Package 'deaR'

Description

Data of 28 airlines with 2 outputs and 4 inputs.

Usage

data("Airlines")

Format

Data frame with 28 rows and 7 columns. Definition of outputs (Y) and inputs (X):

y1 = Pass

Passenger-kilometers flown

y2 = Cargo

Freight tonne-kilometers flown

x1 = Lab

Labor (number of employees)

x2 = Fuel

Fuel (millions of gallons)

x3 = Matl

Other inputs (millions of U.S. dollar equivalent) consisting of operating and maintenance expenses excluding labor and fuel expenses

x4 = Cap

Capital (sum of the maximum takeoff weights of all aircraft flown multiplied by the number of days flown)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Coelli, T.; Griffel-Tatje, E.; Perelman, S. (2002). "Capacity Utilization and Profitability: A Decomposition of Short-Run Profit Efficiency", International Journal of Production Economics 79, 261–278.

See Also

make_deadata, model_sbmeff

Examples

# Example. Replication of results in Aparicio et al. (2007).
data("Airlines")
data_example <- make_deadata(Airlines,
                             inputs = 4:7,
                             outputs = 2:3)
result <- model_sbmeff(data_example)
efficiencies(result)
result2 <- model_sbmeff(data_example,
                        kaizen = TRUE)
efficiencies(result2)

Description

To bootstrap efficiency scores, deaR uses the algorithm proposed by Simar and Wilson (1998). For now, the function bootstrap_basic can only be used with basic DEA models.

Usage

bootstrap_basic(datadea,
                orientation = c("io", "oo"),
                rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                L = 1,
                U = 1,
                B = 2000,
                h = NULL,
                alpha = 0.05)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Behr, A. (2015). Production and Efficiency Analysis with R. Springer.

Bogetoft, P.; Otto, L. (2010). Benchmarking with DEA, SFA, and R. Springer.

Daraio, C.; Simar, L. (2007). Advanced Robust and Nonparametric Methods in Efficiency Analysis: Methodology and Applications. New York: Springer.

Färe, R.; Grosskopf, S.; Kokkenlenberg, E. (1989). "Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach". International Economic Review, 30(3), 655-666.

Löthgren, M.; Tambour, M. (1999). "Bootstrapping the Data Envelopment Analysis Malmquist Productivity Index". Applied Economics, 31, 417-425.

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.

Simar, L.; Wilson, P.W. (1998). "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models". Management Science, 44(1), 49-61.

Simar, L.; Wilson, P.W. (1999). "Estimating and Bootstrapping Malmquist Indices". European Journal of Operational Research, 115, 459-471.

Simar, L.; Wilson, P.W. (2008). Statistical Inference in Nonparametric Frontier Models: Recent Developments and Perspective. In H.O. Fried; C.A. Knox Lovell and S.S. Schmidt (eds.) The Measurement of Productive Efficiency and Productivity Growth. New York: Oxford University Press. doi:10.1093/acprof:oso/9780195183528.001.0001

Examples

# To replicate the results in Simar y Wilson (1998, p. 58) you have to
# set B=2000 (in the example B = 100 to save time)
data("Electric_plants")
data_example <- make_deadata(Electric_plants, 
                             ni = 3, 
                             no = 1)
result <- bootstrap_basic(datadea = data_example,
                             orientation = "io",
                             rts = "vrs",
                             B = 100)
result$score_bc
result$CI

Description

Data of five DMUs with two inputs and one output. Prices for inputs are available. Price for output is not from Coelli et al. (1998).

Usage

data("Coelli_1998")

Format

Data frame with 6 rows and 5 columns. Definition of inputs (X) and outputs (Y):

Input1

Input 1

Input2

Input 2

Output

Output

Price_input1

Price input 1

Price_input2

Price input 2

Price_output

Price output

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Coelli, T.; Prasada Rao, D.S.; Battese, G.E. An introduction to efficiency and productivity analysis. Boston: Kluwer Academic Publishers.

See Also

make_deadata

Examples

# Example. Replication of results in Coelli et al. (1998, p.166).
# Cost efficiency model.
data("Coelli_1994")
# Selection of prices: data_prices is the trasnpose where the prices for inputs are. 
data_prices <- t(Coelli_1998[, 5:6]) 

data_example <- make_deadata(Coelli_1998,
                             dmus = 1,
                             ni = 2,
                             no = 1)
result <- model_profit(data_example,
                       price_input = data_prices,
                       rts = "crs", 
                       restricted_optimal = FALSE) 
# notice that the option by default is restricted_optimal=TRUE
efficiencies(result)

Description

Data of six authorized dealers with two inputs and two outputs.

Usage

data("Coll_Blasco_2006")

Format

Data frame with 6 rows and 5 columns. Definition of inputs (X) and outputs (Y):

x1 = Employees

Number of employees

x2 = Capital

Impairment of assets

y1 = Vehicles

Number of vehicles sold

y2 = Orders

Number of orders received at the garage

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Coll-Serrano, V.; Blasco-Blasco, O. (2006). Evaluacion de la Eficiencia mediante el Análisis Envolvente de Datos. Introduccion a los Modelos Básicos.

See Also

make_deadata

Examples

# Example. How to read data with deaR
data("Coll_Blasco_2006")
data_example <- make_deadata(Coll_Blasco_2006,
                             dmus = 1,
                             ni = 2,
                             no = 2)

Description

Computes arbitrary, benevolent and aggressive formulations of cross-efficiency under any returns-to-scale. Doyle and Green (1994) present three alternatives ways of formulating the secondary goal (wich will minimize or maximize the other DMUs' cross-efficiencies in some way). Methods II and III are implemented in deaR with any returns-to-scale. The maverick index is also calculated.

Usage

cross_efficiency(datadea,
                 dmu_eval = NULL,
                 dmu_ref = NULL,
                 epsilon = 0, 
                 orientation = c("io", "oo"),
                 rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                 L = 1,
                 U = 1,
                 selfapp = TRUE,
                 correction = FALSE,
                 M2 = TRUE,
                 M3 = TRUE)

Arguments

Note

(1) We can obtain negative cross-efficiency in the input-oriented DEA model under no constant returns-to-scale. However, the same does not happen in the case of the output-oriented VRS DEA model. For this reason, the proposal of Lim and Zhu (2015) is implemented in deaR to calculate the input-oriented cross-efficiency model under no constant returns-to-scale.

(2) The multiplier model can have alternate optimal solutions (see note 1 in model_multiplier). So, depending on the optimal weights selected we can obtain different cross-efficiency scores.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Sexton, T.R., Silkman, R.H.; Hogan, A.J. (1986). Data envelopment analysis: critique and extensions. In: Silkman RH (ed) Measuring efficiency: an assessment of data envelopment analysis, vol 32. Jossey-Bass, San Francisco, pp 73–104. doi:10.1002/ev.1441

Doyle, J.; Green, R. (1994). “Efficiency and cross efficiency in DEA: derivations, meanings and the uses”, Journal of Operational Research Society, 45(5), 567–578. doi:10.2307/2584392

Cook, W.D.; Zhu, J. (2015). DEA Cross Efficiency. In: Zhu, J. (ed) Data Envelopment Analysis. A Handbook of Models and Methods. International Series in Operations Research & Management Science, vol 221. Springer, Boston, MA, 23-43. doi:10.1007/978-1-4899-7553-9_2

Lim, S.; Zhu, J. (2015). "DEA Cross-Efficiency Under Variable Returns to Scale". Journal of Operational Research Society, 66(3), p. 476-487. doi:10.1057/jors.2014.13

See Also

model_multiplier, cross_efficiency_fuzzy

Examples

# Example 1.
# Arbitrary formulation. Input-oriented model under constant returns-to-scale.
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989, 
                             inputs = 2:4, 
                             outputs = 5:6)
result <- cross_efficiency(data_example, 
                           orientation = "io", 
                           rts = "crs", 
                           selfapp = TRUE)
result$Arbitrary$cross_eff
result$Arbitrary$e

# Example 2.
# Benevolent formulation (method II). Input-oriented.
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989, 
                             inputs = 2:4, 
                             outputs = 5:6)
result <- cross_efficiency(data_example, 
                           orientation = "io", 
                           selfapp = TRUE)
result$M2_ben$cross_eff
result$M2_ben$e

# Example 3.
# Benevolent formulation (method III). Input-oriented.
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989, 
                             inputs = 2:4, 
                             outputs = 5:6)
result <- cross_efficiency(data_example, 
                           orientation = "io", 
                           selfapp = TRUE)
result$M3_ben$cross_eff
result$M3_ben$e
  
# Example 4.
# Arbitrary formulation. Output-oriented.
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989,
                             inputs = 2:4, 
                             outputs = 5:6)
result <- cross_efficiency(data_example, 
                           orientation = "oo", 
                           selfapp = TRUE)
result$Arbitrary$cross_eff
result$Arbitrary$e

# Example 5.
# Arbitrary formulation. Input-oriented model under vrs returns-to-scale.
data("Lim_Zhu_2015")
data_example <- make_deadata(Lim_Zhu_2015,
                             ni = 1, 
                             no = 5)
cross <- cross_efficiency(data_example,
                          epsilon = 0,
                          orientation = "io",
                          rts = "vrs",
                          selfapp = TRUE,
                          M2 = FALSE,
                          M3 = FALSE)
cross$Arbitrary$e

Description

Computes the cross-efficiency fuzzy tables from DEA fuzzy data or a Guo-Tanaka DEA model solution. The (crisp) relative efficiencies for the case h = 1 are obtained from the CCR model (model_multiplier).

