Data Envelopment Analysis Pattern

Data Envelopment AnalysisRobert M. Hayes2005

OverviewIntroductionData Envelopment AnalysisDEA ModelsExtensions to include a priori ValuationsStrengths and Weaknesses of DEAImplementation of DEAThe Example of LibrariesAnnals of Operations Research 66Annals of Operations Research 73

IntroductionUtility FunctionsCost/EffectivenessInterpretation for Libraries

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.

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.

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.

Cost/EffectivenessMore 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.

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.

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".

Data Envelopment AnalysisData 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.

Data Envelopment AnalysisIf 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.

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).L1L2L3L4L5L6L7

Chart2

22

53

76

89

53

41

107

Input

Output

Sheet1

L122

L235

L367

L498

L553

L641

L7107

Sheet1

00

00

00

00

00

00

00

Input

Output

Sheet2

Sheet3

Graphical IllustrationDEA 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).

Graphical IllustrationThus, 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.

Graphical IllustrationThis 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.

DEA ModelsThe Basic EDA ConceptVariations of DEA FormulationFormulation: Primal or DualOrientation: Input or OutputReturns to Scale: Fixed or Variable

The Basic EDA ConceptAssume 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 inputsBut 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 1Do 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.

FormulationLet (Yk,Xk) = (Yki,Xkj), k = 1 to n, i = 1 to s, j = 1 to mMaximize mYk/nXk for each value of k from 1 to n, subject in each case to mYj/nXj = 0The solution is the set of maximum values for mYk/nXk and the associated values for m and n

Basic Linear Programming ModelFor 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.

Min

Yj

-Xj

Variations of DEA FormulationBut 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.

(1) Formulation

Primal Form

Dual Form

(2) Orientation

Input Minimization

Output Maximization

(3) Returns to Scale

Fixed Returns

Variable Returns

(4) Discretionary?

Discretionary Variables

Non-discretionary Variables

(5) Models

Additive

Multiplicative

(1) Formulation: Primal or DualThe 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.

Primal Formulation

The rows of this display are interpreted as follows:(M) Maximize W = mYk nXk subject to(1) mYj nXj

The Dual Formulation

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

(m)

Yj

-Xj

0

a

-I

-I

b

-I

-I

>=

>=

Yk

- Xk

The Choice of FormulationSince 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)

IllustrationTo 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:

X

Y

W

a

b

L1

2

2

- 1.33

1.33

= 0.67

1

1.67

L2

3

5

0.00

0.00

1

1.67

L3

6

7

- 3.00

3.00

1

1.67

L4

9

8

- 7.00

7.00

1

1.67

L5

5

3

- 5.33

5.33

1

1.67

L6

4

1

- 5.67

5.67

1

1.67

L7

10

7

- 9.67

9.67

1

1.67

IllustrationGraphically, 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).

Chart4

2222222

5333333

6676666

9998999

55552.855

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1010101010107

20121212121212

0000000

23.333333333322222

66106666

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55558.333333333355

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Sheet1

L122

L235

L367

L498

L552.8

L641

L7107

1220

00

23.3333333333

610

915

58.3333333333

46.6666666667

1016.6666666667

Sheet1

2222222

5333333

6676666

9998999

5555355

4444414

1010101010107

20121212121212

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23.333333333322222

66106666

99915999

55558.333333333355

444446.66666666674

10101010101016.6666666667

Sheet2

mn

lY-X

(2) Orientation: Input or OutputThe 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?

Orientation to Input

The linear programming display for the input orientation is as follows:

It adds one additional condition, nXk


The resulting Dual formulation is as follows:(m) Minimize W = c-1 subject to(1) lYj a >= Yk(2) lXj b + (c 1)Xk >= -Xk or lXk + b =

>=

Max

Yk

- Xk

Orientation to InputContinuing 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,

X

Y

W=c-1

a

b

L1

2

2

- 0.40

= 0.40

0.30

0.50

L2

3

5

0.00

0.20

0.33

L3

6

7

- 0.30

0.10

0.17

L4

9

8

- 0.46

0.07

0.11

L5

5

3

- 0.64

0.12

0.20

L6

4

1

- 0.85

0.15

0.25

L7

10

7

- 0.58

0.06

0.10


Chart5

2222222

5333333

6676666

9998999

5555355

4444414

1010101010107

10666666

1.221.21.21.21.21.2

4.24.274.24.24.24.2

4.84.84.884.84.84.8

1.81.81.81.831.81.8

0.60.60.60.60.610.6

4.24.24.24.24.24.27

Sheet1

L122

L235

L367

L498

L553

L641

L7107

610

1.22

4.27

4.88

1.83

0.61

4.27

Sheet1

Sheet2

mn

lY-X

Orientation to Output

The linear programming display for the output orientation is as follows:

It adds one additional condition, mYk


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

>=

Max

Yk

- Xk

Orientation to OutputContinuing 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).


X

Y

W=1-c

a

b

L1

2

2

- 0.67

= 0.67

0.50

0.83

L2

3

5

0.00

0.20

0.33

L3

6

7

- 0.43

0.14

0.24

L4

9

8

- 0.87

0.13

0.21

L5

5

3

- 1.78

0.33

0.56

L6

4

1

- 5.67

1.00

1.67

L7

10

7

- 1.38

0.14

0.24

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

Chart4

2222222

5333333

6676666

9998999

55552.855

4444414

1010101010107

20121212121212

0000000

23.333333333322222

66106666

99915999

55558.333333333355

444446.66666666674

10101010101016.6666666667

Sheet1

L122

L235

L367

L498

L552.8

L641

L7107

1220

00

23.3333333333

610

915

58.3333333333

46.6666666667

1016.6666666667

Sheet1

2222222

5333333

6676666

9998999

5555355

4444414

1010101010107

20121212121212

0000000

23.333333333322222

66106666

99915999

55558.333333333355

444446.66666666674

10101010101016.6666666667

Sheet2

mn

lY-X

(3) Returns to Scale: Fixed or VariableThe 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

Variable Returns to Scale, Basic ModelThe linear programming display for the basic DEA model is as follows:

It adds the variable u to the display.

u

Min

Yj

-Xj

I

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


The resulting Dual formulation is as follows:(m) Minimize W = c-1 subject to(1) lYj a >= Yk(2) lXj b + (c 1)Xk >= -Xk or lXk + b = 1

The new, third condition makes things interesting.

u

(m)

Yj

-Xj

I

0

a

-I

0

b

-I

0

c - 1

Xk

I

>=

>=

Max

Yk

- Xk

I

Orientation to InputContinuing 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).

X

Y

W=c-1

a

b

u

L1

2

2

0.00

0.00

=1.00

0.00

0.00

0.00

L2

3

5

0.00

0.00

1.00

0.00

0.00

0.00

L3

6

7

0.00

0.00

1.00

0.00

0.00

0.00

L4

9

8

0.00

0.00

1.00

0.00

0.00

0.00

L5

5

3

- 4.00

2.00

1.00

0.00

0.00

0.00

L6

4

1

- 5.00

4.00

1.00

0.00

0.00

0.00

L7

10

7

- 4.00

0.00

1.00

0.00

0.00

0.00


Chart5

2222222

5333333

6676666

9998999

5555355

4444414

1010101010107

10666666

1.221.21.21.21.21.2

4.24.274.24.24.24.2

4.84.84.884.84.84.8

1.81.81.81.831.81.8

0.60.60.60.60.610.6

4.24.24.24.24.24.27

Sheet1

L122

L235

L367

L498

L553

L641

L7107

610

1.22

4.27

4.88

1.83

0.61

4.27

Sheet1

Sheet2

mn

lY-X


The linear programming display for the output orientation is as follows:

It adds one additional condition, mYk


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

>=

Max

Yk

- Xk

Orientation to OutputContinuing 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).


X

Y

W=1-c

a

b

L1

2

2

- 0.67

= 0.67

0.50

0.83

L2

3

5

0.00

0.20

0.33

L3

6

7

- 0.43

0.14

0.24

L4

9

8

- 0.87

0.13

0.21

L5

5

3

- 1.78

0.33

0.56

L6

4

1

- 5.67

1.00

1.67

L7

10

7

- 1.38

0.14

0.24

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

Chart4

2222222

5333333

6676666

9998999

55552.855

4444414

1010101010107

20121212121212

0000000

23.333333333322222

66106666

99915999

55558.333333333355

444446.66666666674

10101010101016.6666666667

Sheet1

L122

L235

L367

L498

L552.8

L641

L7107

1220

00

23.3333333333

610

915

58.3333333333

46.6666666667

1016.6666666667

Sheet1

2222222

5333333

6676666

9998999

5555355

4444414

1010101010107

20121212121212

0000000

23.333333333322222

66106666

99915999

55558.333333333355

444446.66666666674

10101010101016.6666666667

Sheet2

mn

lY-X

Extensions to include a priori ValuationsTo 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

Discretionary & Non-discretionaryIn 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.

