Data Envelopment Analysis

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Data Envelopment Analysis

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Title: Data Envelopment Analysis

1
Data Envelopment Analysis

Robert M. Hayes
2005

2
Overview

Introduction
Data Envelopment Analysis
DEA Models
Extensions to include a priori Valuations
Strengths and Weaknesses of DEA
Implementation of DEA
The Example of Libraries
Annals of Operations Research 66
Annals of Operations Research 73

3
Introduction

Utility Functions
Cost/Effectiveness
Interpretation for Libraries

4
Utility Functions

A fundamental requirement in applying operations
research models is the identification of a
"utility function" which combines all variables
relevant to a decision problem into a single
variable which is to be optimized. Underlying the
concept of a utility function is the view that it
should represent the decision-maker's perceptions
of the relative importance of the variables
involved rather than being regarded as uniform
across all decision-makers or externally
imposed.
The problem, of course, is that the resulting
utility functions may bear no relationship to
each other and it is therefore difficult to make
comparisons from one decision context to another.
Indeed, not only may it not be possible to
compare two different decision-makers but it may
not be possible to compare the utility functions
of a single decision-maker from one context to
another.

5
Cost/Effectiveness

A traditional way to combine variables in a
utility function is to use a cost/effectiveness
ratio, called an "efficiency" measure. It
measures utility by the "cost per unit produced".
On the surface, that would appear to make
comparison between two contexts possible by
comparing the two cost/effectiveness ratios. The
problem, though, is that two different
decision-makers may place different emphases on
the two variables.

6
Cost/Effectiveness

It also must be recognized that effectiveness
will usually entail consideration of a number of
products and services and costs a number of
sources of costs. Cost/effectiveness measurement
requires combining the sources of cost into a
single measure of cost and the products and
services into a single measure of effectiveness.
Again, the problem of different emphases of
importance must be recognized. This is especially
the case for the several measures of
effectiveness. But it may also be the case with
the several measure of costs, since some costs
may be regarded as more important than others
even though they may all be measured in dollars.
When some costs cannot be measured in dollars,
the problem is compounded.

7
Cost/Effectiveness

More generally, instead of costs and
effectiveness, the variables may be identified as
"input" and "output". The efficiency ratio is
then no long characterized as cost/effectiveness
but as "output/input", but the issues identified
above are the same.

8
Interpretation for Libraries

This issue can be illustrated by evaluating
library performance. Effectiveness here is the
extent to which library services meet the
expectations or goals set by the organization
served. It is likely to be measured by several
services which are the outputs of library
operationsmaking a collection available for use,
circulation or other uses of materials, answering
of information questions, instructing and
consulting.
Inputs are represented by acquisitions, staff,
and space, to which evident costs can be
assigned, but they are also represented by
measures of the populations served.

9
Interpretation for Libraries

Efficiency measures the librarys ability to
transform its inputs (resources and demands) into
production of outputs (services). The objective
in doing so is to optimize the balance between
the level of outputs and the level of inputs.
The success of the library, like that of other
organizations, depends on its ability to behave
both effectively and efficiently.
The issue at hand, then is how to combine the
several measures of input and output into a
single measure of efficiency. The method we will
examine is that called "data envelopment
analysis".

10
Data Envelopment Analysis

Data Envelopment Analysis (DEA) measures the
relative efficiencies of organizations with
multiple inputs and multiple outputs. The
organizations are called the decision-making
units, or DMUs.
DEA assigns weights to the inputs and outputs of
a DMU that give it the best possible efficiency.
It thus arrives at a weighting of the relative
importance of the input and output variables that
reflects the emphasis that appears to have been
placed on them for that particular DMU.
At the same time, though, DEA then gives all the
other DMUs the same weights and compares the
resulting efficiencies with that for the DMU of
focus.

11
Data Envelopment Analysis

If the focus DMU looks at least as good as any
other DMU, it receives a maximum efficiency
score. But if some other DMU looks better than
the focus DMU, the weights having been calculated
to be most favorable to the focus DMU, then it
will receive an efficiency score less than
maximum.

12
Graphical Illustration

To illustrate, consider seven DMUs which each
have one input and one output L1 (2,2), L2
(3,5), L3 (6,7), L4 (9,8), L5 (5,3), L6
(4,1), L7 (10,7).