Usage

cross_efficiency_fuzzy(datadea,
                       orientation = c("io", "oo"),
                       h = 1,
                       selfapp = TRUE)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Doyle, J.; Green, R. (1994). “Efficiency and Cross Efficiency in DEA: Derivations, Meanings and the Uses”, Journal of Operational Research Society, 45(5), 567–578. doi:10.2307/2584392

Guo, P.; Tanaka, H. (2001). "Fuzzy DEA: A Perceptual Evaluation Method", Fuzzy Sets and Systems, 119, 149–160. doi:10.1016/S0165-0114(99)00106-2

León, T.; Liern, V.; Ruiz, J.L.; Sirvent, I. (2003). "A Fuzzy Mathematical Programming Approach to the assessment of efficiency with DEA Models", Fuzzy Sets Systems, 139(2), 407–419. doi:10.1016/S0165-0114(02)00608-5

Sexton, T.R., Silkman, R.H.; Hogan, A.J. (1986). Data envelopment analysis: critique and extensions. In: Silkman RH (ed) Measuring efficiency: an assessment of data envelopment analysis, vol 32. Jossey-Bass, San Francisco, pp 73–104. doi:10.1002/ev.1441

Examples

data("Guo_Tanaka_2001")
 datadea <- make_deadata_fuzzy(datadea = Guo_Tanaka_2001, 
                               inputs.mL = 2:3, 
                               inputs.dL = 4:5, 
                               outputs.mL = 6:7, 
                               outputs.dL = 8:9)
 result <- cross_efficiency_fuzzy(datadea = datadea, 
                                  h = seq(0, 1, 0.2))

Description

Data from 20 University accounting departments in the UK.

Usage

data("Departments")

Format

Data frame with 20 rows and 11 columns. Definition of inputs (X) and outputs (Y):

x1 = Staff

Average Full Time Academic Staff 82/3-84/5)

x2 = Salaries

1984-5 Salaries Academics and Related (in pounds))

x3 = Other_Exp

1984-5 Other Expenses (in pounds)

y1 = Undergrad

Average Number Undergraduates 82/3-84/5

y2 = Research_post

Research Postgraduates

y3 = Taught_post

Taught Postgraduates

y4 = Res_co_income

Research council income (in pounds)

y5 = Other_res_income

Other research income (in pounds)

y6 = Other_income

Other income (in pounds)

y7 = Publications

Number of publications

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Tomkins, C.; Green, R. (1988). "An Experiment in the Use of Data Envelopment Analysis for Evaluating the Efficiency of UK University Departments of Accounting", Financial Accountability and Management, 4(2), 147-164. doi:10.1111/j.1468-0408.1988.tb00296.x

See Also

make_deadata, model_basic

Examples

# Example.
# Replication of results DEA1 in Tomkins and Green (1988)
data("Departments")
# Calculate Total income
Departments$Total_income <- Departments[, 5] + Departments[, 6] + Departments[, 7]
data_example <- make_deadata(Departments,
                             inputs = 9,
                             outputs = c(2, 3, 4, 12))
result <- model_basic(data_example,
                      orientation = "io",
                      rts = "crs")
efficiencies(result) # Table 3 (p.156)
references(result) # Table 3 (p.157)

Description

Data adapted from Tomkins and Green (1988). 13 DMUs using 3 inputs to produce 2 outputs.

Usage

data("Doyle_Green_1994")

Format

Data frame with 13 rows and 6 columns. Definition of inputs (X) and outputs (Y):

y1 = Undergraduate

Number of undergraduates

y2 = Postgraduates

Number of postgraduates (taught and research)

y3 = Research_income

Research and other income

y4 = Publications

Number of publications

x1 = Salaries

Salaries of academic and related staff

x2 = Other_expenses

Other expenses

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Doyle, J.; Green, R. (1994). “Efficiency and cross efficiency in DEA: derivations, meanings and the uses”, Journal of Operational Research Society, 45(5), 567–578. doi:10.2307/2584392

See Also

make_deadata, model_multiplier, cross_efficiency

Examples

# Example.
data("Doyle_Green_1994")
data_example <- make_deadata(datadea = Doyle_Green_1994,
                            dmus = 1,
                            inputs = 6:7,
                            outputs = 2:5)
result <- cross_efficiency(data_example,
                           orientation = "io",
                           selfapp = TRUE)
result$Arbitrary$cross_eff
result$Arbitrary$e
# Aggressive using method II
result$M2_agg$cross_eff
# Aggressive using method III
result$M3_agg$cross_eff

Description

Data of the industrial economy of China in 2005-2009 (data in wide format).

Usage

data("Economy")

Format

Data frame with 31 rows and 16 columns. Definition of inputs (X) and outputs (Y):

x1 = Capital

Total assets (in 100 million RMB)

x2 = Labor

Annual average employed persons (in 10000 persons)

y1 = GIOV

Gross industrial output value (in 100 million RMB)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Wang, Y.; Lan, Y. (2011). "Measuring Malmquist Productiviy Index: A New Approach Based on Double Frontiers Data Envelopment Analysis". Mathematical and Computer Modelling, 54, 2760-2771. doi:10.1016/j.mcm.2011.06.064

See Also

make_malmquist, malmquist_index

Examples

# Example . Data in wide format.
# Replication of results in Wang and Lan (2011, p. 2768)
data("Economy")
data_example <- make_malmquist(Economy,
                               nper = 5,
                               arrangement = "horizontal",
                               ni = 2,
                               no = 1)
result <- malmquist_index(data_example)

Description

Data of the industrial economy of China in 2005-2009 (data in long format).

Usage

data("EconomyLong")

Format

Data frame with 155 rows and 5 columns. Definition of inputs (X) and outputs (Y):

x1 = Capital

Total assets (in 100 million RMB)

x2 = Labor

Annual average employed persons (in 10000 persons)

y1 = GIOV

Gross industrial output value (in 100 million RMB)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Wang, Y.; Lan, Y. (2011). "Measuring Malmquist Productiviy Index: A New Approach Based on Double Frontiers Data Envelopment Analysis". Mathematical and Computer Modelling, 54, 2760-2771. doi:10.1016/j.mcm.2011.06.064

See Also

make_malmquist, malmquist_index

Examples

# Example. Data in long format.
# Replication of results in Wang and Lan (2011, p. 2768)
data("EconomyLong")
data_example <- make_malmquist(EconomyLong,
                               percol = 2,
                               arrangement = "vertical",
                               ni = 2,
                               no = 1)
result <- malmquist_index(data_example)

Description

Returns the efficient DMUs evaluated in a dea class object.

Usage

eff_dmus(deasol, tol = 1e-04)

Arguments

Value

A numeric vector containing which DMUs has been evaluated as efficient. This vector is empty if there is not any efficient DMU.

Note

If maxslack is FALSE, the slacks computed in the first stage are supposed to be the max slacks.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Examples

dataFortune <- make_deadata(Fortune500,
                            ni = 3,
                            no = 2)
ccrFortune <- model_basic(dataFortune)
eff_dmus(ccrFortune)

Description

Extract the scores (optimal objective values) of the evaluated DMUs from a conventional, fuzzy or stochastic DEA solution. Note that these scores may not always be interpreted as efficiencies.

Usage

efficiencies(x, ...)

Arguments

Description

Extract the scores (optimal objective values) of the evaluated DMUs from a conventional DEA solution. Note that these scores may not always be interpreted as efficiencies.

Usage

## S3 method for class 'dea'
efficiencies(x, ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Tomkins, C.; Green, R. (1988). “An Experiment in the Use of Data Envelopment Analysis for Evaluating the Efficiency of UK University Departments of Accounting”. Financial Accountability and Management 4(2): 147.

Examples

# Replication results model DEA1 in Tomkins and Green (1988)
data("Departments")
# Calculate Total income
Departments$Total_income <- Departments[, 5] + Departments[, 6] + Departments[, 7] 
data_DEA1 <- make_deadata(Departments,
                          inputs = 9,
                          outputs = c(2, 3, 4, 12))
result <- model_basic(data_DEA1,
                      orientation = "io",
                      rts = "crs")
efficiencies(result) # Table 3 (p.156)

Description

Extract the scores (optimal objective values) of the evaluated DMUs from a fuzzy DEA solution. Note that these scores may not always be interpreted as efficiencies.

Usage

## S3 method for class 'dea_fuzzy'
efficiencies(x, ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Boscá, J.E.; Liern, V.; Sala, R.; Martínez, A. (2011). "Ranking Decision Making Units by Means of Soft Computing DEA Models". International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19(1), p.115-134.

Examples

# Replication of results in Boscá, Liern, Sala and Martínez (2011, p.125)
data("Leon2003")
data_example <- make_deadata_fuzzy(datadea = Leon2003,
                                   inputs.mL = 2, 
                                   inputs.dL = 3, 
                                   outputs.mL = 4, 
                                   outputs.dL = 5)
result <- modelfuzzy_kaoliu(data_example,
                            kaoliu_modelname = "basic", 
                            alpha = seq(0, 1, by = 0.1), 
                            orientation = "io", 
                            rts = "vrs")
efficiencies(result)

Description

Data of 19 coal-fired steam-electric generating plants operating in Illinois in 1978. Each plant uses 3 inputs to produce 1 output.

Usage

data("Electric_plants")

Format

Data frame with 18 rows and 5 columns. Definition of inputs (X) and outputs (Y):

x1 = Labor

Labor average annual employment

x2 = Fuel

Fuel $10^{10}$ Btu

x3 = Capital

Capital MW (fixed input)

y1 = Output

Output $10^6$ Kwh

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Färe, R.; Grosskopf, S.; Kokkenlenberg, E. (1989). "Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach". International Economic Review, 30(3), 655-666.