Categorical VariablesIn 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.

A priori Restrictions on WeightsIn 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.

Relationships between WeightsSometimes, 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.

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

Substitutability of VariablesA 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.

Substitutability of VariablesFor 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.

Substitutability of Variables

Chart2

000000

711111

41.21.21.21.21.2

61.51.51.51.51.5

6.11.61.61.61.61.6

21.71.71.71.71.7

4.81.81.81.81.81.8

4.52.12.12.12.12.1

4.52.52.52.52.52.5

8.52.22.22.22.22.2

63.13.13.13.13.1

23.23.23.23.23.2

33.93.93.93.93.9

13.93.93.93.93.9

24.14.14.14.14.1

74.14.14.14.14.1

64.24.24.24.24.2

14.94.94.94.94.9

171111

1.241.21.21.21.2

1.721.71.71.71.7

3.913.93.93.93.9

000000

117111

1.291.2991.291.291.29

000000

1.21.21.241.21.2

2.72.72.792.72.7

000000

1.71.71.71.721.7

7.657.657.657.6597.65

000000

3.93.93.93.93.91

35.135.135.135.135.19

Style 1

Style 4

Style 2

Style 3

Professional Staff

Non-Professional Staff

Sheet1

00

17

1.24

1.56

1.66.1

1.72

1.84.8

2.14.5

2.54.5

2.28.5

3.16

3.22

3.93

3.91

4.12

4.17

4.26

4.91

17

1.24

1.72

3.91

00

17

1.299

00

1.24

2.79

00

1.72

7.659

00

3.91

35.19

Sheet1

000000

000000

000000

000000

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Style 1

Style 4

Style 2

Style 3

Surgery Days

Primary Care Visits

Sheet2

Sheet3

Discrimination among Efficient Units

Strengths & Weaknesses of DEAStrengthsDEA can handle multiple inputs and multiple outputsDEA doesn't require relating inputs to outputs.Comparisons are directly against peersInputs and outputs can have very different unitsWeaknessesMeasurement error can cause significant problemsDEA does not measure"absolute" efficiencyStatistical tests are not applicableLarge problems can be computationally intensive

Implementation of DEAStructureSpreadsheet implementationChoice of ModelSpreadsheet StructureSpreadsheet CalculationsSolver Elements in SpreadsheetVisual Basic ProgramAccess to the ImplementationThe data included in the spreadsheet is for ARL libraries in 1996.

Choice of ModelThe spreadsheet includes means to identify the choice of model by means of three parameters:Form: Dual represented by 0 and Primal by 1Orientation: Addition by 0, Input by 1, Output by 2Convexity: No by 0, Yes by 1Given 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.

Spreadsheet StructureThe DEA Spreadsheet for application to ARL libraries consists of three main parts:(1) The source data, stored in cells B16:R117(2) The spreadsheet calculations, stored in cells D5:R15(3) The Solver related calculations, stored in cells B1:B15, A7:A117, T12:T117The source data consists of the 10 input and 5 output variables for each of the ARL institutions plus, in row B16:R16, a set of normalizing factors, one for each of the variables.

Spreadsheet CalculationsThe Spreadsheet calculations in D5:R14 can be illustrated by D5:D14 and N5:N14:

C

D

5

Discretionary?

1

6

Weights

0.000001

7

8

9

Comp

=SUMPRODUCT(Mult,D17:D113)*D16

10

Slacks

15.2073410229378

11

Mod Comp

=D9+D10

12

=INDEX(C17:C126,MATCH($B$12,$B$17:$B$126,0),1)

=INDEX(Data,MATCH($B$12,$B$17:$B$126,0),COLUMN()-3)*D16

13

=D12*$B$13

14

=IF($B$2=1,D13,D12)

Spreadsheet CalculationsThe Spreadsheet calculations in D5:R14 can be illustrated by D5:D14 and N5:N14:

C

N

5

Discretionary?

1

6

Weights

9.99999999999265E-07

7

8

9

Comp

=SUMPRODUCT(Mult,N17:N113)*N16

10

Slacks

5.56269731722995

11

Mod Comp

=N9-N10

12

=INDEX(C17:C126,MATCH($B$12,$B$17:$B$126,0),1)

=INDEX(Data,MATCH($B$12,$B$17:$B$126,0),COLUMN()-3)*N16

13

=N12*$B$13

14

=IF($B$2=2,N13,N12)

Solver Elements in Spreadsheet

Sheet1

#B1B2B3TargetVaryConditions

0000B7Min$D$10:$R$10,$A$17:$A$113$D$11:$R$11=$D$14:$R$14$A$17:$A$113>=0

1001B7Min$D$10:$R$10,$A$17:$A$113$D$11:$R$11=$D$14:$R$14$A$17:$A$113>=0$B$127=1

2010B8Min$D$10:$R$10,$A$17:$A$113,$B$13$D$11:$R$11=$D$14:$R$14$A$17:$A$113>=0

3011B8Min$D$10:$R$10,$A$17:$A$113,$B$13$D$11:$R$11=$D$14:$R$14$A$17:$A$113>=0$B$127=1

4020B9Min$D$10:$R$10,$A$17:$A$113,$B$13$D$11:$R$11=$D$14:$R$14$A$17:$A$113>=0

5021B9Min$D$10:$R$10,$A$17:$A$113,$B$13$D$11:$R$11=$D$14:$R$14$A$17:$A$113>=0$B$127=1

6100B6Max$D$6:$R$6$T$17:$T$113

Visual Basic Program

Application.Range("B3").Select

Convex = Selection.Value

A = 6 * Form + 2 * Orient + Convex

SolverReset

'Set Target, MaxMinVal, Change

If A = 0 Or A = 1 Then 'Dual, Addition

SolverOk SetCell:="B7", MaxMinVal:=2, ValueOf:="0", _

ByChange:= "$D$10:$R$10,$A$17:$A$113"

End If

If A = 2 Or A = 3 Then 'Dual, Input


ByChange:= "$D$10:$R$10,$A$17:$A$113,$B$13"

End If

If A = 4 Or A = 5 Then 'Dual, Output


ByChange:= "$D$10:$R$10,$A$17:$A$113,$B$13"

End If

If A = 6 Or A = 8 Or A = 10 Then 'Primal, Not Convex (Constant Returns to Scale)


ByChange:= "$D$6:$R$6"

End If

If A = 7 Or A = 9 Or A = 11 Then 'Primal, Convex (Variable Returns to Scale


ByChange:= "$D$6:$R$6,$S$6"

End If


'Set Conditions

If A = 0 Or A = 1 Or A = 2 Or A = 3 Or A = 4 Or A = 5 Then 'Dual

SolverAdd CellRef:="$D$11:$R$11", Relation:=2, FormulaText:="$D$14:$R$14"

SolverAdd CellRef:="$A$17:$A$113", Relation:=3, FormulaText:="0"

SolverAdd CellRef:="$D$10:$R$10", Relation:=3, FormulaText:="0"

End If

If A = 1 Or A = 3 Or A = 5 Then 'Dual, Convex (Variable Returns to Scale)

SolverAdd CellRef:="$A$127", Relation:=2, FormulaText:="1"

End If

If A = 6 Or A = 7 Or A = 8 Or A = 9 Or A = 10 Or A = 11 Then

SolverAdd CellRef:="$T$12", Relation:=2, FormulaText:="1"

SolverAdd CellRef:="$T$17:$T$113", Relation:=1, FormulaText:="0"

End If

If A = 8 Or A = 9 Or A = 10 Or A = 11 Then 'Primal, Input or Output

SolverAdd CellRef:="$D$6:$R$6", Relation:=3, FormulaText:="$B$15"

End If

If A = 6 Or A = 7 Then 'Primal, Addition

SolverAdd CellRef:="$D$6:$R$6", Relation:=3, FormulaText:="1"

End If

SolverOptions MaxTime:=1000, Iterations:=1000, Precision:=0.000001, _

AssumeLinear:=True, StepThru:=False, Estimates:=1, Derivatives:=1, _

SearchOption:=1, IntTolerance:=5, Scaling:=False, Convergence:=0.0001, _

AssumeNonNeg:=False


For m = 1 To 97

Application.StatusBar = "Calculating Efficiency for unit " & Str(m)

' Paste unit 0's number to model worksheet

Sheets("Sheet1").Select

Application.Goto Reference:="unit"

Selection.Value = m

' Run Solver (with the dialog box turned off)

SolverSolve (True)

' Paste unit's number and name to All Results sheet


Application.Range("C12").Select

Selection.Copy


Range("A2").Offset(m, 0).Select

Selection.PasteSpecial Paste:=xlValues



Application.Goto Reference:="Target1"