L4
L3
L7
L2
L5
L1
L6
13
Graphical Illustration

DEA identifies the units in the comparison set
which lie at the top and to the left, as
represented by L1, L2, L3, and L4. These units
are called the efficient units, and the line
connecting them is called the "envelopment
surface" because it envelops all the cases.
DMUs L5 through L7 are not on the envelopment
surface and thus are evaluated as inefficient by
the DEA analysis. There are two ways to explain
their weakness. One is to say that, for example,
L5 could perhaps produce as much output as it
does, but with less input (comparing with L1 and
L2) the other is to say it could produce more
output with the same input (comparing with L2 and
L3).

14
Graphical Illustration

Thus, there are two possible definitions of
efficiency depending on the purpose of the
evaluation. One might be interested in possible
reduction of inputs (in DEA this is called the
input orientation) or augmentation of outputs
(the output orientation) in achieving technical
efficiency. Depending on the purpose of the
evaluation, the analysis provides different sets
of peer groups to which to compare.
However, there are times when reduction of inputs
or augmentation of outputs is not sufficient. In
our example, even when L6 reduces its input from
4 units to 2, there is still a gap between it and
its peer L1 in the amount of one unit of output.
In DEA, this is called the "slack" which means
excess input or missing output that exists even
after the proportional change in the input or the
outputs.

15
Graphical Illustration

This example will be used to illustrate the
several forms that the DEA model can take.
In each case, the results presented are based on
the implementation of DEA that will be discussed
later in this presentation. It is an Excel
spreadsheet using the add-in Solver capability.
The spreadsheet is identical for all of the
forms, but the application of Solver differs in
the target optimized and in the values to be
varied, so for each form the target and the
values to be varied will be identified.

16
DEA Models

The Basic EDA Concept
Variations of DEA Formulation
Formulation Primal or Dual
Orientation Input or Output
Returns to Scale Fixed or Variable

17
The Basic EDA Concept

Assume that each DMU has values for a set of
inputs and a set of outputs.
Choose non-negative weights to be applied to the
inputs and outputs for a focus DMU so as to
maximize the ratio of weighted outputs divided by
weighted inputs
But do so subject to the condition that, if the
same weights are applied to each of the DMUs
(including the focus DMU), the corresponding
ratios are not greater than 1
Do that for each DMU.
The resulting value of the ratio for each DMU is
its EDA efficiency. It is 1 if the DMU is
efficient and less than 1 if it is not.

18
Formulation

Let (Yk,Xk) (Yki,Xkj), k 1 to n, i 1 to s,
j 1 to m
Maximize mYk/nXk for each value of k from 1 to n,
subject in each case to mYj/nXj lt 1, j 1 to n,
where
mYk means Si miYki, i 1 to s,
nXk means Si niXki, i 1 to m
mYj means Si miYji, i 1 to s and j 1 to n
nXj means Si niXji, i 1 to m and j 1 to n.
mi, ni gt 0
The solution is the set of maximum values for
mYk/nXk and the associated values for m and n

19
Basic Linear Programming Model

For solution, this optimization problem is
transformed into a linear programming problem,
schematically displayed as follows
In a moment, we will interpret this display as it
is translated into alternative formulations of
the optimization target and conditional
inequalities.

20
Variations of DEA Formulation

But first, it is necessary to identify several
sources of variation in the basic DEA
formulation, leading to a variety of different
models for implementation
We will now examine and illustrate each of those
sources of variation.

21
(1) Formulation Primal or Dual

The first source of variation is interpretation
of the display for the linear programming model.
One interpretation, called the Primal, treats the
rows of the display as representing the model.
The other interpretation, called the Dual, treats
the columns as representing the model.
Lets examine each of those in turn.

