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Data Envelopment Analysis Software Mac

  1. Data Envelopment Analysis Introduction

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers.[1] It is used to empirically measure productive efficiency of decision making units (DMUs). Although DEA has a strong link to production theory in economics, the tool is also used for benchmarking in operations management, where a set of measures is selected to benchmark the performance of manufacturing and service operations. In benchmarking, the efficient DMUs, as defined by DEA, may not necessarily form a “production frontier”, but rather lead to a “best-practice frontier” (Charnes A., W. W. Cooper and E. Rhodes (1978)).[2]

  1. This software can be used to obtain measures of productivity and efficiency using several different methodologies. Four pieces of free computer software currently available from CEPA are as follows: DEAP Version 2.1. Deap (Ver 2.1) used to conduct data envelopment analysis (DEA). DPIN Version 3.1.
  2. Data Envelopment Analysis (DEA) is a set of Mathematical Programming based models which evaluate the relative efficiencies of Decision Making Units (DMUs), with multiple inputs and outputs. DEA Online Software (DEAOS) is an appropriate package for obtaining DEA results easily and quickly.
  3. DEAOS is a Data Envelopment Analysis Online Software designed for DEA models. DEA models are used to assess a set of similar DMUs (Decision-Making Units) and obtain their relative efficiency. DEAOS is an appropriate tool for obtaining results easily and quickly.
  4. DEA Software. What is the best software for Data Envelopment Analysis (DEA)?

DEA (Data Envelopment Analysis), Introduction to the Theory and Application of Data Envelopment Analysis: A Foundation Text with Integrated Software, Data Envelopment Analysis: A Comprehensive Text Advances in DEA Theory and Applications includes information on a balanced benchmarking tool that is designed. DEA Open Source DEA.

Non-parametric approaches have the benefit of not assuming a particular functional form/shape for the frontier, however they do not provide a general relationship (equation) relating output and input. There are also parametric approaches which are used for the estimation of production frontiers (see Lovell & Schmidt 1988 for an early survey). These require that the shape of the frontier be guessed beforehand by specifying a particular function relating output to input. The relative strengths from each of these approaches can be combined in a hybrid method (Tofallis, 2001,) where the frontier units are identified by DEA, then fitted to a smooth surface. This allows a best-practice relationship between multiple outputs and multiple inputs to be estimated.

'The framework has been adapted from multi-input, multi-output production functions and applied in many industries. DEA develops a function whose form is determined by the most efficient producers. This method differs from the Ordinary Least Squares (OLS) statistical technique that bases comparisons relative to an average producer. Like Stochastic Frontier Analysis (SFA), DEA identifies a 'frontier' which are characterized as an extreme point method that assumes that if a firm can produce a certain level of output utilizing specific input levels, another firm of equal scale should be capable of doing the same. The most efficient producers can form a 'composite producer', allowing the computation of an efficient solution for every level of input or output. Where there is no actual corresponding firm, 'virtual producers' are identified to make comparisons' (Berg 2010).

Attempts to synthesize DEA and SFA, improving upon their drawbacks, were also made in the literature, via proposing various versions of non-parametric SFA, Stochastic DEA.[3] and Stochastic Nonparametric Envelopment of Data (StoNED).[4]

History[edit]

In microeconomic production theory, a firm's input and output combinations are depicted using a production function. Using such a function, one can show the maximum output which can be achieved with any possible combination of inputs, that is, one can construct a production technology frontier (Seiford & Thrall 1990).[5]

Building on the ideas of Farrell (1957), the seminal work 'Measuring the efficiency of decision making units' by Charnes, Cooper & Rhodes (1978) applies linear programming to estimate an empirical production technology frontier for the first time. In Germany, the procedure was used earlier to estimate the marginal productivity of R&D and other factors of production (Brockhoff 1970). Since then, there have been a large number of books and journal articles written on DEA or applying DEA on various sets of problems.