Selection.Copy



Selection.Value = m




Application.Goto Reference:="Results"

Selection.Copy



Selection.Value = m



Next m

Application.Goto Reference:="Start"

End Sub

The Example of LibrariesSelection of DataInput Variables (10):Collection Characteristics (Discretionary)Staff Characteristics (Discretionary)University Characteristics (Non-discretionary)Output Variables (5):Scaling of DataConstraints on WeightsResultsEffects of the several Variables

Selection of Data

The Variables

Scaling of the Variables

Constraints on Weights

Results

Efficiency DistributionThe 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 lineThe seven that are more then 4 million and mildly inefficientThose that are less than 4 million and range in efficiency

Chart2

13.617133000113.6171329999

8.6280288.628028

7.49527499997.495275

7.0102347.0102339999

6.86515800016.8651579999

6.1133466.1133459999

5.9169925.916992

5.71520200015.7152019999

5.51614100015.5161409998

5.49066800015.4906679999

5.08733599995.087336

4.8191864.819186

4.5466674.546667

4.4429614.442961

4.4336284.433628

3.93434400013.9343439999

3.81910000023.8190999999

3.532813.53281

3.3177813.317781

3.22474099993.224741

3.0022613.002261

2.9982282.9982279999

2.9621572.962157

2.7157022.715702

2.6081182.6081179999

2.4939272.4939269999

2.46466600012.464666

2.4629662.4629659999

2.4475982.4475979999

2.3690652.3690649998

2.3460142.346014

2.34135900012.3413589999

2.32730700012.3273069999

2.2232942.223294

2.2160182.2160179999

2.1757062.175706

2.1249642.1249640001

2.1105942.110594

2.0308242.030824

2.0057652.0057649999

1.9654781.965478

1.9648411.9648409998

1.9631571.963157

1.9556151.955615

1.85093199991.8509319999

1.7081091.708109

3.19034614683.2782613105

2.66094472442.7643039399

2.25428250932.3700508243

2.16733770482.2878834069

6.73842366257.2160776337

2.50162388062.7232193768

4.40916183114.8935580796

5.61787913096.660417389

9.076653862610.8681254814

5.32055478366.3764815625

1.76909126682.1640826157

2.90269951483.7025743269

7.787672155310.4572910579

2.51702891333.4172914644

2.59839354613.5750041493

1.67054555752.3325107414

3.23726696274.6815687753

2.02176700952.9514430349

1.64899704352.4082710928

1.83152010112.7529123286

5.60777418418.5038081234

2.01228346893.1844803128

1.61834245172.7719198266

1.96936331563.3895957381

2.76407649884.7771631159

2.90172065765.0358737516

1.66512348243.0173952575

1.98679428463.6125990167

2.17278412294.0030931871

1.92038223973.5930754291

1.35927894442.5728258356

2.46694250764.7355103643

2.09404715074.0879826994

1.71224445883.3545118256

1.35993371762.7229040124

1.51777236223.1088386077

1.67517115893.5601888449

1.40021026713.1084420283

1.87422659454.2619613189

1.25234951683.0080358306

1.79642258794.4530806319

1.47550492593.6903590193

2.59315784526.5395893985

1.76279099924.4999105805

1.83998654684.7310715452

1.54811873564.4293401795

1.18253235063.7863822312

1.16859907183.7648629258

1.70637654537.0089014584

1.72488504397.6388581822

0.96029576455.72805723

1414

11

Collection*Input

Collection*Output

Sheet1

Formulation00 if Dual, 1 if Primal

Orientation20 if Additive, 1 if Input, 2 if Output

Convexity?11 if Convexity, 0 if notVariable returns to scale if Convexity, constant returns to scale if not

200000300020001000583600150403000100010001500030000

InputsOutputs

Discretionary?111111100011111

Target-0.09VolsVolsAdNMonoCurrSerPrfStfNPrfStfStudAstTotStuGradStuFacILLILBPresPtcpRefTransTotCirc

Comp1969.622781.791778.993262.501974.922155.022995.653706.613477.914024.111283.502264.381210.931437.032426.30

Slacks91.3916.6416.8022.9010.348.505.913.170.006.9513.096.091.040.000.000.00

Mod Comp1986.262798.591801.903272.841983.432160.932998.823706.613484.854037.191277.422263.341210.931437.032426.30wVolsVolsAdNMonoCurrSerPrfStfNPrfStfStudAstTotStuGradStuFacILLILBPresPtcpRefTransTotCircU

Unit97YALE49.6657.9167.9753.3540.2038.8831.6717.9436.3444.806.0316.096.4320.7325.350.910.000.000.000.000.000.000.000.060.000.000.000.000.020.010.020.08

Intensity1.0954.3463.3774.3758.3743.9942.5434.6519.6339.7649.026.5917.607.0422.6827.731.00

Mod Unit49.6657.9167.9753.3540.2038.8831.6717.9436.3444.806.5917.607.0422.6827.73

Infinitesimal0.000001Excess, Slack1919.962723.881711.023209.161934.722116.152963.993688.673441.573979.311277.482248.301204.501416.302400.95