Simar, L.; Wilson, P.W. (1998). "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models". Management Science, 44(1), 49-61.

See Also

make_deadata, model_basic

Examples

# Example. Replication of results in Simar and Wilson (1998, p.59)
data("Electric_plants")
data_example <- make_deadata(Electric_plants,
                             dmus = 1,
                             ni = 3,
                             no = 1)
result <- model_basic(data_example,
                      orientation = "io",
                      rts = "vrs")
efficiencies(result)

Description

Find a set of extreme efficient DMUs from a deadata object.

Usage

extreme_efficient(datadea,
             dmu_ref = NULL,
             rts = c("crs", "vrs", "nirs", "ndrs"),
             tol = 1e-6)

Arguments

Value

A numeric vector representing a extreme efficient subset of DMUs.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Charnes, A.; Cooper, W.W.; Thrall, R.M. (1991) "A structure for classifying and characterizing efficiency and inefficiency in data envelopment analysis", Journal of Productivity Analisys, 2, 197–237.

Examples

data("PFT1981")
datadea <- make_deadata(PFT1981,
                        ni = 5,
                        no = 3)
# We find a extreme efficient subset from a cluster formed by the first 20 DMUs
result <- extreme_efficient(datadea = datadea,
                            dmu_ref = 1:20)

Description

This dataset consists of 15 firms from the Fortune 500 list 1995 (https://fortune.com/ranking/fortune500/) with 3 inputs and 2 outputs.

Usage

data("Fortune500")

Format

Data frame with 15 rows and 6 columns. Definition of inputs (X) and outputs (Y):

x1 = Assets

Assets (millions of dollars)

x2 = Equity

Equity (millions of dollars)

x3 = Employees

Number of employees

y1 = Revenue

Revenue (millions of dollars)

y2 = Profit

Profit (millions of dollars)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Zhu, J. (2014). Quantitative Models for Performance Evaluation and Benchmarking. Data Envelopment Analysis with Spreadsheets. 3rd Edition Springer, New York. doi:10.1007/978-3-319-06647-9

See Also

make_deadata, model_multiplier

Examples

data("Fortune500")
data_Fortune <- make_deadata(datadea = Fortune500,
                             dmus = 1,
                             inputs = 2:4,
                             outputs = 5:6)
result <- model_multiplier(data_Fortune,
                           epsilon = 1e-6,
                           orientation = "io",
                           rts = "crs")
# results for General Motors and Ford Motor are not shown
# by deaR because the solution is infeasible
efficiencies(result)
multipliers(result)

Description

Data of 11 DMUs with two inputs and one output.

Usage

data("Fried1993")

Format

Data frame with 11 rows and 4 columns. Definition of inputs (X) and outputs (Y):

x1

Input 1

x2

Input 2

y1

Output 1

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Ali, A.I.; Seiford, L.M. (1993). The Mathematical Programming Approach to Efficiency Analysis. In Fried, H.O.; Knox Lovell, C.A.; Schmidt, S.S.(eds.), The Measurement of Productive Efficiency. Techniques and Applications. New York: Oxford University Press.

See Also

make_deadata, model_basic

Examples

# Example. Replication of results in Ali and (1993, p.143).
data("Fried1993")
data_example <- make_deadata(Fried1993,
                             ni = 2,
                             no = 1)
result <- model_basic(data_example,
                      orientation = "oo",
                      rts = "vrs")
efficiencies(result)
targets(result)

Description

Synthetic dataset of 5 DMUs with 3 inputs and 3 outputs containing fuzzy and crisp data.

Usage

data("FuzzyExample")

Format

Data frame with 5 rows and 15 columns.

DMU

DMU names

Input1.mL

First Input (crisp numbers)

Input2.mL

Second Input (left centers)

Input2.mR

Second Input (right centers)

Input2.dL

Second Input (left radii)

Input2.dR

Second Input (right radii)

Input3.mL

Third Input (centers)

Input3.dL

Third Input (radii)

Output1.mL

First Output (crisp numbers)

Output2.mL

Second Output (left centers)

Output2.mR

Second Output (right centers)

Output2.dL

Second Output (radii)

Output3.mL

Third Output (centers)

Output3.dL

Third Output (left radii)

Output3.dR

Third Output (right radii)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

See Also

make_deadata_fuzzy

Examples

# Example. Reading the data.
data("FuzzyExample")
datafuzzy <- make_deadata_fuzzy(FuzzyExample, 
                                inputs.mL = c(2, 3, 7),
                                inputs.mR = c(NA, 4, NA),
                                inputs.dL = c(NA, 5, 8),
                                inputs.dR = c(NA, 6, NA),
                                outputs.mL = c(9, 10 , 13),
                                outputs.mR = c(NA, 11, NA),
                                outputs.dL = c(NA, 12, 14),
                                outputs.dR = c(NA, NA, 15))

Description

Data of 13 DMUs using 3 inputs to produce 2 outputs.

Usage

data("Golany_Roll_1989")

Format

Data frame with 13 rows and 6 columns. Definition of inputs (X) and outputs (Y):

x1

Input 1

x2

Input 2

x3

Input 3

y1

Output 1

y1

Output 2

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Golany, B.; Roll, Y. (1989). "An Application Procedure for DEA". Omega, International Journal of Management Science, 17(3), 237-250. doi:10.1016/0305-0483(89)90029-7

See Also

make_deadata, model_multiplier, cross_efficiency

Examples

# Example.
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989,
                             dmus = 1,
                             inputs = 2:4,
                             outputs = 5:6)
result <- cross_efficiency(data_example,
                           orientation = "io",
                           selfapp = TRUE)
result$Arbitrary$cross_eff
result$Arbitrary$e

Description

Data of 8 DMUs producing 1 output (Y) by using 1 input (X) for two periods of time.

Usage

data("Grifell_Lovell_1999")

Format

Data frame with 16 rows and 4 columns. Definition of inputs (X) and outputs (Y):

X

Input

Y

Output

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Grifell-Tatjé, E.; Lovel, C.A.K. (1999). "A Generalized Malmquist productivity index". Top, 7(1), 81-101.

See Also

make_malmquist, malmquist_index

Examples

# Example. Replication of results in Grifell-Tatjé and Lovell (1999, p. 100).
data("Grifell_Lovell_1999")
data_example <- make_malmquist(Grifell_Lovell_1999,
                               percol = 1,
                               dmus = 2,
                               inputs = 3,
                               outputs = 4,
                               arrangement = "vertical")

result_fgnz <- malmquist_index(data_example,
                               orientation = "oo",
                               rts = "vrs",
                               type1 = "cont",
                               type2 = "fgnz")

result_fgnz$mi

Description

Data of 5 DMUs with two symmetric triangular fuzzy inputs, Xj = (xj, alphaj), and two symmetric triangular fuzzy outputs, Yj = (yj, betaj).

Usage

data("Guo_Tanaka_2001")

Format

Data frame with 5 rows and 9 columns. Definition of fuzzy inputs (X) and fuzzy outputs (Y):

x1

Input 1

x2

Input 2

alpha1

spread vector Input 1

alpha2

spread vector Input 2

y1

Output 1

y2

Output 2

beta1

spread vector Output 1

beta2

spread vector Output 2

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Guo, P.; Tanaka, H. (2001). "Fuzzy DEA: A Perceptual Evaluation Method", Fuzzy Sets and Systems, 119, 149–160. doi:10.1016/S0165-0114(99)00106-2

See Also

make_deadata_fuzzy, modelfuzzy_guotanaka, cross_efficiency_fuzzy

Examples

data("Guo_Tanaka_2001")
data_example <- make_deadata_fuzzy(Guo_Tanaka_2001,
                                   dmus = 1,
                                   inputs.mL = 2:3,
                                   inputs.dL = 4:5,
                                   outputs.mL = 6:7,
                                   outputs.dL = 8:9)
result <- modelfuzzy_guotanaka(data_example,
                               h = seq(0, 1, by = 0.1),
                               orientation = "io")
efficiencies(result)

Description

This dataset consists of 23 four- and five-plum ITHs in Taipei in 2006. Authors consider 4 inputs and 3 outputs.

Usage

data("Hotels")

Format

Data frame with 23 rows and 8 columns. Definition of inputs (X) and outputs (Y):

x1 = Employees

Total number of employees)

x2 = Guest_rooms

Total number of guest rooms)

x3 = Area_F&B

Total area of F&B departments (in 36 square-feet)

x4 = Operating_cost

Total operating cost (in NT$)

y1 = Room_revenue

Room revenues (in NT$)

y2 = F&B_revenue

F&B revenues (in NT$)

y3 = Other_revenue

Other revenues (in NT$)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Wu, J.; Tsai, H. and Zhou, Z. (2011). "Improving efficiency in International tourist hotels in Taipei using a non-radial DEA mode", Internationl Journal of Contemporary Hospitality Management, 23(1), 66-83. doi:10.1108/09596111111101670

See Also

make_deadata, model_nonradial

Examples

# Example. Replication of results in Wu,Tsai and Zhou (2011)
data("Hotels")
data_hotels <- make_deadata(Hotels,
                            dmus = 1,
                            inputs = 2:5,
                            outputs = 6:8)
result <- model_nonradial(data_hotels,
                          orientation = "oo",
                          rts = "vrs")
efficiencies(result)

Description

Data of 30 DMUs with two desirable inputs, two desirable outputs and one udesirable output.