Other than comparing efficiency across DMUs within an organization, DEA has also been used to compare efficiency across firms. There are several types of DEA with the most basic being CCR based on Charnes, Cooper & Rhodes, however there are also DEA which address varying returns to scale, either CRS (constant returns to scale, VRS (variable), non increasing returns to scale or the non decreasing returns to scale by Ylvinger (2000). The main developments of DEA in the 1970s and 1980s are documented by Seiford & Thrall (1990).

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Techniques[edit]

Data envelopment analysis (DEA) is a linear programming methodology to measure the efficiency of multiple decision-making units (DMUs) when the production process presents a structure of multiple inputs and outputs.[6]

'DEA has been used for both production and cost data. Utilizing the selected variables, such as unit cost and output, DEA software searches for the points with the lowest unit cost for any given output, connecting those points to form the efficiency frontier. Any company not on the frontier is considered inefficient. A numerical coefficient is given to each firm, defining its relative efficiency. Different variables that could be used to establish the efficiency frontier are: number of employees, service quality, environmental safety, and fuel consumption. An early survey of studies of electricity distribution companies identified more than thirty DEA analyses—indicating widespread application of this technique to that network industry. (Jamasb, T. J., Pollitt, M. G. 2001). A number of studies using this technique have been published for water utilities. The main advantage to this method is its ability to accommodate a multiplicity of inputs and outputs. It is also useful because it takes into consideration returns to scale in calculating efficiency, allowing for the concept of increasing or decreasing efficiency based on size and output levels. A drawback of this technique is that model specification and inclusion/exclusion of variables can affect the results.' (Berg 2010)

Under general DEA benchmarking, for example, 'if one benchmarks the performance of computers, it is natural to consider different features (screen size and resolution, memory size, process speed, hard disk size, and others). One would then have to classify these features into “inputs” and “outputs” in order to apply a proper DEA analysis. However, these features may not actually represent inputs and outputs at all, in the standard notion of production. In fact, if one examines the benchmarking literature, other terms, such as “indicators”, “outcomes”, and “metrics”, are used. The issue now becomes one of how to classify these performance measures into inputs and outputs, for use in DEA.' (Cook, Tone, and Zhu, 2014)

Some of the advantages of DEA are:

  • no need to explicitly specify a mathematical form for the production function
  • proven to be useful in uncovering relationships that remain hidden for other methodologies
  • capable of handling multiple inputs and outputs
  • capable of being used with any input-output measurement
  • the sources of inefficiency can be analysed and quantified for every evaluated unit

Some of the disadvantages of DEA are:

  • results are sensitive to the selection of inputs and outputs (Berg 2010).
  • you cannot test for the best specification (Berg 2010).
  • the number of efficient firms on the frontier tends to increase with the number of inputs and output variables (Berg 2010).

A desire to Improve upon DEA, by reducing its disadvantages or strengthening its advantages has been a major cause for many discoveries in the recent literature. The currently most often DEA-based method to obtain unique efficiency rankings is called cross-efficiency. Originally developed by Sexton et al. in 1986,[7] it found widespread application ever since Doyle and Green's 1994 publication.[8] Cross-efficiency is based on the original DEA results, but implements a secondary objective where each DMU peer-appraises all other DMU's with its own factor weights. The average of these peer-appraisal scores is then used to calculate a DMU's cross-efficiency score. This approach avoids DEA's disadvantages of having multiple efficient DMUs and potentially non-unique weights.[9] Another approach to remedy some of DEA's drawbacks is Stochastic DEA, which synthesizes DEA and SFA.[3]

Data Envelopment Analysis Introduction

Sample applications[edit]

DEA is commonly applied in the electric utilities sector. For instance, a government authority can choose data envelopment analysis as their measuring tool to design an individualized regulatory rate for each firm based on their comparative efficiency. The input components would include man-hours, losses, capital (lines and transformers only), and goods and services. The output variables would include number of customers, energy delivered, length of lines, and degree of coastal exposure. (Berg 2010)

DEA is also regularly used to assess the efficiency of public and not-for-profit organizations, e.g. hospitals (Kuntz, Scholtes & Vera 2007), police forces (Thanassoulis 1995; Sun 2002; Aristovnik et al. 2013, 2014), or liberal arts colleges (Eckles, 2010).