Mult000000000000000

1.002ARIZONA4442961998315226825171911758925804532714723074526634387471873711051028-0.85

1.004AUBURN2464666633452555118607518440186751858114521649843314648156465409845-1.08

1.006BRIGHAM YOUNG2462966512124126116003101541472842017231373254631662628308436317774016-1.28

1.008CALIFORNIA, BERKELEY8628028161902792831912511782700774681274546522485925975204664-1.95

1.0011CALIFORNIA, LOS ANGELES701023423738315501094364134279208336221115217528936119745186594791302057143-0.90

1.0012CALIFORNIA, RIVERSIDE1850932497192641412767449236835912924511177117898670050742367025-0.35

1.0015CASE WESTERN RESERVE19654782663813739129737275306653354319096629837826410488038231938-0.31

1.0017CINCINNATI232730759223291951955677107892017547321718745897181113524139064549878-1.14

1.0018COLORADO271570243459311482847355121642113522861217353891768612472245735971809-0.84

1.0019COLORADO STATE1708109520702930421455348160162722494100427272243585165232188500882-0.88

1.0022CORNELL61133461611296177312428815318806532714662400514335166811929091160580-0.45

1.0023DARTMOUTH22232944417825036200155010628509712023171313514523333202-0.22

1.0026EMORY2369065570802402190162479706388970135176188947114111515345919-0.44

1.0027FLORIDA33177815948138539247881112058033838717522294527916052114642142341690298-1.51

1.0028FLORIDA STATE221601839721158645613048238213823100637625166678059223760444979-1.58

1.0031GEORGIA TECH196484148491126721294648594114792736698105382927103893849267291-0.78

1.0032HARVARD136171332668661009914155931741816611074174633094204611443789-0.58

1.0036ILLINOIS, CHICAGO195561540244246741562477163381895352861636744917383111279161920519954-1.07

1.0038INDIANA5916992118246573504193913819714329103491414256068730565208294886311453938-0.90

1.0040IOWA STATE2124964207602849421975481166321073283715492514514149800771322534997-1.37

1.0041JOHNS HOPKINS322474152062404242121593178407582371389924490199476598117069670563-0.00

1.0042KANSAS35328108234743126332648910996209074573164146334230831359301-0.90

1.0043KENT STATE2346014573531292511341698084190771786790196042486612647111684603893-1.03

1.0048MIT249392745280210031735984111269657533179423166125492733101982611031-0.31

1.0052MINNESOTA549066811457828711481059820013823713621214782356021755714545270919863425-1.11

1.0055NEW MEXICO21757068262026729174697917495140653238839363342481511416196057656884-0.48

1.0057NORTH CAROLINA4819186144684730304388612320611019590517824175070710793169522392141671520-0.10

1.0061OHIO21105946675427054557778218292566971642435106718349263142676388-1.03

1.0062OHIO STATE5087336109726601333360310118014239054878026359009365139295896741121489137-1.53

1.0064OKLAHOMA STATE19631576629411370189355563641857218241284228841626420744120472315852-1.07

1.0066PENNSYLVANIA45466671123273381611017890175958111206023092303919435402910558924-0.76

1.0067PENNSYLVANIA STATE3934344108592317531403317557682514734225306426454360824583791094174-3.62

1.0068PITTSBURGH381910060464249961011801062376759431558335171238523095453922608569-1.05

1.0069PRINCETON55161411110548566234182121206574593174771617599100765553280.00

1.0072ROCHESTER296215739822206549814768349689121644982322815710563271556375832-0.21

1.0074SOUTH CAROLINA2998228643644004418051741246917309493090817958263349834171043979107-0.58

1.0076SOUTHERN ILLINOIS234135915002188961648948958617959168396335824244707547133861328583-1.20

1.0077STANFORD686515814821845986191298961408474451535263531367287581655051086732-0.21

1.0084TEXAS7495275165612547895137913438180420291090822393864124535157774899792451468-1.41

1.0085TEXAS A&M24475988052633307227818218110238633564923274127931408121913921051602349-1.88

1.0086TEXAS TECH2030824436622502321237739073221243597143030467436481413173403590473-1.33

1.0088UTAH26081186756815327711861121761039741454313101481811631400387483856-0.79

1.0090VIRGINIA44336287530155309453981011986917730551910263714129048164013500001103182-0.29

1.0091VPI & SU20057652689634639187743797692362436731410264941656510994113401425992-1.61

1.0092WASHINGTON571520211327146896529601342331432843875552939851251325124500687202837171-0.03

1.0095WAYNE STATE3002261420391607124105881118014656578012445031312935162039800095026600.00

1.0194WASHINGTON U.-ST. LOUIS323400571490270571862890141588499344164535540220193162139626348098-0.37

1.0281SYRACUSE271213219985137681627878124611296630008071474296549446103787316323-0.74

1.0324DELAWARE2311442523213301912034541135215818171192014800162598453203778457945-0.84

1.0383TENNESSEE22267953191430554166866914259200573524118419756247146413696622-1.23

1.0350MICHIGAN6973162985146916515129515333057110382858623922726519995253495967789-1.83

1.0463OKLAHOMA261007134246160821647048795715222197280927259252929744228504257803-0.90

1.0525DUKE464505011084250205320031171717911173490184964204142909265168830508203-0.38

1.0916CHICAGO6116978134877666903696171181809968645311863897919408372066860684600-0.29

1.0997YALE99320801737391359365334520131195107635451179218076160856432310901760364-0.09

1.0996WISCONSIN582463986805593764379815419316033717897320139260423700270603427701049186-1.65

1.1171RICE19566455160335248121554761134046134445663487445291923266205758-0.16

1.133ARIZONA STATE3278332102436570123640199207573250259651955280442366213227288969979086-1.85

1.1637ILLINOIS, URBANA9024298183972649019098517124713733571760918406503150879252125036571425946-1.26

1.177BROWN2932818113346297781327882995971891564549127171552081293278354-0.39

1.1779SUNY-BUFFALO30478305654227273211299985771786646321734377621575716800138620473201-0.93

1.1810CALIFORNIA, IRVINE19739725672216391194955311372167683378998214283071014056127177449231-0.90

1.2059NORTHWESTERN38930055256640124108134125139096103219131295234109844154668317134-0.78

1.2189VANDERBILT24427715446019768801418497123894159517120121116813100609350991-0.45

1.2180SUNY-STONY BROOK1992795294321827810520467759133212837122031961105474925106349360172-0.81

1.2365OREGON22454435161728658154525492741471826626292902313247593137024467636-0.89

1.2320COLUMBIA6905609113335649241712561031549110066257127680178359442128733711480-0.65

1.2613CALIFORNIA, SAN DIEGO25314186150640888228856917276173283380107437183292308493197552587494-0.88

1.3149MIAMI21179983386734857203536912453118704498189239167144258074166829307743-0.62

1.3160NOTRE DAME258366958748342062390346156321007822486901829011135686062522376971-0.49

1.3173RUTGERS36337926610235991290051082381063348145391999182791892318226352057847248-1.92

1.3239IOWA382265671060494353913895129812158653231052552322139713037104125619742-1.25

1.3570PURDUE22415033996015283204276314753309574556165123683160909401162834478945-2.24

1.3544KENTUCKY26790844545219915261421001141121847737481239324382260012907191272387121-1.08

1.369CALIFORNIA, DAVIS29492137741734293456655517363216644831135743326171698932171275571781-1.31

1.3746MARYLAND262680087520385782713691123982539842311496253161585413951306530721371-1.36

1.3878SUNY-ALBANY187007727140201291620247794011663204057415735130746107123711269073-0.69

1.3975SOUTHERN CALIFORNIA3417928733084724027937102137852144377271605126891228517776178377791830-0.98

1.4033HAWAII292582137323198212690056897212884258510902160363652829149416575395-0.60

1.4014CALIFORNIA, SANTA BARBARA239661191117364751797640110651768524019602015518600456801-1.29

1.4293WASHINGTON STATE19243103612621185267934610452168922351106027552187947439112948422468-1.05

1.4329GEORGETOWN2172213506093775627503861216211142509114641503579869124171034436249-0.43

1.4654NEBRASKA24421155791519725225795111745189892490126317474172547848101288440186-1.23

1.495BOSTON20862583470319084289346513993231127354122313827164607121101300456193-1.61

1.5147MASSACHUSETTS282628464040309401579753894719870237411641897491237253116272436391-1.31

1.5534HOUSTON1940905416762191215152479468190724017100525271154836722233842294386-1.27

1.5721CONNECTICUT2828359472962730618604731017015892391011064524425813737481779275800-1.09

1.5835HOWARD2333483343251159614553508238590627651737630423614054113000228401-0.23

1.5951MICHIGAN STATE411803270555408892718462103112332715509202232533149259311209820589540-2.34

1.6053MISSOURI28164524754129437236185513053187733122154335030182577436105987402191-1.24

1.6045LOUISIANA STATE29504427157617811186145910153220494148123414386174357221197129406289-1.48

1.6958NORTH CAROLINA STATE26186157828738974264509113583189372039154419149115784692128103483814-1.22

1.7987TULANE2116015397792571214283559551933843059121677113941370140724299761-0.55

1.791ALABAMA209752639940197751417158805114792229176111367106314605119589310920-0.98

2.0330GEORGIA34582986606042448452588520268253204965180332630102297041149659515305-1.74

2.1056NEW YORK3629897121896674282924794245972400196962238230642245811145294926-1.84

2.4482TEMPLE234534244073253661591972103531828640891574990492594461144208266868-1.32

0.0098ALBERTA518917710411732259259936121045231952935152865126267143958721077205

0.0099BRITISH COLUMBIA385344210770751159187841052326524429523118394671120314177742666583806278

0.00100GUELPH209988927859613623949116181490610571711129275049976314528

0.00101LAVAL2286304731673127913655631731218674119152524368130727543190166868207

0.00102MANITOBA17400252954589915513822167012063115119076114501310586435728777

0.00103MCGILL29941564552330131164246416248222805204154117313106617450218087902908

0.00104MCMASTER178720822367166001188031114181390514619271776811172485076132414674

0.00105QUEEN'S213971325760186521089539125211299920037449289100361063587008456005

0.00106SASKATCHEWAN16986903380918325141794011514149401332971983710022739364843489878

0.00107TORONTO848717921506313476944574159369112382467445280127767975795914139132482871

0.00108WATERLOO18434713930817610137453810524163531518715119699561376862397520990

0.00109WESTERN ONTARIO2248139261992827515353451411915481231712581941837566494162753854299

0.00110YORK2206107446373562212076511254928431241611251452339388470160842973857

115.62

0.00

-0.09

114.00

0.00

0.00

0.00

0.00

0.00

100.00

Sheet2

SlacksInputOutputCollectionlog(Coll)