Usage

data("Hua_Bian_2007")

Format

Data frame with 30 rows and 6 columns. Definition of inputs (X) and outputs (Y):

x1 = D-Input1

Desirable Input 1

x2 = D-Input2

Desirable Input 2

y1 = D-Output1

Desirable Output 1

y2 = D-Output2

Desirable Output 2

y3 = UD-Output1

Undesirable Output 1

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Hua Z.; Bian Y. (2007). DEA with Undesirable Factors. In: Zhu J., Cook W.D. (eds) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Springer, Boston, MA. doi:10.1007/978-0-387-71607-7_6

See Also

make_deadata, model_basic

Examples

# Example. Replication of results in Hua and Bian (2007).
data("Hua_Bian_2007")
# The third output is an undesirable output
data_example <- make_deadata(Hua_Bian_2007,
                             ni = 2,
                             no = 3,
                             ud_outputs = 3)

# Translation parameter (vtrans_o) is set to 1500
result <- model_basic(data_example,
                      orientation = "oo",
                      rts = "vrs",
                      vtrans_o = 1500)
eff <- efficiencies(result)
1 / eff # results M5 in Table 6-5 (p.119)

Description

Checks whether an R object is of dea class or not.

Usage

is.dea(x)

Arguments

Value

Returns TRUE if its argument is a dea object (that is, has "dea" amongst its classes) and FALSE otherwise.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Description

Checks whether an R object is of dea_fuzzy class or not.

Usage

is.dea_fuzzy(x)

Arguments

Value

Returns TRUE if its argument is a dea_fuzzy object (that is, has "dea_fuzzy" amongst its classes) and FALSE otherwise.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Description

Checks whether an R object is of deadata class or not.

Usage

is.deadata(x)

Arguments

Value

Returns TRUE if its argument is a deadata object (that is, has "deadata" amongst its classes) and FALSE otherwise.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Description

Checks whether an R object is of deadata_fuzzy class or not.

Usage

is.deadata_fuzzy(x)

Arguments

Value

Returns TRUE if its argument is a deadata_fuzzy object (that is, has "deadata_fuzzy" amongst its classes) and FALSE otherwise.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Description

Checks whether a subset of DMUs is friends or not, according to Tone (2010).

Usage

is.friends(datadea,
             dmu_eval = NULL,
             dmu_ref = NULL,
             rts = c("crs", "vrs", "nirs", "ndrs"),
             tol = 1e-6)

Arguments

Value

Returns TRUE if dmu_eval is friends of dmu_ref, and FALSE otherwise.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Tone, K. (2010). "Variations on the theme of slacks-based measure of efficiency in DEA", European Journal of Operational Research, 200, 901-907. doi:10.1016/j.ejor.2009.01.027

See Also

maximal_friends, model_sbmeff

Examples

data("PFT1981")
datadea <- make_deadata(PFT1981,
                        ni = 5,
                        no = 3)
subset1 <- c(15, 16, 17, 19) # Subset of DMUs to be checked
result1 <- is.friends(datadea = datadea,
                      dmu_eval = subset1,
                      dmu_ref = 1:20) # We only consider a cluster formed by the first 20 DMUs
subset2 <- c(15, 16, 17, 20) # Another subset of DMUs to be checked
result2 <- is.friends(datadea = datadea,
                      dmu_eval = subset2,
                      dmu_ref = 1:20) # We only consider a cluster formed by the first 20 DMUs

Description

Data of 24 university libraries in Taiwan with one input and five outputs.

Usage

data("Kao_Liu_2003")

Format

Data frame with 24 rows and 11 columns. Definition of fuzzy inputs (X) and fuzzy outputs (Y):

x1 = Patronage

It is a weighted sum of the standardized scores of faculty, graduate students, undergraduate students, and extension students in the range of 0 and 1.

y1 = Collections

Books, serials, microforms, audiovisual works, and database.

y2 = Personnel

Classified staff, unclassified staff, and student assistants.

y3 = Expenditures

Capital expenditure, operating expenditure, and special expenditure.

y4 = Buildings

Area and seats

y5 = Services

Operating hours, attendance, circulation, communication channels, range of services, amount of services, etc.

beta3_l

lower spread vector Expenditures

beta3_u

upper spread vector Expenditures

beta5_l

lower spread vector Services

beta5_u

upper spread vector Services

Note

There are three observations that are missing: expenditures of Library 24 and services of Library 22 and Library 23. Kao and Liu (2000b) represent the expenditures of Library 24 by the triangular fuzzy number Y = (0.11; 0.41; 1.0). The services of Library 22 and Library 23 are expressed by a same triangular fuzzy number Y = (0.41; 0.69; 1.0).

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Kao, C., Liu, S.T. (2003). “A mathematical programming approach to fuzzy efficiency ranking”, International Journal of Production Economics, 85. doi:10.1016/S0925-5273(03)00026-4

See Also

make_deadata_fuzzy, model_basic

Examples

# Example. Replication of results in Kao and Liu (2003, p.152)
data_example <- make_deadata_fuzzy(Kao_Liu_2003,
                                   dmus = 1,
                                   inputs.mL = 2,
                                   outputs.mL = 3:7,
                                   outputs.dL = c(NA, NA, 8, NA, 10),
                                   outputs.dR = c(NA, NA, 9, NA, 11))
result <- modelfuzzy_kaoliu(data_example,
                            kaoliu_modelname = "basic",
                            orientation = "oo",
                            rts = "vrs",
                            alpha = 0)
eff <- efficiencies(result)
eff

Description

Extract the lambdas of the DMUs from a dea or dea_fuzzy solution.

Usage

lambdas(deasol)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Examples

data("Coll_Blasco_2006")
data_example <- make_deadata(Coll_Blasco_2006,
                             ni = 2, 
                             no = 2)
result <- model_multiplier(data_example, 
                           orientation = "io",
                           rts = "crs")
lambdas(result)

Description

Data of 8 DMUs with one symmetric triangular fuzzy inputs: Xj = (xj, alphaj), and one symmetric triangular fuzzy outputs: Yj = (yj, betaj).

Usage

data("Leon2003")

Format

Data frame with 8 rows and 5 columns. Definition of fuzzy inputs (X) and fuzzy outputs (Y):

x1

Input 1

alpha1

spread vector Input 1

y1

Output 1

beta1

spread vector Output 1

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Leon, T.; Liern, V. Ruiz, J.; Sirvent, I. (2003). "A Possibilistic Programming Approach to the Assessment of Efficiency with DEA Models", Fuzzy Sets and Systems, 139, 407–419. doi:10.1016/S0165-0114(02)00608-5

See Also

make_deadata_fuzzy, modelfuzzy_possibilistic, cross_efficiency_fuzzy, modelfuzzy_guotanaka

Examples

# Example. Replication of results in Leon et. al (2003, p. 416)
data("Leon2003")
data_example <- make_deadata_fuzzy(Leon2003,
                                   dmus = 1,
                                   inputs.mL = 2,
                                   inputs.dL = 3,
                                   outputs.mL = 4,
                                   outputs.dL = 5)
result <- modelfuzzy_possibilistic(data_example,
                                   h = seq(0, 1, by = 0.1),
                                   orientation = "io",
                                   rts = "vrs")
efficiencies(result)

Description

Data for 23 public libraries of the Tokyo Metropolitan Area in 1986.

Usage

data("Libraries")

Format

Data frame with 23 rows and 7 columns. Definition of inputs (X) and outputs (Y):

x1 = AREA

Floor area (unit=1000 m2)

x2 = BOOKS

Number of books (unit=1000)

x3 = STAFF

Staff

x4 = POPULATION

Population (unit=1000)

y1 = REGISTERED

Registered residents (unit=1000)

y2 = BORROWED

Borrowed books (unit=1000)

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Cooper, W.W.; Seiford, L.M. and Tone, K. (2007). Data Envelopment Analysis. A Comprehensive Text with Models, Applications, References and DEA-Solver Software. Springer.

See Also

make_deadata, model_basic

Examples

# Example 1. Non-controllable input (POPULATION).
# Replication of results in Cooper, Seiford and Tone (2007, p.221)
data(Libraries)
# POPULATION (non-controllable input) is the 4th input.
data_example <- make_deadata(Libraries,
                             dmus = 1,
                             inputs = 2:5,
                             nc_inputs = 4,
                             outputs = 6:7)
result <- model_basic(data_example,
                      orientation = "io",
                      rts = "crs")
efficiencies(result)
targets(result)

# Example 2. Non-discretionary input (POPULATION).
data(Libraries)
# POPULATION (non-controllable input) is the 4th input.
data_example2 <- make_deadata(Libraries,
                              dmus=1,
                              inputs=2:5,
                              nd_inputs=4,
                              outputs=6:7)
result2 <- model_basic(data_example2,
                       orientation="io",
                       rts="crs")
efficiencies(result2)
targets(result2)

Description

Data of 37 R&D project proposal relating to the Turkish iron and steel industry. Authors consider one input and five outputs.

Usage

data("Lim_Zhu_2015")

Format

Data frame with 37 rows and 7 columns. Definition of inputs (X) and outputs (Y):

x1 = Budget

Budget

y1 = Indirect_economic

Indirect economic contribution

y2 = Direct_economic

Direct economic contribution

y3 = Technical

Technical contribution

y4 = Social

Social contribution

y5 = Scientific

Scientific contribution

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Source

Lim, S.; Zhu, J. (2015). "DEA Cross-Efficiency Under Variable Returns to Scale". Journal of Operational Research Society, 66(3), p. 476-487. doi:10.1057/jors.2014.13

See Also

make_deadata, model_multiplier, cross_efficiency

Examples

# Example. Arbitrary formulation.
# Input-oriented model under variable returns-to-scale.
data("Lim_Zhu_2015")
data_example <- make_deadata(Lim_Zhu_2015,
                             dmus = 1,
                             ni = 1,
                             no = 5)
cross <- cross_efficiency(data_example,
                          epsilon = 0,
                          orientation = "io",
                          rts = "vrs",
                          selfapp = TRUE,
                          M2 = FALSE,
                          M3 = FALSE)
cross$Arbitrary$e

Description

This function creates, from a data frame, a deadata structure, which is as list with fields input, output, dmunames, nc_inputs, nc_outputs, nd_inputs, nd_outputs.