22
Primal Formulation

The rows of this display are interpreted as
follows
(M) Maximize W mYk nXk subject to
(1) mYj nXj lt 0, j 1 to n
(2) -m lt -1, or m gt 1
(3) -n lt -1, or n gt 1

23
The Dual Formulation

The Columns of this display are interpreted as
follows
(m) Minimize W -a - b subject to
(1) lYj a gt Yk
(2) lXj - b gt -Xk

24
The Choice of Formulation

Since the results from the two formulation are
equal, though expressed differently, the choice
between them is based on computational efficiency
or, perhaps, ease of interpretation.
The Dual form is more efficient in computation if
the number of DMUs is large compared to the
number of input and output variables. Note that
the Primal form entails n conditions (n being the
number of DMUs) which, in the Dual form, are
replaced by just m s conditions (m being the
number of input variables and s, the number of
output variables)

25
Illustration

To illustrate, consider the example previously
presented. The target to be minimized in the Dual
form is W a b. The values to be varied are
(l, a, b), or (m, n).
The following table shows the solution for both
forms

26
Illustration

Graphically, the results are as follows
The maximum value for W, over all cases, is at
L2, where W 0 and the ratio of Y/X is a
maximum. The slack for each other case is the
vertical distance to the line which goes from the
origin (0,0) through L2 (3,5).

27
(2) Orientation Input or Output

The second source of variation, orientation,
provides the means for focusing on minimizing
input or on maximizing output.
These represent two quite different objectives in
making assessments of efficiency. Is the
objective to be minimally expensive (e.g., to
save money) or is it to be maximally effective?

28
Orientation to Input

The linear programming display for the input
orientation is as follows
It adds one additional condition, nXk lt 1, to
the display.

29
Orientation to Input

The resulting Dual formulation is as follows
(m) Minimize W c-1 subject to
(1) lYj a gt Yk
(2) lXj b (c 1)Xk gt -Xk or lXk b lt
cXk

30
Orientation to Input

Continuing with the same example, the following
table shows the solutions in both formulations.
The target is W c 1. Values to be varied are
now (l, a, b, c) or (m and n).
Note that L2 still dominates the solution, but
the graph is now quite different,

31
Orientation to Input
32
Orientation to Output

The linear programming display for the output
orientation is as follows
It adds one additional condition, mYk lt 1, to
the display.

33
Orientation to Output

The resulting Dual formulation is as follows
(m) Minimize W 1 c subject to
(1) lYj a gt cYk
(2) lXj b gt Xk or lXk b lt Xk

34
Orientation to Output

Continuing with the same example, the following
table shows the solutions in both formulations.
The target is W 1 c. Values to be varied are
still (l, a, b, c) or (m and n).
Note that L2 still dominates the solution, but
the graph is now quite different,

35
Orientation to Output

Note that the graphical display is identical to
that for the general form, though the
interpretation is somewhat different (replacing
efficiencies by slacks).

36
(3) Returns to Scale Fixed or Variable

The third basis for variation among DEA models is
returns to scale.
The examples presented to this point have each
involved constant returns to scale. That is,
the ratio mY/nX can be replaced by the inequality
mY nX lt 0.
These variations of the DEA model are called CCR
models and reflect the requirement of constant
returns to scale,
But if there are variable returns to scale, the
ratio mY/nX must now be replaced by mY nX u
lt 0 where u can now vary to reflect the variable
returns to scale.
The results from that change are dramatic and
make the DEA model much more interesting. The
resulting models are called BCC models.

37
Variable Returns to Scale, Basic Model

The linear programming display for the basic DEA
model is as follows
It adds the variable u to the display.

38
Variable Returns Orientation to Input

The linear programming display for the variables
returns to scale, input orientation is as
follows
It adds one additional condition, nXk lt 1, to
the display.

39
Orientation to Input

The resulting Dual formulation is as follows
(m) Minimize W c-1 subject to
(1) lYj a gt Yk
(2) lXj b (c 1)Xk gt -Xk or lXk b lt
cXk
(3) l gt 1
The new, third condition makes things
interesting.

40
Orientation to Input

Continuing with the same example, the following
table shows the solutions in both formulations.
The target is W c 1. Values to be varied are
now (l, a, b, c) or (m, n, u).

41
Orientation to Input
42
Orientation to Output

The linear programming display for the output
orientation is as follows
It adds one additional condition, mYk lt 1, to
the display.