HARVARD320.000.001.001.00136171337.1313.6213.62

CALIFORNIA, BERKELEY80.00-0.001.001.0086280286.948.638.63

TEXAS840.000.001.001.0074952756.877.507.50

CALIFORNIA, LOS ANGELES110.00-0.001.001.0070102346.857.017.01

STANFORD770.00-0.001.001.0068651586.846.876.87

CORNELL220.00-0.001.001.0061133466.796.116.11

INDIANA380.00-0.001.001.0059169926.775.925.92

WASHINGTON920.00-0.001.001.0057152026.765.725.72

PRINCETON690.00-0.001.001.0055161416.745.525.52

MINNESOTA520.000.001.001.0054906686.745.495.49

OHIO STATE620.000.001.001.0050873366.715.095.09

NORTH CAROLINA570.000.001.001.0048191866.684.824.82

PENNSYLVANIA660.00-0.001.001.0045466676.664.554.55

ARIZONA20.000.001.001.0044429616.654.444.44

VIRGINIA900.00-0.001.001.0044336286.654.434.43

PENNSYLVANIA STATE670.000.001.001.0039343446.593.933.93

PITTSBURGH680.000.001.001.0038191006.583.823.82

KANSAS420.000.001.001.0035328106.553.533.53

FLORIDA270.000.001.001.0033177816.523.323.32

JOHNS HOPKINS410.00-0.001.001.0032247416.513.223.22

WAYNE STATE950.00-0.001.001.0030022616.483.003.00

SOUTH CAROLINA740.00-0.001.001.0029982286.483.003.00

ROCHESTER720.000.001.001.0029621576.472.962.96

COLORADO180.00-0.001.001.0027157026.432.722.72

UTAH880.000.001.001.0026081186.422.612.61

MIT480.00-0.001.001.0024939276.402.492.49

AUBURN40.000.001.001.0024646666.392.462.46

BRIGHAM YOUNG60.000.001.001.0024629666.392.462.46

TEXAS A&M850.000.001.001.0024475986.392.452.45

EMORY260.000.001.001.0023690656.372.372.37

KENT STATE430.000.001.001.0023460146.372.352.35

SOUTHERN ILLINOIS760.00-0.001.001.0023413596.372.342.34

CINCINNATI170.00-0.001.001.0023273076.372.332.33

DARTMOUTH230.000.001.001.0022232946.352.222.22

FLORIDA STATE280.00-0.001.001.0022160186.352.222.22

NEW MEXICO550.00-0.001.001.0021757066.342.182.18

IOWA STATE400.000.001.001.0021249646.332.122.12

OHIO610.00-0.001.001.0021105946.322.112.11

TEXAS TECH860.000.001.001.0020308246.312.032.03

VPI & SU910.00-0.001.001.0020057656.302.012.01

CASE WESTERN RESERVE150.00-0.001.001.0019654786.291.971.97

GEORGIA TECH310.000.001.001.0019648416.291.961.96

OKLAHOMA STATE640.00-0.001.001.0019631576.291.961.96

ILLINOIS, CHICAGO360.00-0.001.001.0019556156.291.961.96

CALIFORNIA, RIVERSIDE120.00-0.001.001.0018509326.271.851.85

COLORADO STATE190.000.001.001.0017081096.231.711.71

WASHINGTON U.-ST. LOUIS940.000.000.991.0132340056.513.283.19

SYRACUSE810.000.000.981.0227121326.432.762.66

DELAWARE240.00-0.000.981.0323114426.362.372.25

TENNESSEE830.00-0.000.971.0322267956.352.292.17

MICHIGAN500.000.000.971.0369731626.847.226.74

OKLAHOMA630.00-0.000.961.0426100716.422.722.50

DUKE250.0073.470.951.0546450506.674.894.41

CHICAGO160.00107.520.921.0961169786.796.665.62

YALE970.00222.730.911.0999320807.0010.879.08

WISCONSIN960.00-0.000.911.0958246396.776.385.32

RICE710.00-0.000.901.1119566456.292.161.77

ARIZONA STATE30.0085.620.891.1332783326.523.702.90

ILLINOIS, URBANA370.000.000.861.1690242986.9610.467.79

BROWN70.000.000.861.1729328186.473.422.52

SUNY-BUFFALO790.0059.240.851.1730478306.483.582.60

CALIFORNIA, IRVINE100.0021.040.851.1819739726.302.331.67

NORTHWESTERN590.000.000.831.2038930056.594.683.24

VANDERBILT890.00-0.000.831.2124427716.392.952.02

SUNY-STONY BROOK800.00-0.000.831.2119927956.302.411.65

OREGON650.000.000.821.2322454436.352.751.83

COLUMBIA200.00108.480.811.2369056096.848.505.61

CALIFORNIA, SAN DIEGO130.0064.620.791.2625314186.403.182.01

MIAMI490.0058.890.761.3121179986.332.771.62

NOTRE DAME600.00-0.000.761.3125836696.413.391.97

RUTGERS730.0096.210.761.3136337926.564.782.76

IOWA390.00114.480.761.3238226566.585.042.90

PURDUE700.0051.880.741.3522415036.353.021.67

KENTUCKY440.0082.280.741.3526790846.433.611.99

CALIFORNIA, DAVIS90.0099.940.741.3629492136.474.002.17

MARYLAND460.0097.840.731.3726268006.423.591.92

SUNY-ALBANY780.00-0.000.731.3818700776.272.571.36

SOUTHERN CALIFORNIA750.00104.270.721.3934179286.534.742.47

HAWAII330.00-0.000.721.4029258216.474.092.09

CALIFORNIA, SANTA BARBARA140.0054.400.711.4023966116.383.351.71

WASHINGTON STATE930.000.000.711.4219243106.282.721.36

GEORGETOWN290.0075.460.701.4321722136.343.111.52

NEBRASKA540.0043.510.691.4624421156.393.561.68

BOSTON50.0079.390.671.4920862586.323.111.40

MASSACHUSETTS470.0044.640.661.5128262846.454.261.87

HOUSTON340.00-0.000.651.5519409056.293.011.25

CONNECTICUT210.0057.680.641.5728283596.454.451.80

HOWARD350.000.000.631.5823334836.373.691.48

MICHIGAN STATE510.00114.300.631.5941180326.616.542.59

MISSOURI530.0058.160.631.6028164526.454.501.76

LOUISIANA STATE450.0060.600.621.6029504426.474.731.84

NORTH CAROLINA STATE580.0098.340.591.6926186156.424.431.55

TULANE870.0032.800.561.7921160156.333.791.18

ALABAMA10.0020.460.561.7920975266.323.761.17

GEORGIA300.00152.220.492.0334582986.547.011.71

NEW YORK560.00176.180.482.1036298976.567.641.72

TEMPLE820.0079.950.412.4423453426.375.730.96

14.0014

1.001

Sheet2

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Collection*Input

Collection*Output

Sheet4

Input OrientedOutput OrientedAdditiveIn-Out Total

Name#IntensitySlacksIntensitySlacksIntensitySlacksSlacksIntensitySlacks

ALABAMA10.9612.931.286.750.0027.9619.680.0067.62

ARIZONA21.001.000.000.00

ARIZONA STATE30.9342.891.1045.130.00105.9088.020.0085.76

AUBURN1.001.000.000.00

BOSTON0.9785.131.1872.820.00113.49157.950.0097.91

BRIGHAM YOUNG1.001.000.000.00

BROWN1.001.000.000.00101.54

CALIFORNIA, BERKELEY81.001.000.000.00

CALIFORNIA, DAVIS90.8865.821.2571.550.00128.00137.370.00111.45

CALIFORNIA, IRVINE100.9922.471.0324.090.0030.5746.560.0048.67

CALIFORNIA, LOS ANGELES111.001.000.000.00

CALIFORNIA, RIVERSIDE121.001.000.000.00

CALIFORNIA, SAN DIEGO130.8622.141.2529.020.0070.6451.160.0074.52

CALIFORNIA, SANTA BARBARA140.9751.941.0951.570.0066.90103.510.0099.56

CASE WESTERN RESERVE1.001.000.000.00

CHICAGO0.96113.551.07119.990.00130.89233.540.00137.62

CINCINNATI1.001.000.000.00

COLORADO181.001.000.000.00

COLORADO STATE191.001.000.000.00

COLUMBIA0.8681.651.21113.420.00182.25195.060.00124.20

CONNECTICUT210.8620.701.4022.790.0062.4643.500.0075.66

CORNELL1.001.000.000.00-0.00

DARTMOUTH1.001.000.000.000.00

DELAWARE241.001.000.000.0041.72

DUKE0.9972.731.0173.230.0083.46145.970.00102.12

EMORY1.001.000.000.00-0.00

FLORIDA271.001.000.000.000.00

FLORIDA STATE281.001.000.000.000.00

GEORGETOWN0.9576.561.1078.210.0095.89154.760.0088.81

GEORGIA300.6227.382.0146.960.00178.4774.340.00152.22

GEORGIA TECH1.001.000.000.00-0.00

HARVARD1.001.000.000.00-0.00

HAWAII331.001.000.000.0069.69

HOUSTON1.001.000.000.0056.06

HOWARD1.001.000.000.0059.10

ILLINOIS, CHICAGO361.001.000.000.00-0.00

ILLINOIS, URBANA371.001.000.000.00-0.00

INDIANA381.001.000.000.000.00

IOWA390.8249.681.3167.940.00132.40117.620.00114.48

IOWA STATE401.001.000.000.000.00

JOHNS HOPKINS1.001.000.000.00-0.00

KANSAS421.001.000.000.00-0.00

KENT STATE1.001.000.000.000.00