Usage

make_deadata(datadea = NULL,
          ni = NULL,
          no = NULL,
          dmus = 1,
          inputs = NULL,
          outputs = NULL,
          nc_inputs = NULL,
          nc_outputs = NULL,
          nd_inputs = NULL,
          nd_outputs = NULL,
          ud_inputs = NULL, 
          ud_outputs = NULL)

Arguments

Value

An object of class deadata

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Examples

data("Coll_Blasco_2006")
data_example <- make_deadata(datadea = Coll_Blasco_2006,
                             ni = 2, 
                             no = 2)
# This is the same as:
data_example <- make_deadata(Coll_Blasco_2006,
                             inputs = 2:3, 
                             outputs = 4:5)
# And the same as:
dmunames <- c("A", "B", "C", "D", "E", "F")
nd <- length(dmunames) # Number of DMUs
inputnames <- c("Employees", "Capital")
ni <- length(inputnames) # Number of Inputs
outputnames <- c("Vehicles", "Orders")
no <- length(outputnames) # Number of Outputs
inputs <- matrix(c(8, 8, 11, 15, 14, 12, 12, 13, 11, 18, 18, 20),
                 nrow = ni, ncol = nd, dimnames = list(inputnames, dmunames))
outputs <- matrix(c(14, 20, 25, 42, 8, 30, 25, 8, 40, 22, 24, 30),
                  nrow = no, ncol = nd, dimnames = list(outputnames, dmunames))
data_example <- make_deadata(inputs = inputs,
                             outputs = outputs)                
# If the first input is a non-controllable input:
data_example <- make_deadata(Coll_Blasco_2006,
                             inputs = 2:3,
                             outputs = 4:5, 
                             nc_inputs = 1)
# If the second output is a non-discretionary output:
data_example <- make_deadata(Coll_Blasco_2006,
                             inputs = 2:3, 
                             outputs = 4:5, 
                             nd_outputs = 2)
# If the second input is a non-discretionary input and the second output is an undesirable:
data_example <- make_deadata(Coll_Blasco_2006,
                             inputs = 2:3, 
                             outputs = 4:5, 
                             nd_inputs = 2, 
                             ud_outputs = 2)

Description

This function creates, from a data frame, a deadata_fuzzy structure, which is as list with fields input, output and dmunames. At the same time, input and output are lists with fields mL, mR, dL and dR.

Usage

make_deadata_fuzzy(datadea,
                dmus = 1,
                inputs.mL = NULL,
                inputs.mR = NULL,
                inputs.dL = NULL,
                inputs.dR = NULL,
                outputs.mL = NULL,
                outputs.mR = NULL,
                outputs.dL = NULL,
                outputs.dR = NULL,
                nc_inputs = NULL,
                nc_outputs = NULL,
                nd_inputs = NULL,
                nd_outputs = NULL,
                ud_inputs = NULL,
                ud_outputs = NULL)

Arguments

Value

An object of class deadata_fuzzy.

Examples

# Example 1. If inputs and/or outputs are symmetric triangular fuzzy numbers
data("Leon2003")
data_example <- make_deadata_fuzzy(datadea = Leon2003, 
                                   inputs.mL = 2,
                                   inputs.dL = 3,
                                   outputs.mL = 4,
                                   outputs.dL = 5)
# Example 2. If inputs and/or outputs are non-symmetric triangular fuzzy numbers
data("Kao_Liu_2003")
data_example <- make_deadata_fuzzy(Kao_Liu_2003, 
                                   inputs.mL = 2, 
                                   outputs.mL = 3:7, 
                                   outputs.dL = c(NA, NA, 8, NA, 10),
                                   outputs.dR = c(NA, NA, 9, NA, 11))

Description

This function creates, from a data frame, a list of deadata objects.

Usage

make_malmquist(datadea,
               nper = NULL,
               percol = NULL,
               arrangement  = c("horizontal", "vertical"),
               ...)

Arguments

Value

An object of class deadata

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

Examples

# Example 1. If you have a dataset in wide format.
data("Economy")
data_example <- make_malmquist(datadea = Economy, 
                               nper = 5, 
                               arrangement = "horizontal",
                               ni = 2, 
                               no = 1)
# This is the same as:
data_example <- make_malmquist(datadea = Economy,
                               nper = 5, 
                               arrangement = "horizontal",
                               inputs = 2:3, 
                               outputs = 4)
# Example 2. If you have a dataset in long format.
data("EconomyLong")
data_example2 <- make_malmquist(EconomyLong,
                                percol = 2, 
                                arrangement = "vertical",
                                inputs = 3:4, 
                                outputs = 5)

Description

This function calculates the input/output oriented Malmquist productivity index under constant or variable returns-to-scale.

Usage

malmquist_index(datadealist,
                dmu_eval = NULL,
                dmu_ref = NULL,
                orientation = c("io", "oo"),
                rts = c("crs", "vrs"),
                type1 = c("cont", "seq", "glob"),
                type2 = c("fgnz", "rd", "gl", "bias"),
                tc_vrs = FALSE,
                vtrans_i = NULL,
                vtrans_o = NULL)

Arguments

Value

A numeric list with Malmquist index and other parameters.

Note

In the results: EC = Efficiency Change, PTEC = Pure Technical Efficiency Change, SEC = Scale Efficiency Change, TC = Technological Change, MI = Malmquist Index

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolos ([email protected]). Department of Business Mathematics

Rafael Benitez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Caves, D.W.; Christensen, L. R.; Diewert, W.E. (1982). “The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity”. Econometrica, 50(6), 1393-1414.

Fare, R.; Grifell-Tatje, E.; Grosskopf, S.; Lovell, C.A.K. (1997). "Biased Technical Change and the Malmquist Productivity Index". Scandinavian Journal of Economics, 99(1), 119-127.

Fare, R.; Grosskopf, S.; Lindgren, B.; Roos, P. (1989). “Productivity Developments in Swedish Hospitals: A Malmquist Output Index Approach”. Discussion paper n. 89-3. Southern Illinois University. Illinois.

Fare, R.; Grosskopf, S.; Lindgren, B.; Roos, P. (1992). “Productivity changes in Swedish Pharmacies 1980-89: A nonparametric Malmquist Approach”. Journal of productivity Analysis, 3(3), 85-101.

Fare, R.; Grosskopf, S.; Norris, M.; Zhang, Z. (1994). “Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries”. American Economic Review, 84(1), 66-83.

Fare, R.; Grosskopf, S.; Roos, P. (1998), Malmquist Productivity Indexes: A Survey of Theory and Practice. In: Fare R., Grosskopf S., Russell R.R. (eds) Index Numbers: Essays in Honour of Sten Malmquist. Springer.

Grifell-Tatje, E.; Lovell, C.A.K. (1999). "A Generalized Malmquist productivity index". Top, 7(1), 81-101.

Pastor, J.T.; Lovell, C.A.k. (2005). "A global Malmquist productiviyt index". Economics Letters, 88, 266-271.

Ray, S.C.; Desli, E. (1997). "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment". The American Economic Review, 87(5), 1033-1039.

Shestalova, V. (2003). "Sequential Malmquist Indices of Productivity Growth: An Application to OECD Industrial Activities". Journal of Productivity Analysis, 19, 211-226.

Examples

# Example 1. With dataset in wide format.
# Replication of results in Wang and Lan (2011, p. 2768)
data("Economy")
data_example <- make_malmquist(datadea = Economy,
                               nper = 5, 
                               arrangement = "horizontal",
                               ni = 2, 
                               no = 1)
result <- malmquist_index(data_example, orientation = "io")
mi <- result$mi
effch <- result$ec
tech <- result$tc

# Example 2. With dataset in long format.
# Replication of results in Wang and Lan (2011, p. 2768)
data("EconomyLong")
data_example2 <- make_malmquist(EconomyLong,
                                percol = 2, 
                                arrangement = "vertical",
                                inputs = 3:4, 
                                outputs = 5)
result2 <- malmquist_index(data_example2, orientation = "io")
mi2 <- result2$mi
effch2 <- result2$ec
tech2 <- result2$tc

# Example 3. Replication of results in Grifell-Tatje and Lovell (1999, p. 100).
data("Grifell_Lovell_1999")
data_example <- make_malmquist(Grifell_Lovell_1999,
                               percol = 1,
                               dmus = 2,
                               inputs = 3,
                               outputs = 4,
                               arrangement = "vertical")
result_fgnz <- malmquist_index(data_example,
                               orientation = "oo",
                               rts = "vrs",
                               type1 = "cont",
                               type2 = "fgnz")
mi_fgnz <- result_fgnz$mi 

result_rd <- malmquist_index(data_example,
                             orientation = "oo",
                             rts = "vrs",
                             type1 = "cont",
                             type2 = "rd")
mi_rd <- result_rd$mi
 
result_gl <- malmquist_index(data_example,
                             orientation = "oo",
                             rts = "vrs",
                             type1 = "cont",
                             type2 = "gl")
mi_gl <- result_gl$mi

Description

Finds the maximal friends subsets of a given set of DMUs, according to Tone (2010). It uses an ascending algorithm in order to find directly maximal subsets.