43
Orientation to Output

The resulting Dual formulation is as follows
(m) Minimize W 1 c subject to
(1) lYj a gt cYk
(2) lXj b gt Xk or lXk b lt Xk

44
Orientation to Output

Continuing with the same example, the following
table shows the solutions in both formulations.
The target is W 1 c. Values to be varied are
still (l, a, b, c) or (m and n).
Note that L2 still dominates the solution, but
the graph is now quite different,

45
Orientation to Output

Note that the graphical display is identical to
that for the general form, though the
interpretation is somewhat different (replacing
efficiencies by slacks).

46
Extensions to include a priori Valuations

To this point, DEA has been essentially a
mathematical process in which the data for input
and output are taken as given, without further
interpretation with respect to the reality of
operations.
But reality needs to be recognized, so there are
several extensions that can be made to the basic
DEA model, applicable to any of the variations.
They fall into seven categories
(1) Discretionary and Non-discretionary Variables
(2) Categorical Variables
(3)A priori restrictions on Weights
(4) Relationships between Weights on Variables
(5) A priori assessments of Efficient Units
(6) Substitutability of Variables
(7) Discrimination among Efficient Units

47
Discretionary Non-discretionary

In identifying input and output variables, one
wants to include all that are relevant to the
operation. For example, the level of output is
determined not only by what the unit itself does
but by the size of the market to which the output
is delivered.
The result, though, is that some relevant
variables, such as the size of the market, are
not under the control of management. Such
variables, called non-discretionary, are in
contrast to those that are under management
control, called discretionary.
In assessing efficiency, all variables are
considered, but in determining the criterion
function to be maximized or minimized, only the
discretionary variables are included.

48
Categorical Variables

In the DEA model as so far presented, the
variables are treated as essentially
quantitative, but sometimes one would like to
identify non-quantitative variables, such as
ordinal or nominal variables.
For example, one might like to compare
institutions of the same type, such as public or
private universities.
This is accomplished by introducing categorical
variables containing numbers for order or
identifiers for names.

49
A priori Restrictions on Weights

In the model as presented, the weights are
limited only by the requirements that they be
non-negative.
However, there may be reason to require that
weights be further limited.
For example, it may be felt that a given variable
must be included in the assessment so its weight
must have at least a minimal value greater than
zero. This might represent an output that is
essential in assessment.
As another example, a variable may be such a
large weight would over-emphasize its a priori
importance so that there should be an upper limit
on the weight. This might represent an output
variable that is counter-productive.

50
Relationships between Weights

Sometimes, a priori knowledge may imply that
there is a necessary relationship among
variables. For example, an output variable may
absolutely require some level of an input
variable.
Such a priori knowledge may be expressed as a
ratio between the weights assigned to the related
variables.

51
A priori assessments of Efficient Units

Some DMUs may be regarded, based on a priori
knowledge, as eminently efficient or notoriously
inefficient. While one might argue about the
validity of such a priori judgments, frequently
they must be recognized.
To do so, additional conditions may be imposed
upon the choice of weights. For example, the
condition mYj/nXj lt 1 may be replaced by
equality for a given DMU which is regarded as
eminently efficient.

52
Substitutability of Variables

A still unresolved issue is the means for
representing substitutability of variables. For
example, two input variables may represent two
different type of labor which may be, to some
extent, substitutable for each other.
How is such substitutability to be incorporated?
Lets explore this issue a bit further since, by
doing so, we can illuminate some additional
perspectives on the basic DEA model.

53
Substitutability of Variables

For simplicity in description, consider two input
variables and a single output variable that has
the same value for all DMUs. The graphic
representation of the envelopment surface can now
best be presented not in terms of the
relationship between output and input, as
previously shown, but between the variables of
input.
The two variables are Professional Staff and
Non-Professional Staff. The assumption is that
they are completely substitutable and that
physicians differ only in their styles of
providing service, represented by the mix of the
two means for doing so.
The efficient DMUs are located on the red
envelopment surface, which shows the minimums in
use of variables.

54
Substitutability of Variables
55
Discrimination among Efficient Units
56
Strengths Weaknesses of DEA

Strengths
DEA can handle multiple inputs and multiple
outputs
DEA doesn't require relating inputs to outputs.
Comparisons are directly against peers
Inputs and outputs can have very different units
Weaknesses
Measurement error can cause significant problems
DEA does not measure"absolute" efficiency
Statistical tests are not applicable
Large problems can be computationally intensive

57
Implementation of DEA

Structure
Spreadsheet implementation
Choice of Model
Spreadsheet Structure
Spreadsheet Calculations
Solver Elements in Spreadsheet
Visual Basic Program
Access to the Implementation
The data included in the spreadsheet is for ARL
libraries in 1996.

