e

r

j

R

rirr

J

jijj

R

rorr

J

jojj

J

jojj

R

rorr

J

jojj

ojr v,u

Max


Empirical IsoquantEmpirical Isoquant

Degeneracy and its graphical interpretationDegeneracy and its graphical interpretation

O

x1

Q’( )

Q’( )

x2

A

B

C

DE

y

y




O

x1

Q’( )

Q’( )

x2

A

B

C

DE

Technically and economically efficient points

y

y

y

y

O

x1

Q’( )

Q’( )

x2

A

B

C

DE

Technically and economically efficient points

y

y




O

x1

Q’( )

Q’( )

x2

A

B

C

DETechnically and

economically efficient points

y

y

y

y

O

x1

Q’( )

Q’( )

x2

A

B

C

DETechnically and

economically efficient points

y

y


The geometry of degeneracyThe geometry of degeneracy












Budget line associated with marginal valuesBudget line associated with marginal values

Proposed solutionProposed solution

y

y

y

y

y

y

O

x1

Q’( )

Q’( )

x2

A

B

C

DE




y

y

y

y

y

y

O

x1

Q’( )

Q’( )

x2

A

B

C

DE


O

x1

Q’( )

Q’( )

x2

A

B

C

DE



y

y

y

y

y

y


Fuente: Beasley(1995)

Dual values associated with the university of Essex

Example: Example: Chemistry departments in UK UniversitiesChemistry departments in UK Universities

Universidad

Transferencias

corrientes

Ingresos por

investigaciones

Numero de estudiantes de carrera

Numero de estudiantes postgrado.

Exeter Cardiff Brunel

Durham Kent Essex

931 483 490 986 714 585

293 531 106 776 269 353

191 117 91 203 132 80

20 23 21 32 24 27

University Basic Research Grant income

Under- Post- graduate graduate students students

Variable

Solución 1

Solución 2

Solución 3

Final

u1 u2 v1 v2

0.00157 0.00023 0.00058 0.03532

0.00165 0.00011 0 0.03723

0.00152 0.00032 0 0.03715

0.00164 0.00012 0.00058 0.03532

Solution 1 Solution 2 Solution 3


The end?

3rd International Workshop on Innovation3rd International Workshop on Innovationand Performance Managementand Performance Management

University of Kent, UKUniversity of Kent, UK1-4 July 20101-4 July 2010

NON-HOMOGENEITY IN DATA NON-HOMOGENEITY IN DATA ENVELOPMENT ANALYSISENVELOPMENT ANALYSIS

Cecilio Mar MolineroCecilio Mar Molinero, , Kent Business School, University of Kent, UKKent Business School, University of Kent, UK


SummarySummary Production and frontier functions Properties of efficient points The Linear Programming formulation Degeneracy and its graphical interpretation Proposed solution An example Models for non-homogeneous organisations


Teaching and ResearchTeaching and Research

Models for non-homogeneous organisationsModels for non-homogeneous organisations

3rd International Workshop on Innovation and Performance Management, University of Kent, UK, 1-4 July 2010 232323Cecilio Mar Molinero- UPCCecilio Mar Molinero- UPC

— An equation for the T function

— An equation for the R function

— An equation for the overall unit to be assessed

— To be efficient you need to be efficient at each activity and efficient overall



―This model was used forThis model was used for

NHS trusts in the UKNHS trusts in the UK

Police forces in SpainPolice forces in Spain

Railways in the US (not published) and TaiwanRailways in the US (not published) and Taiwan

Information system architectureInformation system architecture

― There has been a review paper in 2010There has been a review paper in 2010

― It is non-linear in the constraints and It is non-linear in the constraints and “simplifications” have been published.“simplifications” have been published.

― Not related to Network DEA (Fare and Not related to Network DEA (Fare and Grosskopft) as both models are Grosskopft) as both models are contemporaneous.contemporaneous.



― The model is homogeneous: all units The model is homogeneous: all units use the same inputs to produce the same use the same inputs to produce the same outputs, and have the same internal outputs, and have the same internal structure.structure.

― Properties studied by means of Kuhn Properties studied by means of Kuhn Tucker theory.Tucker theory.

― To progress we need to look at To progress we need to look at envelopment formulation for DEAenvelopment formulation for DEA





Unit of assessment that engages only in one activityUnit of assessment that engages only in one activity





Example: Socially responsible financial Example: Socially responsible financial institutions in Boliviainstitutions in Bolivia



―Example: Socially responsible Example: Socially responsible financial institutions in Boliviafinancial institutions in Bolivia

―In Ross Wyatt’s PhD we looked at In Ross Wyatt’s PhD we looked at efficiency in various types of financial efficiency in various types of financial institutions in Bolivia: NGOs, Building institutions in Bolivia: NGOs, Building Societies, Consumer Cooperatives, Societies, Consumer Cooperatives, Commercial Banks, and so on.Commercial Banks, and so on.

―These make microcredit loans, These make microcredit loans, mortgage loans, commercial loans, and mortgage loans, commercial loans, and consumer loans.consumer loans.




―The idea can be extended to activities that The idea can be extended to activities that take place in sequence: supply chains are the take place in sequence: supply chains are the obvious example.obvious example.

―In this case we are not interested in In this case we are not interested in specialisation versus diversification, but in vertical specialisation versus diversification, but in vertical integration.integration.

―The model allows for The model allows for

outsourcingoutsourcing

selling partly manufactured componentsselling partly manufactured components

buying intermediate componentsbuying intermediate components



―Example from Huiling Zhao’s PhD: Example from Huiling Zhao’s PhD: Primary schools in Kent.Primary schools in Kent.

Children in Kent can attend school from Children in Kent can attend school from ages four to seven (infant schools) and from ages four to seven (infant schools) and from the ages of seven to eleven (middle the ages of seven to eleven (middle schools).schools).

They can also attend schools from ages They can also attend schools from ages four to eleven (primary schools).four to eleven (primary schools).

Taking into account poverty (free meals), Taking into account poverty (free meals), special needs incidence, and funding, which special needs incidence, and funding, which system delivers the best test results at 11?system delivers the best test results at 11?












Questions?Questions?


Technology

Paper 3: DEA Weights (Mar Molinero & Portillo)