Usage

maximal_friends(datadea,
             dmu_ref = NULL,
             rts = c("crs", "vrs", "nirs", "ndrs"),
             tol = 1e-6,
             silent = FALSE)

Arguments

Value

A list with numeric vectors representing maximal friends subsets of DMUs.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Tone, K. (2010). "Variations on the theme of slacks-based measure of efficiency in DEA", European Journal of Operational Research, 200, 901-907. doi:10.1016/j.ejor.2009.01.027

See Also

is.friends, model_sbmeff

Examples

## Not run: 
data("PFT1981")
datadea <- make_deadata(PFT1981,
                        ni = 5,
                        no = 3)
# We find maximal friends of a cluster formed by the first 20 DMUs
result <- maximal_friends(datadea = datadea,
                          dmu_ref = 1:20)

## End(Not run)

Description

Solve the additive model of Charnes et. al (1985). With the current version of deaR, it is possible to solve input-oriented, output-oriented, and non-oriented additive model under constant and non-constant returns to scale.

Besides, the user can set weights for the input slacks and/or output slacks. So, it is also possible to solve weighted additive models. For example: Measure of Inefficiency Proportions (MIP), Range Adjusted Measure (RAM), etc.

Usage

model_additive(datadea,
               dmu_eval = NULL,
               dmu_ref = NULL,
               orientation = NULL,
               weight_slack_i = 1,
               weight_slack_o = 1,
               rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
               L = 1,
               U = 1,
               compute_target = TRUE,
               returnlp = FALSE,
               ...)

Arguments

Note

In this model, the efficiency score is the sum of the slacks. Therefore, a DMU is efficient when the objective value (objval) is zero.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Charnes, A.; Cooper, W.W.; Golany, B.; Seiford, L.; Stuz, J. (1985) "Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions", Journal of Econometrics, 30(1-2), 91-107. doi:10.1016/0304-4076(85)90133-2

Charnes, A.; Cooper, W.W.; Lewin, A.Y.; Seiford, L.M. (1994). Data Envelopment Analysis: Theory, Methology, and Application. Boston: Kluwer Academic Publishers. doi:10.1007/978-94-011-0637-5

Cooper, W.W.; Park, K.S.; Pastor, J.T. (1999). "RAM: A Range Adjusted Measure of Inefficiencies for Use with Additive Models, and Relations to Other Models and Measures in DEA". Journal of Productivity Analysis, 11, p. 5-42. doi:10.1023/A:1007701304281

See Also

model_addsupereff

Examples

# Example 1. 
# Replication of results in Charnes et. al (1994, p. 27)
x <- c(2, 3, 6, 9, 5, 4, 10) 
y <- c(2, 5, 7, 8, 3, 1, 7)
data_example <- data.frame(dmus = letters[1:7], x, y)
data_example <- make_deadata(data_example, 
                             ni = 1, 
                             no = 1)
result <- model_additive(data_example, 
                         rts = "vrs")
efficiencies(result)
slacks(result)
lambdas(result)

# Example 2.
# Measure of Inefficiency Proportions (MIP).
x <- c(2, 3, 6, 9, 5, 4, 10) 
y <- c(2, 5, 7, 8, 3, 1, 7)
data_example <- data.frame(dmus = letters[1:7], x, y)
data_example <- make_deadata(data_example,
                             ni = 1,
                             no = 1)
result2 <- model_additive(data_example,
                          rts = "vrs",
                          weight_slack_i = 1 / data_example[["input"]],
                          weight_slack_o = 1 / data_example[["output"]])
slacks(result2)

# Example 3.
# Range Adjusted Measure of Inefficiencies (RAM).
x <- c(2, 3, 6, 9, 5, 4, 10) 
y <- c(2, 5, 7, 8, 3, 1, 7)
data_example <- data.frame(dmus = letters[1:7], x, y)
data_example <- make_deadata(data_example,
                             ni = 1,
                             no = 1)
range_i <- apply(data_example[["input"]], 1, max) -
           apply(data_example[["input"]], 1, min)
range_o <- apply(data_example[["output"]], 1, max) -
           apply(data_example[["output"]], 1, min)
w_range_i <- 1 / (range_i * (dim(data_example[["input"]])[1] +
                             dim(data_example[["output"]])[1]))
w_range_o <- 1 / (range_o * (dim(data_example[["input"]])[1] +
                             dim(data_example[["output"]])[1]))
result3 <- model_additive(data_example,
                          rts = "vrs",
                          weight_slack_i = w_range_i,
                          weight_slack_o = w_range_o)
slacks(result3)

Description

Solve the weighted version of the additive-min (mADD) model of Aparicio et. al (2007) with different returns to scale. For non constant returns to scale, a modification given by Zhu et al. (2018) is done.

Usage

model_addmin(datadea,
               dmu_eval = NULL,
               dmu_ref = NULL,
               orientation = NULL,
               weight_slack_i = 1,
               weight_slack_o = 1,
               rts = c("crs", "vrs", "nirs", "ndrs"),
               method = c("mf", "milp"),
               extreff = NULL,
               M_d = NULL,
               M_lambda = 1e3,
               maxfr = NULL,
               tol = 1e-6,
               silent = TRUE,
               compute_target = TRUE,
               check_target = FALSE,
               returnlp = FALSE,
               ...)

Arguments

Note

In this model, the efficiency score is the sum of the slacks. Therefore, a DMU is efficient when the objective value (objval) is zero.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Aparicio, J.; Ruiz, J.L.; Sirvent, I. (2007) "Closest targets and minimum distance to the Pareto-efficient frontier in DEA", Journal of Productivity Analysis, 28, 209-218. doi:10.1007/s11123-007-0039-5

Zhu, Q.; Wu, J.; Ji, X.; Li, F. (2018) "A simple MILP to determine closest targets in non-oriented DEA model satisfying strong monotonicity", Omega, 79, 1-8. doi:10.1016/j.omega.2017.07.003

See Also

model_additive, extreme_efficient, maximal_friends

Examples

# Example 1.
data("Airlines")
datadea <- make_deadata(Airlines,
                        inputs = 4:7,
                        outputs = 2:3)
result <- model_addmin(datadea = datadea,
                       method = "milp")
targets(result)

## Not run: 
# Example 2. Directional model with Additive-min model in second stage 
data("Airlines")
datadea <- make_deadata(Airlines,
                        inputs = 4:7,
                        outputs = 2:3)
resdir <- model_basic(datadea = datadea,
                      orientation = "dir",
                      maxslack = FALSE)
proj_input <- targets(resdir)[[1]] + slacks(resdir)[[1]]
proj_output <- targets(resdir)[[2]] - slacks(resdir)[[2]]
nd <- ncol(datadea$dmunames) # Number of DMUs
maxfr <- maximal_friends(datadea = datadea)
for (i in 1:nd) {
  datadea2 <- datadea
  datadea2$input[, i] <- proj_input[i, ]
  datadea2$output[, i] <- proj_output[i, ]
  DMUaux <- model_addmin(datadea = datadea2,
                         method = "mf",
                         maxfr = maxfr,
                         dmu_eval = i)$DMU[[1]]
  resdir$DMU[[i]]$slack_input <- DMUaux$slack_input
  resdir$DMU[[i]]$slack_output <- DMUaux$slack_output
  resdir$DMU[[i]]$target_input <- DMUaux$target_input
  resdir$DMU[[i]]$target_output <- DMUaux$target_output
}
targets(resdir)

## End(Not run)

Description

Solve the additive super-efficiency model proposed by Du, Liang and Zhu (2010). It is an extension of the SBM super-efficiency to the additive DEA model.

Usage

model_addsupereff(datadea,
                  dmu_eval = NULL,
                  dmu_ref = NULL,
                  orientation = NULL,
                  weight_slack_i = NULL,
                  weight_slack_o = NULL,
                  rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                  L = 1,
                  U = 1,
                  compute_target = TRUE,
                  returnlp = FALSE,
                  ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Du, J.; Liang, L.; Zhu, J. (2010). "A Slacks-based Measure of Super-efficiency in Data Envelopment Analysis. A Comment", European Journal of Operational Research, 204, 694-697. doi:10.1016/j.ejor.2009.12.007

Zhu, J. (2014). Quantitative Models for Performance Evaluation and Benchmarking. Data Envelopment Analysis with Spreadsheets. 3rd Edition Springer, New York. doi:10.1007/978-3-319-06647-9

See Also

model_additive, model_supereff, model_sbmsupereff

Examples

# Replication of results in Du, Liang and Zhu (2010, Table 6, p.696)
data("Power_plants")
Power_plants <- make_deadata(Power_plants, 
                             ni = 4, 
                             no = 2)
result <- model_addsupereff(Power_plants, 
                            rts = "crs")  
efficiencies(result)

Description

It solves input and output oriented, along with directional, basic DEA models (envelopment form) under constant (CCR model), variable (BCC model), non-increasing, non-decreasing or generalized returns to scale. By default, models are solved in a two-stage process (slacks are maximized).

You can use the model_basic function to solve directional DEA models by choosing orientation = "dir".

The model_basic function allows to treat with non-discretional, non-controllable and undesirable inputs/outputs.

Usage

model_basic(datadea,
            dmu_eval = NULL,
            dmu_ref = NULL,
            orientation = c("io", "oo", "dir"),
            dir_input = NULL,
            dir_output = NULL,
            rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
            L = 1,
            U = 1,
            maxslack = TRUE,
            weight_slack_i = 1,
            weight_slack_o = 1,
            vtrans_i = NULL,
            vtrans_o = NULL,
            compute_target = TRUE,
            compute_multiplier = FALSE,
            returnlp = FALSE,
            silent_ud = FALSE,
            ...)