58
Choice of Model

The spreadsheet includes means to identify the
choice of model by means of three parameters
Form Dual represented by 0 and Primal by 1
Orientation Addition by 0, Input by 1, Output by
2
Convexity No by 0, Yes by 1
Given the specification, solution of the
resulting model is initiated by pressing Ctrl-q.
The solution is effected by a Visual Basic
program that determines the model from the
parameters and then launches the Excel Add-In
called Solver.
The program then produces the output on Sheet 3
that shows the results.

59
Spreadsheet Structure

The DEA Spreadsheet for application to ARL
libraries consists of three main parts
(1) The source data, stored in cells B16R117
(2) The spreadsheet calculations, stored in cells
D5R15
(3) The Solver related calculations, stored in
cells B1B15, A7A117, T12T117
The source data consists of the 10 input and 5
output variables for each of the ARL institutions
plus, in row B16R16, a set of normalizing
factors, one for each of the variables.

60
Spreadsheet Calculations

The Spreadsheet calculations in D5R14 can be
illustrated by D5D14 and N5N14

61
Spreadsheet Calculations

The Spreadsheet calculations in D5R14 can be
illustrated by D5D14 and N5N14

62
Solver Elements in Spreadsheet
63
Visual Basic Program
64
Visual Basic Program
65
Visual Basic Program
66
Visual Basic Program
67
The Example of Libraries

Selection of Data
Input Variables (10)
Collection Characteristics (Discretionary)
Staff Characteristics (Discretionary)
University Characteristics (Non-discretionary)
Output Variables (5)
Scaling of Data
Constraints on Weights
Results
Effects of the several Variables

68
Selection of Data
69
The Variables
70
Scaling of the Variables
71
Constraints on Weights
72
Results
73
Efficiency Distribution

The following chart display the efficiency
distribution for the 97 U.S. ARL libraries.
The input and output components for each
institution have been multiplied by the size of
the collection.
Note the cluster of inefficient institutions
below the 3,000,000 volumes of holdings.
There appear to be three groups of institutions
The efficient ones, lying on the red line
The seven that are more then 4 million and mildly
inefficient
Those that are less than 4 million and range in
efficiency

74
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75
Sum of Projections

The following chart show the distribution of the
sum of the projections as a function of the
Intensity.

76
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77
Distribution of Weights

The following chart shows the magnitudes of the
weights on each of the Input and Output components

78
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79
Annals of Operations Research 66 (1996)

Preface

80
Part I DEA models, methods and interrelations

Chapter 1. Introduction Extensions and new
developments in DEA
W W Cooper, R.G. Thompson and R.M. Thrall
Chapter 2. A generalized data envelopment
analysis model A unification and extension of
existing methods for efficiency analysis of
decision making units
G.Yu, Q. Wet and P Binckett

81
Extensions in DEA

Covers (1) new measures of efficiency, (2) new
models, and (3) new implementations.
The TDT measure of relative efficiency takes
the criterion measure (weighted output/weighted
input) relative to the maximum for that measure
The Pareto-Koopman measure applies the Pareto
criterion (no variables can be improved without
worsening others)
The BCC model (variable returns to scale) is
presented.
Congestion arises when excess inputs interfere
with outputs. It thus represents relationships
among variables.

82
Generalized DEA model

Essentially, this paper does what I have been
trying to do in implementation of DEA.
It does so by identifying the primal and dual (P
and D), the two returns to scale (fixed and
variable), and three binary parameters (d1, d2,
d3) in the equations
d1 d1eT d1d2(-1)d3?n1 (for the dual)
d1d2(-1)d3l0 (for the primal)
Values of (d1, d2, d3) include
(0,-,-) the CCR model
(1,0,-) the BCC model
(1,1,0) the FG model
(1,1,1) the ST model
The relationships among the several models are
discussed.