Examples[edit]

In the DEA methodology, formally developed by Charnes, Cooper and Rhodes (1978), efficiency is defined as a ratio of weighted sum of outputs to a weighted sum of inputs, where the weights structure is calculated by means of mathematical programming and constant returns to scale (CRS) are assumed. In 1984, Banker, Charnes and Cooper developed a model with variable returns to scale (VRS).

Assume that we have the following data:

  • Unit 1 produces 100 items per day, and the inputs per item are 10 dollars for materials and 2 labour-hours
  • Unit 2 produces 80 items per day, and the inputs are 8 dollars for materials and 4 labour-hours
  • Unit 3 produces 120 items per day, and the inputs are 12 dollars for materials and 1.5 labour-hours

To calculate the efficiency of unit 1, we define the objective function (OF) as

  • MaxEfficiency:(100u1)/(10v1+2v2){displaystyle MaxEfficiency:(100u_{1})/(10v_{1}+2v_{2})}

which is subject to (ST) all efficiency of other units (efficiency cannot be larger than 1):

  • Efficiency of unit 1: (100u1)/(10v1+2v2)≤1{displaystyle (100u_{1})/(10v_{1}+2v_{2})leq 1}
  • Efficiency of unit 2: (80u1)/(8v1+4v2)≤1{textstyle (80u_{1})/(8v_{1}+4v_{2})leq 1}
  • Efficiency of unit 3: (120u1)/(12v1+1.5v2)≤1{displaystyle (120u_{1})/(12v_{1}+1.5v_{2})leq 1}

and non-negativity:

  • u,v≥0{displaystyle u,vgeq 0}

A fraction with decision variables in the numerator and denominator is nonlinear. Since we are using a linear programming technique, we need to linearize the formulation, such that the denominator of the objective function is constant (in this case 1), then maximize the numerator.

The new formulation would be:

  • OF
    • MaxEfficiency:100u1{displaystyle MaxEfficiency:100u_{1}}
  • ST
    • Efficiency of unit 1: 100u1−(10v1+2v2)≤0{displaystyle 100u_{1}-(10v_{1}+2v_{2})leq 0}
    • Efficiency of unit 2: 80u1−(8v1+4v2)≤0{textstyle 80u_{1}-(8v_{1}+4v_{2})leq 0}
    • Efficiency of unit 3: 120u1−(12v1+1.5v2)≤0{displaystyle 120u_{1}-(12v_{1}+1.5v_{2})leq 0}
    • Denominator of nonlinear OF:10v1+2v2=1{displaystyle 10v_{1}+2v_{2}=1}
    • Non-negativity: u,v≥0{displaystyle u,vgeq 0}

Inefficiency measuring[edit]

Data Envelopment Analysis (DEA) has been recognized as a valuable analytical research instrument and a practical decision support tool. DEA has been credited for not requiring a complete specification for the functional form of the production frontier nor the distribution of inefficient deviations from the frontier. Rather, DEA requires general production and distribution assumptions only. However, if those assumptions are too weak, inefficiency levels may be systematically underestimated in small samples. In addition, erroneous assumptions may cause inconsistency with a bias over the frontier. Therefore, the ability to alter, test and select production assumptions is essential in conducting DEA-based research. It is also useful to compare the results with another popular alternative such as Stochastic Frontier Analysis (SFA) approach [10]

Notes[edit]