KENTUCKY440.8522.981.3233.420.0082.7156.400.0092.33

LOUISIANA STATE450.8526.391.4336.270.0080.2862.660.0078.41

MARYLAND460.8241.951.3643.110.00118.8985.060.0097.84

MASSACHUSETTS470.9334.181.2131.300.0066.8865.470.0078.28

MIAMI0.9550.821.1651.290.0071.89102.110.000.00

MICHIGAN501.001.000.000.0070.94

MICHIGAN STATE510.7760.491.51109.210.00175.03169.690.000.00

MINNESOTA521.001.000.000.00114.30

MISSOURI530.8930.611.3728.540.0078.2259.140.00-0.00

MIT1.001.000.000.0080.96

NEBRASKA540.9130.521.2831.570.0062.3062.100.0071.94

NEW MEXICO551.001.000.000.000.00

NEW YORK0.6069.081.97123.220.00248.39192.300.00176.18

NORTH CAROLINA571.001.000.000.00-0.00

NORTH CAROLINA STATE580.7645.771.6749.910.00122.5195.680.00119.96

NORTHWESTERN1.001.000.000.00108.13

NOTRE DAME1.001.000.000.0082.52

OHIO611.001.000.000.000.00

OHIO STATE621.001.000.000.000.00

OKLAHOMA631.001.000.000.0032.40

OKLAHOMA STATE641.001.000.000.000.00

OREGON651.001.000.000.0066.53

PENNSYLVANIA1.001.000.000.000.00

PENNSYLVANIA STATE671.001.000.000.000.00

PITTSBURGH1.001.000.000.00-0.00

PRINCETON1.001.000.000.000.00

PURDUE700.9352.601.1744.540.0090.2597.130.0069.77

RICE1.001.000.000.0058.68

ROCHESTER1.001.000.000.000.00

RUTGERS730.7822.681.2839.950.00137.5962.620.0096.21

SOUTH CAROLINA741.001.000.000.000.00

SOUTHERN CALIFORNIA0.8346.781.3156.880.00146.90103.660.00104.27

SOUTHERN ILLINOIS761.001.000.000.00-0.00

STANFORD1.001.000.000.00-0.00

SUNY-ALBANY781.001.000.000.0049.20

SUNY-BUFFALO790.9130.581.1539.240.0080.5169.820.0066.53

SUNY-STONY BROOK801.001.000.000.0048.89

SYRACUSE1.001.000.000.0042.33

TEMPLE0.8427.112.0419.720.0090.6546.830.0090.67

TENNESSEE831.001.000.000.0040.98

TEXAS841.001.000.000.00-0.00

TEXAS A&M1.001.000.000.000.00

TEXAS TECH1.001.000.000.000.00

TULANE0.9427.321.3121.220.0046.5848.540.0070.93

UTAH881.001.000.000.000.00

VANDERBILT1.001.000.000.0066.17

VIRGINIA901.001.000.000.000.00

VPI & SU1.001.000.000.00-0.00

WASHINGTON921.001.000.000.00-0.00

WASHINGTON STATE931.001.000.000.0058.55

WASHINGTON U.-ST. LOUIS1.001.000.000.0059.10

WAYNE STATE1.001.000.000.000.00

WISCONSIN961.001.000.000.000.00

YALE0.96207.801.04228.460.00245.06436.250.00231.90

Chart1

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00.009399452800.009807116600.001092716300.0077633670.014428754100.00483554740.0012677842000.01857400650.0140701630.00824726160.012320714200.01850751330.017130740600.028091246100.01303713770.02971498240.00921277590.026266106500.01520343970.0630143583000.023682388400.000325505900.00537252720.00992061640.015668504700.00008351400.0034408921000.00762792540.02175680590.016331897900.00637704990.00819624580.017487441700.015489973600.000203080500.02218215470.02639636870.01416234650.0073041087000.0176380530.0006660031000000.005879401200.00000000020.00000000020.0148806354000.01714063570.041624633500000000.0206609740.001054271900.02491394670.00706750160.02304220270.01914157510.00951279860.00840581880

0.00873266860.00091276310.0024641610.00000729890.00544606820.00426392320.02432608680.00106122160.00000009310.00781587650.00213404110.01438279110.00959737560.01347956190.01155827050.0124789090.00758935480.00623900050.007741676500.00449613510.0059566070.02137516880.01105957930.01137862680.01413248870.0008484770.00060922220.009212954400.00000039580.003395577600.009086566500.00733048370.00567263310.00219953830.000360075400.01261595150.00365736630.01239355340.00525364710.007692280100.00173906830.00745722740.00153745250000.00028862070.00812622480.0043961910.00608242710.00462320170.01202340330.00224099540.00094609090.0002060120.00017312390.0210545230.00590254180.00566516730.013751490.00086760090.00068441310.01663542830.01663443760.01773093150.01674108660.00114044210.00527188210.00193431480.007391976400.0147577479000.0072729780.00450626770.01083576390.00346744160.00410343590.01146285120.01758455970.00121839420.00910504290.008445564600.00033227620.00030061110.01868299240.009498669100

00.00711597840.01546092840.03187569580.03045041110.012574346400.03203816210.01848544150.043131626400.015690508100000.00117238300.00024497190.03337409010.03535839990.02892423420.01332232700.03760636080.00946590990.00000090200.03561035010.00228078450.04575180340.000002676000.08354012890.02010937660.014330279400.0193653590.054567141700.001016456800.04537512490.0002889290.01774019660.020407667700.00947275960000.02272982720.02338243980.00984101730.01863670340.0019707600.0300645760.03267874820.01699869330.006633842700.03962650810000.00722297180.0039648010.00396454650.09407457240.03292343480.02306072560.01247282580.01814214550.017511263700.02455486330.03790380730.00152260020.05892996740.01751992770000.001689505300.02790125450.04921872540.00445661320.04760762260.01394315970.0452574697000.01569189720.015579005

0.01847237960.00576514330.00722289370.01489486940.00163458220.00464346510.024553162900.005741787700.00394184010.00227700190.0095566205000.00002094610.00056786230.00917626880.0201361024000.00216263580.02456033160.02823752290.003939353500.00528707830.01278689020.00546864920.00991145840.03330057390.00704013290.02026151630.01956831090.00987989090.00316914850.00256032950.005247933000.01715901920.000546799800.00000001140.0125028360.006177480.01322875730.01383008510.008179729300.010375260.00523801340.005045290600.0073944140.00665674950.009638602200.02441478430.01221270910.00413812210.00402139750.02796052760.010208440200.01267109310.01269004580.01288748540.02647246710.026471043800.01075819130.00175297350.00755824520.00434372510.01249064970.00930504910.010063588800.01195505500.010025321300.0020426540.005363361800.0115289580.0044417810.02865664810.00696174360.00006689030.000006142600.01399728960.007401675800.0110663512

0.03058878690.01517437830.01481375860.02246337970.02325595910.01662022340.037465383400.015618145500.01003210290.05106791560.01984000470.03045467380.01970217410.02161743930.0124843150.01833662960.02985572430.013753583800.01045117290.05101199010.02697972030.00677935410.02751133610.01369835460.03166524920.01635877050.01240647780.05867896890.01933501990.026793041300.02879389980.01094387630.00784898550.01347655360.01530972840.02421062210.02748870730.02017847030.034368103800.02385874150.01486088790.02395605360.0316376040.01741893240.02995639820.02113973890.00909323470.0157953880.02466861460.02257525400.01363217340.02802720400.02512316530.01338133310.0079044357000.03656549250.01269929320.01615625430.02142973760.0449670170.0449640860.0725418620.03629784020.00983052930.01998743160.01218926010.03631957090.0247714570.033555214700.02430221510.0332706790.02164963240.03038247110.01037993330.01368464450.02417363830.02826272210.0200410390.01571248550.01411751510.01803363010.00479443530.01084863790.01879318220.01396659620.00655831350.0230533894

Sheet3

2.188.9911.024.646.484.979.5013.955.974.697.796.1015.618.0620.26

Name#IntensityVolsVolsAdNMonoCurrSerPrfStfNPrfStfStudAstTotStuGradStuFacILLILBPresPtcpRefTransTotCircU