83
Part II Desirable properties of models, measures
and solutions (1)

Chapter 3. Translation invariance in data
envelopment analysis A generalization
J.T Pastor
Chapter 4. The lack of invariance of optimal dual
solutions under translation
R.M. Thrall
Chapter 5. Duality, classification and slacks in
DEA
R.M. Thrall

84
Translation invariance

This paper proves that several of the DEA model
are translation invariant (i.e., optimal
solutions are not changed if the original
variable values are translated, that is all
values for a variable are replaced by some
constant minus the values).
Specifically, the primal additive model is
translation invariant.
The BCC input oriented primal model is output
translation invariant.
The CCR models are not translation invariant.

85
Lack of invariance

This paper supplements the prior one. It shows
that in neither the BCC model nor the additive
model are the optimal solutions for the dual
(i.e., multipler) formulation invariant under
translation.

86
Duality, classification and slack

This paper considers the role of slacks
especially in the context of radial measures of
efficiency. The effect of alternative optima is
to make slacks difficult to deal with the theory
presented resolves the difficulties.
The CCT model presented eliminates the need for
non-Archimedean models and permits dealing with
zero values for the variables.
The concept of an admissible virtual multiplier
is introduced and the maximizing virtual
multiplier w is the basis for categorizing
efficient DMUs into 3 groups
Extreme Efficient all variables are included in
w
Efficient the variables in w are all positive
Weak efficient w has at least one zero variable
Similarly for non-efficient DMUs

87
Part II Desirable properties of models, measures
and solutions (2)

Chapter 6. On the construction of strong
complementarity slackness solutions for DEA
linear programming problems using a primal-dual
interior-point method
M.D. Gonzdlez-Ltma, R.A. Tapta and R.M. Thralt
Chapter 7. DEA multiplier analytic center
sensitivity with an illustrative application to
independent oil companies
R.C. Thompson, PS. Ditarmapala, f Diaz, M.D.
Gonzdlez-Lima and R.M. Thrall

88
Complementarity Slackness Solutions

This paper proposes use of primary-dual
interior-point methods for solution of the DEA
linear programming problem (an iterative process
that generates interior point that converge to
the solution).
The primary form minimizes Cx the dual form
maximizes By.
The condition for solution is that Cx By,
called the complementarity slackness condition.
These methods attempt to solve the primary and
dual linear programs simultaneously.
Solutions are classified as radially efficient or
inefficient using the CCT model.

89
Multiplier Sensitivity

The stability of the set E of extreme efficient
DMUs is examined to determine the sensitivity to
changes in the data,

90
Part III Frontier shifts and efficiency
evaluations

Chapter 8. Estimating production frontier shifts
An application of DEA to technology assessment
R.D. Banker and R.C. Morey
Chapter 9. Moving frontier analysis An
application of data envelopment analysis for
competitive analysis of a high-technology
manufacturing plant
K.K. Sinha
Chapter 10. Profitability and productivity
changes An application to Swedish pharmacies
R. Aithin, R. Fare and S. Grosskopf 219

91
Production Frontier Shifts

This paper divides the set of DMUs into two
categories (representing the use or non-use of a
technology). For a DMU without the technology,
comparison is made only with others without the
technology for those with the technology,
comparison is made with all DMUs.
The result is a basis for assessment of the
impact of the technology.

92
Moving Frontier Analysis

This paper proposes a method for assessing when
some data may not be available. It uses aggregate
data on best practices. It depends upon time
series data

93
Profitability productivity changes

It is not evident how this relates to DEA.

94
Part IV Statistical and stochastic
characterizations

Chapter 11. Simulation studies of efficiency,
returns to scale and misspecification with
nonlinear functions in DEA
RD. Banker H. Chang and WW Cooper
Chapter 12. New uses of DEA and statistical
regressions for efficiency evaluation and
estimation - with an illustrative application to
public secondary schools in Texas
VL Arnold, LR. Bardhan, WW Cooper and S.C.
Kumbhakar
Chapter 13. Satisficing DEA models under chance
constraints
W W Cooper Z Huang and S.X. Li

95
Simulation studies

Well, so be it.