Arguments

Note

(1) Model proposed by Seiford and Zhu (2002) is applied for undesirable inputs/outputs and non-directional orientation (i.e., input or output oriented). You should select "vrs" returns to scale (BCC model) in order to maintain translation invariance. If deaR detects that you are not specifying rts = "vrs", it makes the change to "vrs" automatically.

(2) With undesirable inputs and non-directional orientation use input-oriented BCC model, and with undesirable outputs and non-directional orientation use output-oriented BCC model. Alternatively, you can also treat the undesirable outputs as inputs and then apply the input-oriented BCC model (similarly with undesirable inputs).

(3) Model proposed by Fare and Grosskopf (2004) is applied for undesirable inputs/outputs and directional orientation.

(4) With orientation = "dir" (directional distance function model), efficient DMUs are those for which beta = 0.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Charnes, A.; Cooper, W.W.; Rhodes, E. (1978). “Measuring the efficiency of decision making units”, European Journal of Operational Research 2, 429–444.

Charnes, A.; Cooper, W.W.; Rhodes, E. (1979). “Short communication: Measuring the efficiency of decision making units”, European Journal of Operational Research 3, 339.

Charnes, A.; Cooper, W.W.; Rhodes, E. (1981). "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through", Management Science, 27(6), 668-697.

Banker, R.; Charnes, A.; Cooper, W.W. (1984). “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis”, Management Science; 30; 1078-1092.

Undesirable inputs/outputs:

Pastor, J.T. (1996). "Translation Invariance in Data Envelopment Analysis: a Generalization", Annals of Operations Research, 66(2), 91-102.

Seiford, L.M.; Zhu, J. (2002). “Modeling undesirable factors in efficiency evaluation”, European Journal of Operational Research 142, 16-20.

Färe, R. ; Grosskopf, S. (2004). “Modeling undesirable factors in efficiency evaluation: Comment”, European Journal of Operational Research 157, 242-245.

Hua Z.; Bian Y. (2007). DEA with Undesirable Factors. In: Zhu J., Cook W.D. (eds) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Springer, Boston, MA.

Non-discretionary/Non-controllable inputs/outputs:

Banker, R.; Morey, R. (1986). “Efficiency Analysis for Exogenously Fixed Inputs and Outputs”, Operations Research; 34; 513-521.

Ruggiero J. (2007). Non-Discretionary Inputs. In: Zhu J., Cook W.D. (eds) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Springer, Boston, MA.

Directional DEA model:

Chambers, R.G.; Chung, Y.; Färe, R. (1996). "Benefit and Distance Functions", Journal of Economic Theory, 70(2), 407-419.

Chambers, R.G.; Chung, Y.; Färe, R. (1998). "Profit Directional Distance Functions and Nerlovian Efficiency", Journal of Optimization Theory and Applications, 95, 351-354.

See Also

model_multiplier, model_supereff

Examples

# Example 1. Basic DEA model with desirable inputs/outputs.
# Replication of results in Charnes, Cooper and Rhodes (1981).
data("PFT1981") 
# Selecting DMUs in Program Follow Through (PFT)
PFT <- PFT1981[1:49, ] 
PFT <- make_deadata(PFT, 
                    inputs = 2:6, 
                    outputs = 7:9 )
eval_pft <- model_basic(PFT, 
                        orientation = "io", 
                        rts = "crs")
eff <- efficiencies(eval_pft)
s <- slacks(eval_pft) 
lamb <- lambdas(eval_pft)
tar <- targets(eval_pft)
ref <- references(eval_pft) 
returns <- rts(eval_pft)

# Example 2. Basic DEA model with undesirable outputs.
# Replication of results in Hua and Bian (2007).
data("Hua_Bian_2007")
# The third output is an undesirable output.
data_example <- make_deadata(Hua_Bian_2007, 
                             ni = 2,
                             no = 3, 
                             ud_outputs = 3) 
# Translation parameter (vtrans_o) is set to 1500                          
result <- model_basic(data_example, 
                      orientation = "oo", 
                      rts = "vrs", 
                      vtrans_o = 1500) 
eff <- efficiencies(result)
1 / eff # results M5 in Table 6-5 (p.119)

# Example 3. Basic DEA model with non-discretionary (fixed) inputs.
# Replication of results in Ruggiero (2007).
data("Ruggiero2007") 
# The second input is a non-discretionary input.
datadea <- make_deadata(Ruggiero2007, 
                        ni = 2,
                        no = 1, 
                        nd_inputs = 2) 
result <- model_basic(datadea,
                      orientation = "io", 
                      rts = "crs")
efficiencies(result)

Description

With this non-radial DEA model (Zhu, 1996), the user can specify the preference input (or output) weigths that reflect the relative degree of desirability of the adjustments of the current input (or output) levels.

Usage

model_deaps(datadea,
            dmu_eval = NULL,
            dmu_ref = NULL,
            weight_eff = 1,
            orientation = c("io", "oo"),
            rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
            L = 1,
            U = 1,
            restricted_eff = TRUE,
            maxslack = TRUE,
            weight_slack = 1,
            compute_target = TRUE,
            returnlp = FALSE,
            ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Zhu, J. (1996). “Data Envelopment Analysis with Preference Structure”, The Journal of the Operational Research Society, 47(1), 136. doi:10.2307/2584258

Zhu, J. (2014). Quantitative Models for Performance Evaluation and Benchmarking. Data Envelopment Analysis with Spreadsheets. 3rd Edition Springer, New York. doi:10.1007/978-3-319-06647-9

See Also

model_nonradial, model_profit, model_sbmeff

Examples

data("Fortune500")
 data_deaps <- make_deadata(datadea = Fortune500,
                            ni = 3, 
                            no = 2)
 result <- model_deaps(data_deaps, 
                       weight_eff = c(1, 2, 3), 
                       orientation = "io", 
                       rts = "vrs")
 efficiencies(result)

Description

FDH model allows the free disposability to construct the production possibility set. The central feature of the FDH model is the lack of convexity for its production possibility set (Thrall, 1999).

Usage

model_fdh(datadea,
          fdh_modelname = c("basic"),
          ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Cherchye, L.; Kuosmanen, T.; Post, T. (2000). "What Is the Economic Meaning of FDH? A Reply to Thrall". Journal of Productivity Analysis, 13(3), 263–267.

Deprins, D.; Simar, L. and Tulkens, H. (1984). Measuring Labor-Efficiency in Post Offices. In M. Marchand, P. Pestieau and H. Tulkens (eds.), The Performance of Public Entreprises: Concepts and Measurement. Amsterdam: North-Holland.

Sanei, M.; Mamizadeh Chatghayeb, S. (2013). “Free Disposal Hull Models in Supply Chain Management”, International Journal of Mathematical Modelling and Computations, 3(3), 125-129.

Thrall, R. M. (1999). "What Is the Economic Meaning of FDH?", Journal of Productivity Analysis, 11(3), 243–50.

Examples

# Example 1. FDH input-oriented.
# Replication of results in Sanei and Mamizadeh Chatghayeb (2013)
data("Supply_Chain")
data_fdh1 <- make_deadata(Supply_Chain, 
                          inputs = 2:4, 
                          outputs = 5:6)
result <- model_fdh(data_fdh1) # by default orientation = "io"
efficiencies(result)

# Example 2. FDH output-oriented.
# Replication of results in Sanei and Mamizadeh Chatghayeb (2013)
data("Supply_Chain")
data_fdh2 <- make_deadata(Supply_Chain, 
                          inputs = 5:6, 
                          outputs = 7:8)
result2 <- model_fdh(data_fdh2, 
                    orientation = "oo")
efficiencies(result2)

Description

Solve input-oriented and output-oriented basic DEA models (multiplicative form) under constant (CCR DEA model), variable (BCC DEA model), non-increasing, non-decreasing or generalized returns to scale. It does not take into account non-controllable, non-discretionary or undesirable inputs/outputs.

Usage

model_multiplier(datadea,
                 dmu_eval = NULL,
                 dmu_ref = NULL,
                 epsilon = 0,
                 orientation = c("io", "oo"),
                 rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                 L = 1,
                 U = 1,
                 returnlp = FALSE,
                 compute_lambda = TRUE,
                 ...)

Arguments

Note

(1) Very important with the multiplier model: "The optimal weights for an efficient DMU need not be unique" (Cooper, Seiford and Tone, 2007:31). "Usually, the optimal weights for inefficient DMUs are unique, the exception being when the line of the DMU is parallel to one of the boundaries of the feasible region" (Cooper, Seiford and Tone, 2007:32).

(2) The measure of technical input (or output) efficiency obtained by using multiplier DEA models is better the smaller the value of epsilon.

(3) Epsilon is usually set equal to 10^-6. However, if epsilon is not set correctly, the multiplier model can be infeasible (Zhu,2014:49).