123456789101112131415

ALABAMA10.560.000.000.000.020.000.000.010.000.010.020.000.010.000.020.030.150.00

ARIZONA21.000.000.000.000.010.000.000.000.000.000.010.010.000.010.010.020.150.00

ARIZONA STATE30.890.010.000.000.000.000.010.020.000.000.000.000.000.020.010.010.150.00

AUBURN41.000.000.000.000.000.000.030.040.000.020.000.010.000.030.010.020.150.00

BOSTON50.670.010.060.020.000.000.000.000.000.000.000.000.010.030.000.020.150.00

BRIGHAM YOUNG61.000.010.030.010.000.000.000.000.000.000.000.000.000.010.000.020.150.00

BROWN70.860.000.000.000.010.000.000.000.050.030.000.000.020.000.020.040.150.00

CALIFORNIA, BERKELEY81.000.000.000.02-0.000.000.000.000.020.000.000.010.000.030.000.000.150.00

CALIFORNIA, DAVIS90.740.000.000.000.000.050.000.020.000.000.000.010.000.020.010.020.150.00

CALIFORNIA, IRVINE100.850.050.000.000.000.000.000.000.020.000.000.000.010.040.000.000.150.00

CALIFORNIA, LOS ANGELES111.000.010.000.000.000.000.000.000.010.000.010.000.000.000.000.010.150.00

CALIFORNIA, RIVERSIDE121.000.000.00-0.000.010.000.000.000.020.020.050.000.010.020.000.050.150.00

CALIFORNIA, SAN DIEGO130.790.000.000.000.010.000.000.000.020.010.010.000.010.000.010.020.150.00

CALIFORNIA, SANTA BARBARA140.710.000.000.000.000.120.000.000.000.000.000.000.010.000.000.030.150.00

CASE WESTERN RESERVE151.000.000.000.000.000.030.010.000.020.010.000.020.010.000.000.020.150.00

CHICAGO160.920.000.000.000.000.010.000.000.040.000.010.010.010.000.000.020.150.00

CINCINNATI171.000.000.000.000.000.000.000.000.020.000.010.010.010.000.000.010.150.00

COLORADO181.000.000.010.000.000.000.000.010.010.020.000.010.010.000.010.020.150.00

COLORADO STATE191.000.000.000.000.000.090.000.000.010.010.000.000.010.000.020.030.150.00

COLUMBIA200.810.000.000.060.000.000.000.000.030.000.000.020.000.030.000.010.150.00

CONNECTICUT210.640.000.010.000.010.000.010.000.010.000.000.020.000.040.000.000.150.00

CORNELL221.000.000.000.010.000.000.000.000.030.000.000.000.010.030.000.010.150.00

DARTMOUTH231.000.000.000.000.000.000.000.000.070.030.020.030.020.010.020.050.150.00

DELAWARE240.980.000.000.000.020.000.000.020.000.040.000.000.010.000.030.030.150.00

DUKE250.950.000.000.000.000.000.000.000.040.000.010.010.010.040.000.010.150.00

EMORY261.000.000.000.080.000.000.000.000.050.000.010.030.010.010.000.030.150.00

FLORIDA271.000.000.010.020.000.000.000.020.000.000.000.010.000.000.010.010.150.00

FLORIDA STATE281.000.000.010.040.020.020.000.030.000.000.000.030.000.000.010.030.150.00

GEORGETOWN290.700.020.000.000.000.000.000.000.040.000.000.000.010.040.010.020.150.00

GEORGIA300.490.000.000.000.000.000.000.030.000.010.000.020.000.000.010.010.150.00

GEORGIA TECH311.000.000.000.000.000.000.040.120.000.030.000.060.000.050.030.060.150.00

HARVARD321.000.000.000.010.000.000.000.000.010.000.010.000.000.000.010.020.150.00

HAWAII330.720.000.000.000.00-0.000.000.000.020.030.000.000.000.000.020.030.150.00

HOUSTON340.650.000.000.000.020.080.000.000.000.000.000.020.010.000.020.000.150.00

HOWARD350.630.000.000.000.000.000.000.000.100.000.000.000.000.080.010.030.150.00

ILLINOIS, CHICAGO361.000.000.000.000.000.000.000.000.020.000.000.000.010.020.000.010.150.00

ILLINOIS, URBANA371.110.000.000.000.000.000.000.000.020.000.000.000.010.010.000.010.150.00

INDIANA381.000.000.010.000.010.000.000.000.000.000.010.010.000.000.010.010.080.00

IOWA390.760.000.020.000.000.000.000.000.000.000.020.010.000.020.000.020.080.00

IOWA STATE401.000.000.080.010.000.000.000.010.000.000.000.020.000.050.000.020.080.00

JOHNS HOPKINS411.000.000.000.000.000.000.000.020.020.020.000.000.010.000.020.030.080.00

KANSAS421.000.000.000.000.000.000.050.000.000.000.010.000.000.000.000.020.080.00

KENT STATE431.000.000.000.000.030.000.050.000.000.000.000.000.010.000.000.030.080.00

KENTUCKY440.740.000.030.010.000.000.000.000.010.000.000.000.010.050.000.000.080.00

LOUISIANA STATE450.620.000.000.000.000.000.040.030.000.000.000.000.010.000.010.020.080.00

MARYLAND460.730.030.000.000.000.000.000.010.000.000.010.000.000.020.010.010.080.00

MASSACHUSETTS470.660.000.000.000.010.000.020.020.000.010.000.010.000.020.010.020.080.00

MIT481.000.000.000.000.000.000.000.030.030.000.010.020.010.000.010.030.080.00

MIAMI490.580.000.000.00-0.000.000.000.030.020.000.000.020.000.010.010.020.080.00

MICHIGAN500.970.000.030.070.000.000.000.000.00-0.000.000.000.000.000.000.030.080.00

MICHIGAN STATE510.630.000.000.000.000.030.050.000.000.000.000.010.000.000.010.020.080.00

MINNESOTA521.000.000.000.000.000.010.030.000.000.000.000.010.000.000.010.010.080.00

MISSOURI530.630.000.000.000.000.030.000.030.000.000.000.020.000.020.010.020.080.00

NEBRASKA540.690.000.000.000.000.020.000.040.000.010.000.000.010.020.000.020.080.00

NEW MEXICO551.000.010.000.000.020.000.000.000.010.000.010.020.000.010.010.020.080.00

NEW YORK560.480.000.000.000.010.020.000.000.010.000.000.000.010.020.010.000.080.00

NORTH CAROLINA571.000.000.000.000.000.000.000.000.010.020.000.000.000.000.010.010.080.00

NORTH CAROLINA STATE580.590.000.000.000.000.000.000.000.000.06-0.000.000.010.000.000.030.080.00

NORTHWESTERN590.830.000.000.180.000.000.000.000.040.000.000.020.000.030.020.000.080.00

NOTRE DAME600.760.000.000.000.000.000.000.050.010.020.010.030.000.030.010.030.080.00

OHIO611.000.000.000.000.000.000.000.030.000.010.000.010.000.020.000.010.080.00

OHIO STATE621.000.000.000.000.010.000.000.010.000.000.000.010.000.010.000.010.080.00

OKLAHOMA630.960.000.030.000.010.000.000.000.000.040.000.000.020.000.030.000.080.00

OKLAHOMA STATE641.000.030.000.000.010.000.010.020.000.000.000.000.010.040.010.000.080.00

OREGON650.820.000.000.000.020.000.000.000.000.010.040.020.010.000.000.040.080.00

PENNSYLVANIA661.000.000.000.050.000.000.000.000.030.000.000.000.010.000.010.010.080.00

PENNSYLVANIA STATE671.000.000.000.070.010.000.000.010.010.000.000.000.000.000.010.020.080.00

PITTSBURGH681.000.000.000.070.010.000.000.010.010.000.000.000.000.010.010.020.080.00

PRINCETON691.000.000.000.000.000.000.000.000.040.030.010.000.020.000.030.040.080.00

PURDUE701.310.000.000.000.000.000.000.000.040.030.010.000.020.000.030.040.080.00

RICE710.900.000.000.000.000.000.000.140.060.000.000.000.020.090.000.070.080.00

ROCHESTER721.000.000.010.000.020.000.000.000.040.000.020.010.020.030.010.040.080.00

RUTGERS730.760.000.030.000.000.000.000.010.000.000.000.000.000.020.000.010.080.00

SOUTH CAROLINA741.000.000.010.000.010.000.000.010.000.000.010.000.010.010.010.020.080.00

SOUTHERN CALIFORNIA750.720.020.010.000.000.000.010.010.000.000.000.000.000.020.000.010.080.00

SOUTHERN ILLINOIS761.000.000.060.020.020.010.000.000.000.010.000.010.010.020.010.040.080.00

STANFORD771.000.000.000.040.000.000.000.010.000.000.000.000.000.000.010.020.080.00

SUNY-ALBANY780.730.000.060.000.000.000.000.000.000.000.030.000.010.020.010.030.080.00

SUNY-BUFFALO790.850.000.010.000.000.000.030.010.010.000.000.020.000.040.000.000.080.00

SUNY-STONY BROOK800.830.000.000.000.080.000.020.000.000.000.000.040.000.000.010.020.080.00

SYRACUSE810.980.000.090.040.000.000.000.010.000.000.000.000.010.060.000.030.080.00

TEMPLE820.410.000.010.000.010.000.020.030.000.000.000.000.000.020.010.020.080.00

TENNESSEE830.970.000.050.000.000.000.000.000.000.000.010.000.010.000.000.030.080.00

TEXAS841.000.000.010.000.000.000.000.000.000.000.010.000.000.000.000.010.080.00

TEXAS A&M851.000.000.010.000.000.000.000.000.000.000.010.000.000.000.010.010.080.00

TEXAS TECH861.000.000.030.000.000.000.020.000.000.010.000.000.010.000.000.020.080.00

TULANE870.560.000.000.000.000.000.020.000.040.000.010.000.020.000.010.030.080.00