  1. ^Charnes A., W. W. Cooper and E. Rhodes (1978). “Measuring the Efficiency of Decision Making Units.” EJOR 2: 429-444.
  2. ^For more details and discussions, see Chapter 8 in Sickles, R., & Zelenyuk, V. (2019). Measurement of Productivity and Efficiency: Theory and Practice. Cambridge: Cambridge University Press. doi:10.1017/9781139565981 https://assets.cambridge.org/97811070/36161/frontmatter/9781107036161_frontmatter.pdf
  3. ^ abOle B. Olesen, Niels Christian Petersen (2016) Stochastic Data Envelopment Analysis—A review, European Journal of Operational Research, 251 (1): 2-21, https://doi.org/10.1016/j.ejor.2015.07.058
  4. ^Kuosmanen, T., Kortelainen, M. Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints. J Prod Anal38, 11–28 (2012). https://doi.org/10.1007/s11123-010-0201-3
  5. ^L.M. Seiford; R.M. Thrall (1990). 'Recent Developments in DEA: The Mathematical Programming Approach to Frontier Analysis'. Journal of Econometrics. 46 (1–2): 7–38. doi:10.1016/0304-4076(90)90045-u.
  6. ^Yishi Zhang; Anrong Yang; Chan Xiong; Teng Wang; Zigang Zhang (2014). 'Feature selection using data envelopment analysis'. Knowledge-Based Systems. 64: 70–80. doi:10.1016/j.knosys.2014.03.022.
  7. ^Sexton, Thomas R. (1986). 'Data envelopment analysis: Critique and extension'. New Directions for Program Evaluation. 32: 73–105.
  8. ^Doyle, John; Green, Rodney (1994-05-01). 'Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses'. Journal of the Operational Research Society. 45 (5): 567–578. doi:10.1057/jors.1994.84. ISSN0160-5682.
  9. ^Dyson, R. G.; Allen, R.; Camanho, A. S.; Podinovski, V. V.; Sarrico, C. S.; Shale, E. A. (2001-07-16). 'Pitfalls and protocols in DEA'. European Journal of Operational Research. Data Envelopment Analysis. 132 (2): 245–259. doi:10.1016/S0377-2217(00)00149-1.
  10. ^For more details and discussions, see Chapters 8, 9 and 10 for DEA and Chapters 11 through 16 for SFA in Sickles, R., & Zelenyuk, V. (2019). Measurement of Productivity and Efficiency: Theory and Practice. Cambridge: Cambridge University Press. doi:10.1017/9781139565981 https://assets.cambridge.org/97811070/36161/frontmatter/9781107036161_frontmatter.pdf

References[edit]