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Charnes, A.; Cooper, W.W. (1962). “Programming with Linear Fractional Functionals”, Naval Research Logistics Quarterly 9, 181-185. doi:10.1002/nav.3800090303

Charnes, A.; Cooper, W.W.; Rhodes, E. (1978). “Measuring the Efficiency of Decision Making Units”, European Journal of Operational Research 2, 429–444. doi:10.1016/0377-2217(78)90138-8

Charnes, A.; Cooper, W.W.; Rhodes, E. (1979). “Short Communication: Measuring the Efficiency of Decision Making Units”, European Journal of Operational Research 3, 339. doi:10.1016/0377-2217(79)90229-7

Golany, B.; Roll, Y. (1989). "An Application Procedure for DEA", OMEGA International Journal of Management Science, 17(3), 237-250. doi:10.1016/0305-0483(89)90029-7

Seiford, L.M.; Thrall, R.M. (1990). “Recent Developments in DEA. The Mathematical Programming Approach to Frontier Analysis”, Journal of Econometrics 46, 7-38. doi:10.1016/0304-4076(90)90045-U

Zhu, J. (2014). Quantitative Models for Performance Evaluation and Benchmarking. Data Envelopment Analysis with Spreadsheets. 3rd Edition Springer, New York. doi:10.1007/978-3-319-06647-9

See Also

model_basic, cross_efficiency

Examples

# Example 1.
# Replication of results in Golany and Roll (1989).
data("Golany_Roll_1989")
data_example <- make_deadata(datadea = Golany_Roll_1989[1:10, ],
                             inputs = 2:4, 
                             outputs = 5:6) 
result <- model_multiplier(data_example, 
                           epsilon = 0, 
                           orientation = "io", 
                           rts = "crs") 
efficiencies(result)
multipliers(result)

# Example 2.
# Multiplier model with infeasible solutions (See note).
data("Fortune500")
data_Fortune <- make_deadata(datadea = Fortune500, 
                             inputs = 2:4, 
                             outputs = 5:6) 
result2 <- model_multiplier(data_Fortune, 
                           epsilon = 1e-6, 
                           orientation = "io", 
                           rts = "crs") 
# Results for General Motors and Ford Motor are not shown by deaR 
# because the solution is infeasible.
efficiencies(result2)
multipliers(result2)

Description

Non-radial DEA model allows for non-proportional reductions in each input or augmentations in each output.

Usage

model_nonradial(datadea,
                dmu_eval = NULL,
                dmu_ref = NULL,
                orientation = c("io", "oo"),
                rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                L = 1,
                U = 1,
                maxslack = TRUE,
                weight_slack = 1,
                compute_target = TRUE,
                returnlp = FALSE,
                ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Banker, R.D.; Morey, R.C. (1986). "Efficiency Analysis for Exogenously Fixed Inputs and Outputs", Operations Research, 34, 80-97. doi:10.1287/opre.34.4.513

Färe, R.; Lovell, C.K. (1978). "Measuring the Technical Efficiency of Production", Journal of Economic Theory, 19(1), 150-162. doi:10.1016/0022-0531(78)90060-1

Wu, J.; Tsai, H.; Zhou, Z. (2011). "Improving Efficiency in International Tourist Hotels in Taipei Using a Non-Radial DEA Model", International Journal of Contemporary Hospitatlity Management, 23(1), 66-83. doi:10.1108/09596111111101670

Zhu, J. (1996). “Data Envelopment Analysis with Preference Structure”, The Journal of the Operational Research Society, 47(1), 136. doi:10.2307/2584258

See Also

model_deaps, model_profit, model_sbmeff

Examples

# Replication of results in Wu, Tsai and Zhou (2011)
data("Hotels")
data_hotels <- make_deadata(Hotels, 
                            inputs = 2:5, 
                            outputs = 6:8)
result <- model_nonradial(data_hotels, 
                          orientation = "oo", 
                          rts = "vrs")
efficiencies(result)

Description

Cost, revenue and profit efficiency DEA models.

Usage

model_profit(datadea,
             dmu_eval = NULL,
             dmu_ref = NULL,
             price_input = NULL,
             price_output = NULL,
             rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
             L = 1,
             U = 1,
             restricted_optimal = TRUE,
             returnlp = FALSE,
             ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Coelli, T.; Prasada Rao, D.S.; Battese, G.E. (1998). An introduction to efficiency and productivity analysis. Jossey-Bass, San Francisco, pp 73–104. doi:10.1002/ev.1441

See Also

model_deaps, model_nonradial, model_sbmeff

Examples

# Example 1. Replication of results in Coelli et al. (1998, p.166).
# Cost efficiency model.
data("Coelli_1998")
# Selection of prices: input_prices is the transpose where the prices for inputs are. 
input_prices <- t(Coelli_1998[, 5:6]) 

data_example1 <- make_deadata(Coelli_1998,
                              ni = 2,
                              no = 1)
result1 <- model_profit(data_example1,
                       price_input = input_prices,
                       rts = "crs", 
                       restricted_optimal = FALSE) 
# notice that the option by default is restricted_optimal = TRUE
efficiencies(result1)

# Example 2. Revenue efficiency model.
data("Coelli_1998")
# Selection of prices for output: output_prices is the transpose where the prices for outputs are. 
output_prices <- t(Coelli_1998[, 7]) 
data_example2 <- make_deadata(Coelli_1998,
                             ni = 2,
                             no = 1)
result2 <- model_profit(data_example2,
                       price_output = output_prices,
                       rts = "crs", 
                       restricted_optimal = FALSE) 
# notice that the option by default is restricted_optimal = TRUE
efficiencies(result2)

# Example 3. Profit efficiency model.
data("Coelli_1998")
# Selection of prices for inputs and outputs: input_prices and output_prices are 
# the transpose where the prices (for inputs and outputs) are. 
input_prices <- t(Coelli_1998[, 5:6]) 
output_prices <- t(Coelli_1998[, 7]) 
data_example3 <- make_deadata(Coelli_1998,
                              ni = 2,
                              no = 1)
result3 <- model_profit(data_example3,
                        price_input = input_prices,
                        price_output = output_prices,
                        rts = "crs", 
                        restricted_optimal = FALSE) 
# notice that the option by default is restricted_optimal = TRUE
efficiencies(result3)

Description

Range directional model from Portela et al. (2004).

Usage

model_rdm(datadea,
            dmu_eval = NULL,
            dmu_ref = NULL,
            orientation = c("no", "io", "oo"),
            irdm = FALSE,
            maxslack = TRUE,
            weight_slack_i = 1,
            weight_slack_o = 1,
            compute_target = TRUE,
            returnlp = FALSE,
            ...)

Arguments

Note

Undesirable inputs/outputs are treated as negative inputs/outputs in this model.

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Portela, M.; Thanassoulis, E.; Simpson, G. (2004). "Negative data in DEA: a directional distance approach applied to bank branches", Journal of the Operational Research Society, 55 1111-1121.

Description

Calculate the SBM model proposed by Tone (2001).

Usage

model_sbmeff(datadea,
             dmu_eval = NULL,
             dmu_ref = NULL,
             weight_input = 1,
             weight_output = 1,
             orientation = c("no", "io", "oo"),
             rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
             L = 1,
             U = 1,
             kaizen = FALSE,
             maxfr = NULL,
             tol = 1e-6,
             silent = FALSE,
             compute_target = TRUE,
             returnlp = FALSE,
             ...)

Arguments

Author(s)

Vicente Coll-Serrano ([email protected]). Quantitative Methods for Measuring Culture (MC2). Applied Economics.

Vicente Bolós ([email protected]). Department of Business Mathematics

Rafael Benítez ([email protected]). Department of Business Mathematics

University of Valencia (Spain)

References

Tone, K. (2001). "A Slacks-Based Measure of Efficiency in Data Envelopment Analysis", European Journal of Operational Research, 130, 498-509. doi:10.1016/S0377-2217(99)00407-5

Tone, K. (2010). "Variations on the theme of slacks-based measure of efficiency in DEA", European Journal of Operational Research, 200, 901-907. doi:10.1016/j.ejor.2009.01.027

Cooper, W.W.; Seiford, L.M.; Tone, K. (2007). Data Envelopment Analysis. A Comprehensive Text with Models, Applications, References and DEA-Solver Software. 2nd Edition. Springer, New York. doi:10.1007/978-0-387-45283-8

Aparicio, J.; Ruiz, J.L.; Sirvent, I. (2007) "Closest targets and minimum distance to the Pareto-efficient frontier in DEA", Journal of Productivity Analysis, 28, 209-218. doi:10.1007/s11123-007-0039-5

See Also

model_nonradial, model_deaps, model_profit, model_sbmsupereff

Examples

# Example 1. Replication of results in Tone (2001, p.505)
data("Tone2001")
data_example <- make_deadata(Tone2001, 
                             ni = 2, 
                             no = 2)
result_SBM <- model_sbmeff(data_example, 
                           orientation = "no", 
                           rts = "crs")
result_CCR <- model_basic(data_example, 
                          orientation = "io", 
                          rts = "crs")
efficiencies(result_SBM)
efficiencies(result_CCR)
slacks(result_SBM)
slacks(result_CCR)
 
# Example 2. Replication of results in Tone (2003), pp 10-11 case 1:1.
data("Tone2003")
data_example <- make_deadata(Tone2003,
                             ni = 1,
                             no = 2,
                             ud_outputs = 2)
result <- model_sbmeff(data_example,
                       rts = "vrs")
efficiencies(result)
targets(result)

# Example 3. Replication of results in Aparicio (2007).
data("Airlines")
datadea <- make_deadata(Airlines,
                        inputs = 4:7,
                        outputs = 2:3)
result <- model_sbmeff(datadea = datadea, kaizen = TRUE)
efficiencies(result)
targets(result)

Description

Slack based measure of superefficiency model (Tone 2002) with n DMUs, m inputs and s outputs.

Usage

model_sbmsupereff(datadea,
                  dmu_eval = NULL,
                  dmu_ref = NULL,
                  weight_input = 1,
                  weight_output = 1,
                  orientation = c("no", "io", "oo"),
                  rts = c("crs", "vrs", "nirs", "ndrs", "grs"),
                  L = 1,
                  U = 1,
                  compute_target = TRUE,
                  compute_rho = FALSE,
                  kaizen = FALSE,
                  silent = FALSE,
                  returnlp = FALSE)