96
DEA and statistical regressions

Compares the two methods. It uses a Cobb-Douglas
production model (in log form) and estimates the
parameters by a regression on the set of DMUs.
(Actually, it does a set of regressions, one for
each output variable against the uniform set of
input variables.)
It then applies DEA to the same set of input
variables (separately for each output variable in
turn).
It then considers the joint outputs, taken
together.

97
Satisficing DEA models

Introduces stochastic variables (characterized by
probability distributions) and the concept of
stochastic efficiency.
It distinguishes between a rule (which has a
probability of 1) and a policy (which has a
probability between 0.5 and 1).

98
Part V Some new applications

Chapter 14. Evaluating the efficiency of vehicle
manufacturing with different products
G. Zeng
Chapter 15. DEA/AR analysis of the 1988-1989
performance of the Nanjing Textiles Corporation
J. Zhu 311

99
China vehicle manufacturing

Evaluates the efficiency of vehicle manufacturing
in China.
It deals with the problem of zero values for some
variables.

100
DEA/AR analysis

Another application in China.

101
Annals of Operations Research 73 (1997)

Contents
Preface
Foreword

102
Part VI Extending Frontiers

Extending the frontiers of Data Envelopment
Analysis
A.Y Lewin and LM. Seijord
Weights restrictions and value judgements in Data
Envelopment Analysis Evolution, development and
future directions
R.Allen, A. Athanassopoulos, R.O. Dyson and F.
Thanassoulis

103
Extending the frontiers

See earlier in this presentation

104
Weights restrictions value judgments

See earlier in this presentation.

105
Part VII Applications

DEA and primary care physician report cards
Deriving preferred practice cones from managed
care service concepts and operating strategies
IA. Chilingerian and H.D. Sherman
An analysis of staffing efficiency in U.S.
manufacturing 1983 and 1989
PT Ward, J.E. Storbeck, S.L. Mangum and RE Byrnes
Applications of DEA to measure the efficiency of
software production at two large Canadian banks
J.C. Paradi, D.N. Reese and D. Rosen

106
Primary care physician

This papers identifies styles of management
based on ratios of input variables aimed at input
cost minimizing.
The example used is comparison of hospital days
versus office visits

107
Staffing efficiency

Again, styles of management are identified, this
time based on ratios of types of staffing (e.g.,
professional vs. non-professional). Industries
are divided into types (batch vs. line processing
industries) and best practices for each type
are identified by DEA.

108
software production

Input to software production is taken as cost
outputs as size (measure by function points),
quality (measured by defects or rework hours),
and time to market.
The DEA is compared to performance ratio
analyses, such as Cost/Function,
Defects/Function, Days/Function.
Then, constraints on the weights are introduced.
One set of constraints consisted of bounds on
ratios of weights. A second set of constraints
consisted of tradeoffs between variables, again
represented by bounds on ratios.

109
Part VII Applications

Restricted best practice selection in DEA An
overview with a case study evaluating the
socio-economic performance of nations
B.Golany and S. Thore
A new measure of baseball batters using DEA
T.R. Anderson and G.P Sharp
Efficiency of families managing home health care
CE. Smith, S. VM. Kiembeck, K. Fernengel and L.S.
Mayer

110
Economic performance of nations

To apply DEA to evaluation of economic
performance of nations, it is necessary to
recognize some constraints
International requirements (treaties, bilateral
agreements)
Externalities (e.g., mandated quotas)
Issues of equity
These constraints are then incorporated into DEA

111
Baseball batters

Traditional methods for evaluating batters
include fixed and variable weight statistics
(homers, batting average, slugging average, RBI,
etc.). The point in this article is that use of
DEA allows one to determine the effect of changes
over time.
Another effect of interest is noise. To correct
for noise, the DEA model derates the data for
each player by a factor based on the players
standard deviation for each variable

112
Efficiency of families

Family home health care is assessed using a
stepped procedure in DEA.
The stepped procedure involves a series of steps
in which variables are successively introduced

113
Part VII Applications

A DEA-based analysis of productivity change and
intertemporal managerial performance
E.Grifell-Tatje and C.A.K. LoveII
Use of Data Envelopment Analysis in assessing
Information Technology impact on firm performance
C.H. Wang, R.D. Gopal and S. Zionts

114
Productivity managerial performance

Examines the productivity of an organization over
time.