  • Charnes A., W. W. Cooper and E. Rhodes (1978). “Measuring the Efficiency of Decision Making Units.” EJOR 2: 429-444.
  • Banker R.D. (1984). 'Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis'. Management Science. 30 (9): 1078–1092. doi:10.1287/mnsc.30.9.1078.
  • Berg, S. (2010). 'Water Utility Benchmarking: Measurement, Methodology, and Performance Incentives.' International Water Association.
  • Brockhoff K. (1970). 'On the Quantification of the MArginal Productivity of Industrial Research by Estimating a Production Function for a Single Firm'. German Economic Review. 8: 202–229.
  • Charnes A. (1978). 'Measuring the efficiency of decision-making units'(PDF). European Journal of Operational Research. 2 (6): 429–444. doi:10.1016/0377-2217(78)90138-8.
  • Coelli, T.J., D.P. Rao, C.J. O'Donnell, and G.E. Battese, An Introduction to Efficiency and Productivity Analysis, Springer, 2005.
  • Cook, W.D., Tone, K., and Zhu, J., Data envelopment analysis: Prior to choosing a model, OMEGA, 2014, Vol. 44, 1-4.
  • Eckles, J.E. Res High Educ (2010) 51: 266. https://doi.org/10.1007/s11162-009-9157-4.
  • Farrell M.J. (1957). 'The Measurement of Productive Efficiency'. Journal of the Royal Statistical Society. 120 (3): 253–281. doi:10.2307/2343100. JSTOR2343100.
  • Emrouznejad, A., G. L. Yang (2018) A survey and analysis of the first 40 years of scholarly literature in DEA: 1978-2016, Socio-Economic Planning Sciences, 61 (1): 4-8. (doi) (supplement)
  • Kuntz L.; Scholtes S.; Vera A. (2007). 'Incorporating Efficiency in Hospital Capacity Planning in Germany'. European Journal of Health Economics. 8 (3): 213–223. doi:10.1007/s10198-006-0021-6. PMID17216425.
  • Lovell, C.A.L., & P. Schmidt (1988) 'A Comparison of Alternative Approaches to the Measurement of Productive Efficiency, in Dogramaci, A., & R. Färe (eds.) Applications of Modern Production Theory: Efficiency and Productivity, Kluwer: Boston.
  • Ramanathan, R. (2003) An Introduction to Data Envelopment Analysis: A tool for Performance Measurement, Sage Publishing.
  • Sickles, R., & Zelenyuk, V. (2019). Measurement of Productivity and Efficiency: Theory and Practice. Cambridge: Cambridge University Press. doi:10.1017/9781139565981 https://assets.cambridge.org/97811070/36161/frontmatter/9781107036161_frontmatter.pdf
  • Simar L.; Zelenyuk V. (2007). 'Statistical inference for aggregates of Farrell-type efficiencies'. Journal of Applied Econometrics. 22 (7): 1367–1394. doi:10.1002/jae.991. hdl:2078.1/123051.
  • Simar L.; Zelenyuk V. (2006). 'On Testing Equality of Distributions of Technical Efficiency Scores'. Econometric Reviews. 25 (4): 497–522. doi:10.1080/07474930600972582. hdl:2078.1/122683.
  • Sun S (2002). 'Measuring the relative efficiency of police precincts using data envelopment analysis'. Socio-Economic Planning Sciences. 36 (1): 51–71. doi:10.1016/s0038-0121(01)00010-6.
  • Thanassoulis E (1995). 'Assessing police forces in England and Wales using data envelopment analysis'. European Journal of Operational Research. 87 (3): 641–657. doi:10.1016/0377-2217(95)00236-7.
  • Tofallis C (2001). 'Combining two approaches to efficiency assessment'. Journal of the Operational Research Society. 52 (11): 1225–1231. doi:10.1057/palgrave.jors.2601231. hdl:2299/917. SSRN1353122.

External links[edit]

  • ..all you need to know about DEA @DataEnvelopment
  • OR Notes by J E Beasley DEA
  • The most comprehensive source of Data Envelopment Analysis at DEAzone
  • [1], Journal of Productivity Analysis, Kluwer Publishers
  • On 40th anniversary of DEA method proposed by William W Cooper
  • Who is William W Cooper
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Data_envelopment_analysis&oldid=961665356'

Data Development Analysis (DEA) was developed in 1978, as a benchmarking technique for evaluating the efficiency or performance of a group of entities (Cooper, Seiford, & Tone, 2007). DEA analysis has emerged as a powerful tool of efficiency and benchmarking-based analyses, as it uses linear programming methodology. DEA analysis remains possible over various software. However, DEA Solver is the most recent and popular software for DEA analysis. Data Envelopment Analysis using DEA Solver, which is basically an MS Excel plugin and downloadable freely from http://www.saitech-inc.com/Products/Prod-DSP.asp. DEA solver 8.0 includes 28 clusters of DEA models (“User ’ s Guide to DEA-Solver-Learning Version,” 2015). However, there are two versions of DEA solver, free and paid versions and can compute the results for maximum 50 decision-making units (DMUs).

The basic process of the data envelopment analysis using DEA-Solver

The process of incorporating the DEA solver into the MS Excel spreadsheet requires a few steps as mentioned in the following steps;

  1. Install and enable the excel spreadsheet to choose the program referred to as add in.
  2. MS Excel>Excel options>Add-ins>Excel Addins>Go>Solver>OK.
  3. After setting up the DEA model, involve the solver by using the solver option indicated under Data tools.
  4. To run the solver model, set the input and output parameters in the solver and indicate the type of DEA analysis.