UTAH881.000.000.000.020.040.000.000.000.010.000.000.020.000.030.000.020.080.00

VANDERBILT890.830.000.000.190.000.000.000.000.060.000.000.000.010.050.030.020.080.00

VIRGINIA901.000.000.000.000.000.000.010.000.020.010.000.000.010.000.010.010.080.00

VPI & SU911.000.000.050.000.010.040.000.010.000.000.000.020.000.050.000.020.080.00

WASHINGTON921.000.000.010.000.000.010.000.000.000.000.000.010.000.010.000.000.080.00

WASHINGTON STATE930.710.000.050.000.000.030.000.010.000.000.000.020.000.050.000.010.080.00

WASHINGTON U.-ST. LOUIS940.990.000.000.000.000.000.000.000.050.000.020.020.020.000.010.020.080.00

WAYNE STATE951.000.000.000.000.000.000.000.000.020.000.010.010.010.000.010.010.080.00

WISCONSIN960.910.000.020.000.000.000.000.000.000.000.000.010.000.020.000.010.080.00

YALE970.910.000.000.000.000.000.000.000.060.000.000.000.000.020.010.020.080.00

1.0020.26TotCirc

2.0015.61PresPtcp

3.0013.95TotStu

4.0011.02Mono

5.009.50StudAst

6.008.99VolsAdN

7.008.06RefTrans

8.007.79ILL

9.006.48PrfStf

10.006.10ILB

11.005.97GradStu

12.004.97NPrfStf

13.004.69Fac

14.004.64CurrSer

15.002.18Vols

U

0.000.000.010.000.010.010.000.000.000.050.010.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.020.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.030.000.000.000.000.000.000.000.000.010.000.000.000.000.000.000.000.000.030.000.000.000.000.000.000.000.000.000.000.020.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00

0.000.000.000.000.060.030.000.000.000.000.000.000.000.000.000.000.000.010.000.000.010.000.000.000.000.000.010.010.000.000.000.000.000.000.000.000.000.010.020.080.000.000.000.030.000.000.000.000.000.030.000.000.000.000.000.000.000.000.000.000.000.000.030.000.000.000.000.000.000.000.000.010.030.010.010.060.000.060.010.000.090.010.050.010.010.030.000.000.000.000.050.010.050.000.000.020.00

0.000.000.000.000.020.010.000.020.000.000.00-0.000.000.000.000.000.000.000.000.060.000.010.000.000.000.080.020.040.000.000.000.010.000.000.000.000.000.000.000.010.000.000.000.010.000.000.000.000.000.070.000.000.000.000.000.000.000.000.180.000.000.000.000.000.000.050.070.070.000.000.000.000.000.000.000.020.040.000.000.000.040.000.000.000.000.000.000.020.190.000.000.000.000.000.000.000.00

0.020.010.000.000.000.000.01-0.000.000.000.000.010.010.000.000.000.000.000.000.000.010.000.000.020.000.000.000.020.000.000.000.000.000.020.000.000.000.010.000.000.000.000.030.000.000.000.010.00-0.000.000.000.000.000.000.020.010.000.000.000.000.000.010.010.010.020.000.010.010.000.000.000.020.000.010.000.020.000.000.000.080.000.010.000.000.000.000.000.040.000.000.010.000.000.000.000.000.00

0.000.000.000.000.000.000.000.000.050.000.000.000.000.120.030.010.000.000.090.000.000.000.000.000.000.000.000.020.000.000.000.00-0.000.080.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.030.010.030.020.000.020.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.010.000.000.000.000.000.000.000.000.000.000.000.000.000.000.040.010.030.000.000.000.00

0.000.000.010.030.000.000.000.000.000.000.000.000.000.000.010.000.000.000.000.000.010.000.000.000.000.000.000.000.000.000.040.000.000.000.000.000.000.000.000.000.000.050.050.000.040.000.020.000.000.000.050.030.000.000.000.000.000.000.000.000.000.000.000.010.000.000.000.000.000.000.000.000.000.000.010.000.000.000.030.020.000.020.000.000.000.020.020.000.000.010.000.000.000.000.000.000.00

0.010.000.020.040.000.000.000.000.020.000.000.000.000.000.000.000.000.010.000.000.000.000.000.020.000.000.020.030.000.030.120.000.000.000.000.000.000.000.000.010.020.000.000.000.030.010.020.030.030.000.000.000.030.040.000.000.000.000.000.050.030.010.000.020.000.000.010.010.000.000.140.000.010.010.010.000.010.000.010.000.010.030.000.000.000.000.000.000.000.000.010.000.010.000.000.000.00

0.000.000.000.000.000.000.050.020.000.020.010.020.020.000.020.040.020.010.010.030.010.030.070.000.040.050.000.000.040.000.000.010.020.000.100.020.020.000.000.000.020.000.000.010.000.000.000.030.020.000.000.000.000.000.010.010.010.000.040.010.000.000.000.000.000.030.010.010.040.040.060.040.000.000.000.000.000.000.010.000.000.000.000.000.000.000.040.010.060.020.000.000.000.050.020.000.06

0.010.000.000.020.000.000.030.000.000.000.000.020.010.000.010.000.000.020.010.000.000.000.030.040.000.000.000.000.000.010.030.000.030.000.000.000.000.000.000.000.020.000.000.000.000.000.010.000.00-0.000.000.000.000.010.000.000.020.060.000.020.010.000.040.000.010.000.000.000.030.030.000.000.000.000.000.010.000.000.000.000.000.000.000.000.000.010.000.000.000.010.000.000.000.000.000.000.00

0.020.010.000.000.000.000.000.000.000.000.010.050.010.000.000.010.010.000.000.000.000.000.020.000.010.010.000.000.000.000.000.010.000.000.000.000.000.010.020.000.000.010.000.000.000.010.000.010.000.000.000.000.000.000.010.000.00-0.000.000.010.000.000.000.000.040.000.000.000.010.010.000.020.000.010.000.000.000.030.000.000.000.000.010.010.010.000.010.000.000.000.000.000.000.020.010.000.00

0.000.010.000.010.000.000.000.010.010.000.000.000.000.000.020.010.010.010.000.020.020.000.030.000.010.030.010.030.000.020.060.000.000.020.000.000.000.010.010.020.000.000.000.000.000.000.010.020.020.000.010.010.020.000.020.000.000.000.020.030.010.010.000.000.020.000.000.000.000.000.000.010.000.000.000.010.000.000.020.040.000.000.000.000.000.000.000.020.000.000.020.010.020.020.010.010.00

0.010.000.000.000.010.000.020.000.000.010.000.010.010.010.010.010.010.010.010.000.000.010.020.010.010.010.000.000.010.000.000.000.000.010.000.010.010.000.000.000.010.000.010.010.010.000.000.010.000.000.000.000.000.010.000.010.000.010.000.000.000.000.020.010.010.010.000.000.020.020.020.020.000.010.000.010.000.010.000.000.010.000.010.000.000.010.020.000.010.010.000.000.000.020.010.000.00

0.000.010.020.030.030.010.000.030.020.040.000.020.000.000.000.000.000.000.000.030.040.030.010.000.040.010.000.000.040.000.050.000.000.000.080.020.010.000.020.050.000.000.000.050.000.020.020.000.010.000.000.000.020.020.010.020.000.000.030.030.020.010.000.040.000.000.000.010.000.000.090.030.020.010.020.020.000.020.040.000.060.020.000.000.000.000.000.030.050.000.050.010.050.000.000.020.02

0.020.010.010.010.000.000.020.000.010.000.000.000.010.000.000.000.000.010.020.000.000.000.020.030.000.000.010.010.010.010.030.010.020.020.010.000.000.010.000.000.020.000.000.000.010.010.010.010.010.000.010.010.010.000.010.010.010.000.020.010.000.000.030.010.000.010.010.010.030.030.000.010.000.010.000.010.010.010.000.010.000.010.000.000.010.000.010.000.030.010.000.000.000.010.010.000.01

0.030.020.010.020.020.020.040.000.020.000.010.050.020.030.020.020.010.020.030.010.000.010.050.030.010.030.010.030.020.010.060.020.030.000.030.010.010.010.020.020.030.020.030.000.020.010.020.030.020.030.020.010.020.020.020.000.010.030.000.030.010.010.000.000.040.010.020.020.040.040.070.040.010.020.010.040.020.030.000.020.030.020.030.010.010.020.030.020.020.010.020.000.010.020.010.010.02

5.461.160.510.690.360.661.221.980.040.480.311.025.521.072.060.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00

1.1641.919.692.254.781.563.971.522.953.576.274.8424.273.2118.700.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00

0.519.69103.673.101.020.384.1630.870.520.999.995.1224.2214.0718.120.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00

0.692.253.1012.222.343.632.342.572.452.596.642.474.504.5810.100.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.0

Data Envelopment Analysis Pattern

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Transcript of Data Envelopment Analysis Pattern