115
Information Technology impact

Examines the impact of information technology on
performance of firms. It divides operations into
two stages (1) Accumulation of resources and (2)
Use of resources. (These are illustrated in
banking by (1) the collection of funds from
depositors and (2) use of those funds for
generating income).
It examines separately the effect of information
technology (represented by ATM machines) on the
two stages.

116
Part VIII Theoretical Extensions

Comparative advantage and disadvantage in DEA
A.I. Alt and CS. LeTine
Model misspecification in Data Envelopment
Analysis
P Smith
Dominant Competitive Factors for evaluating
program efficiency in grouped data
J.J.Rousseau and J.H. Semple
DEA-based yardstick competition. The optimality
of best practice regulation
P Bogetoft

117
Comparative advantage disadvantage

This paper introduces a cost function into DEA
analysis as the means for calculating a
comparative advantage or disadvantage as the
difference between the costs of input and the
income from output.
It interprets the weights in each DMUs optimum as
prices for the respective inputs and outputs. The
result is virtual cost, revenue, and profit.
The profit (or loss) is then compared with the
maximum profit obtained by a best practice unit
and that of the evaluated unit.
For an efficient unit, the comparison is between
the virtual profit of the valuated unit and the
maximum profit across all other units.

118
Comparative disadvantage

The DEA model for determining comparative
disadvantage is
Max R C w subject to Min h - w
- uY1 R -1 - w Y1 Yk T0r 0
vX1 C 1 hX1 Xk T1r1 0
uY vX Iw lt 0 Ik 1
uT0 lt 0, vT1 lt 0 h lt 1, w gt 1
R, C gt 0 k gt 0

119
Comparative advantage

The DEA model for determining comparative
advantage is applied to the set removing the
target unit
Max R C w subject to Min h - w
- uY1 R 1 - w Y1 Y1k T0r 0
vX1 C 1 hX1 X1k T1r1 0
uY1 vX1 Iw lt 0 Ik 1
uT0 lt 0, vT1 lt 0 h gt 1, w lt 1
R, C gt 0 k gt 0

120
Model mis-specification

This paper examines the effects of various types
of mis-specifications of the DEA model. They
include
Omission of a necessary input
Inclusion of an extraneous variable
Erroneous assumption about returns to scale

121
Dominant Competitive Factors

This paper treats DEA as a tool in game theory.
One player has control over the weights applied
to the variables, the other over the weights
applied to the DMUs. Each tries to optimize
against the other.
The solution is of the pair of prime-dual
problems
Player 1 Maximizes vy0 ux0 subject to vyj
uxj lt 0 and vy0 ux0 1, u, v gt0
Player 2 Minimizes a subject to Yk ay0 gt y0,
Xk ax0 lt x0, k gt 0, a unrestricted

122
Best practice regulation

The use of DEA in regulatory practice is
discussed. The underlying game is represented by
a series of steps
Costs and demands for service are observed or
identified
Schemes are proposed by the regulator
The schemes are rejected or accepted by the DMUs
Costs are selected by the DMUs
Data on performance are observed
Compensations are paid
The aim of the regulator is to minimize the
expected costs of making the DMUs accept, fulfil,
and minimize costs.
The use of DEA is to determine the best practce
norms.

123
Part VIII Theoretical Extensions

A Data Envelopment Analysis approach to
Discriminant Analysis
D.L. Retzlaff-Roberts
Derivation of the Maximum Efficiency Ratio mode
from the maximum decisional efficiency principle
M.D. Trouft

124
Discriminant Analysis

Discriminant analysis is a means for determining
group classification for a set of similar units
or observations. It determines a set of factor
weights which best separate the groups, given
units for which membership is already known.
This paper proposes the use of DEA as a means for
doing DA

125
Maximum Efficiency Ratio

Maximum efficiency ratio (MER) is intended to
prioritize the DEA efficient DMUs by defining
common weights. This paper supposes the existence
of a ratio form criterion common to all the DMUs
but not necessarily frontier oriented.
Maxu,v (Minj (?uryrj/ ?vixij), subject to ?uryrj/
?vixij lt 1 for all j, ?ur 1, u, v gt 0

126
Part IX Computational Implementation