Challenges faced while conducting data envelopment analysis using DEA-Solver

From the process of installation of DEA-Solver to the computation of the analysis, the DEA process undergoes a various set of challenges. The first challenge incurs at the time of the installation itself, as it requires to be manually included in MS Excel. However, the free version allows analysis on a certain set of models. This free version of DEA-Solver allows the analysis only on Slack-based model and the Malmquist productivity summary. The output and input-oriented models such as CCR-O, CCR-I, BCC-O, BCC-I, and other non-discretionary variable models can’t be analyzed through this version. A paid version of the DEA-Solver allows all types of DEA model analysis.

Another challenge includes a longer process of entering the data and defining variables in the free version of DEA-Solver. Every time, the researcher needs to characterize the data into input and output units. Further, the free version of DEA-Solver software does not provide the option to save the results or data file. However, there are a certain set of solutions that can be used by the researcher to avoid these challenges that are explained in the following section.

Missing data as a challenge of DEA-Solver

DEA analysis using DEA-Solver does not help analyze incomplete data for inputs and outputs. There are many situations under which one may face the problem of missing data, especially from secondary data. The most common solution for this problem is to eliminate the DMUs, inputs, and output variables that have missing data. However, eliminating the DMU’s may cause inefficiency in developing the model. Another alternative comprises using previous year value to fill the missing data.

Data envelopment analysis in excel

Another alternative approach is to use the Fuzzy mathematics approach (Qian, 2009). This technique involves significant effort to find the missing values. Through this approach, the missing values are forecasted based on the value of mean and the series of variations. Therefore, the best solution is to fill the gap of the missing data using previous year values or use the predicted values calculated using the series of variations.

Time-consuming as a challenge of DEA-Solver

Importing data and defining the input and output variables requires multiple insertions. This is because the DEA-Solver does not provide any option to save the data and result file. So, after analyzing the results of a particular model for each year, the results have to be copied in a separate excel sheet. This is in the case of the free version of DEA-Solver. One needs to import the data file multiple times and define the input and output variables for further analysis. This process continues for each assessment and is time-consuming.

Negative values as a challenge of DEA-Solver

Many a time, the data set entered can have negative values. DEA analysis using DEA-Solver can’t execute the analysis with negative numbers. Again this is a limitation of the free DEA-Solver version. For this purpose, it is necessary to ensure that all negative values are removed from the data before importing it. The solution includes the reduction of the magnitude of negative values by defining the values based on a constant value. Another method includes the rejection of data that have negative values and choosing all positive values for the DEA analysis.

Alternative models as a major challenge of DEA-Solver

The free version of DEA-solver does not provide the output for CCR and BCC models. The software provides the output only for Slack-based model (SBM) and the components of Malmquist Index Productivity. In order to analyze the score of CCR technical efficiency and BCC models, the paid version of DEA frontier software should be used. One can also use a variety of user interfaces and advanced modelling options like Max DEA software and DEA Frontier.

Recommendations of conducting DEA analysis using DEA-Solver

Following recommendations help to obtain accurate results for DEA analysis.

  • The number of DMU’s selected for the analysis should be chosen carefully. A large set of the population causes homogeneity of data and in result cause exogenous impacts on the data.
  • Use Max DEA 7 software in combination to DEA-Solver, for calculating CCR technical efficiency scores and output of BCC models which is not allowed under the free version of DEA-Solver (Qian, 2009).
  • Avoid imbalances in the data set and comprise of a similar magnitude.
  • Select the DMU’s with sufficient data available for inputs and output variables are available. In addition to this, ensure that all the values in the data set are non-negative.

References

  • Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software: Second edition. Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software: Second Edition, (June), 1–490. https://doi.org/10.1007/978-0-387-45283-8.
  • Qian, C. and. (2009). Data Envelopment Analysis : Methods and MaxDEA Software.
  • User ’ s Guide to DEA-Solver-Learning Version. (2015), 15(1), 1–17.
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