DEA is a special application of linear programming based on frontier methodology of Farrell  as advanced by Charnes, Cooper and Rhodes  and Banker, Charnes, and Cooper . DEA compares the inputs and outputs of decision-making units (DMUs) and assesses their relative efficiency. DMUs found to be inefficient are strictly inefficient in a Pareto sense in that at least one other DMU can produce outputs for less input. A significant feature of DEA is that it allows for the inclusion of multiple input and output variables that are calculated simultaneously. This ability sets DEA apart from the other single dimension analytical techniques generally used in comparative analysis (e. g., ratio analysis and regression analysis). DEA is used to calculate relative efficiency in a variety of organizations including banks, logistics departments, hospitals, schools and restaurants.
A detailed description of DEA is beyond the scope of this review. However, excellent descriptions of DEA can be found in Seiford , Norman, M. and Stoker. B. , and Banker, et al .
Frontier Analyst is a 16-bit application. The accompanying manual indicates that it will run under Windows 3.1 or later on a 386 with no co-processor. As a practical matter, you should have a minimum of a 486 DX33 with 4MB RAM for most applications. For this review, Frontier Analyst was tested under Windows 95 and NT with Pentium 100 and 200 computers. The software performed well, even under conditions approaching its maximum input parameters.
Documentation and Installation
Frontier Analyst is well documented. Installation is simple and straightforward. The accompanying manual contains adequate instructions to perform most DEA functions. There is a basic overview of the DEA process, but it is not a tutorial on DEA. The user should be familiar with DEA concepts and limitations to fully realize the potential of the software. The help menu is an excellent online resource. It is easy to use and contains all materials from the manual and a comprehensive search menu.
The initial menu screen provides a complete overview of the features of Frontier Analyst. The Menu and Tool Bar icons are easy to interpret and simple to use. The Data Editor Window shown in Figure 1 simultaneously appears and can quickly be maximized for input. At this point, most of Frontier Analysts features are visible to the user.
Figure 1 - Data Editor Window
Frontier Analyst provides for input of data into a standard spreadsheet format. It also provides for importing of data from existing *.dat and *.txt files and "pasting" from existing spreadsheets. The inputs can be continuous, ordinal or categorical variables. Frontier Analyst has a large capacity of up to 256 DMUs and 32 input/output variables. This is adequate for most PC-based DEA applications.
Data variables are designated as controlled, uncontrolled and output. Designation of "uncontrollable" inputs (exogenous or environmental variables ) is an important feature of DEA. An uncontrollable input is one that can affect the relative efficiency of a DMU, but over which it has little or no control. The argument is frequently made that multiple unit comparisons are not feasible because of the importance of uncontrollable variables. For example, evaluations of school districts can include socioeconomic inputs such as median income as a mitigating factor in explaining variance in scores on standardized tests. Similarly, location and number of competitors affect performance of retail operators but are not under the control of the manager. Frontier Analyst adjusts individual efficiency ratings (DEA scores) for the influences of designated uncontrollable inputs.
Data is automatically designated as a controllable input, but changing the designation is simply accomplished by a pull down menu on the Data Editor Window.
DEA Model Options
To run Frontier Analyst, you simply "click" on two (or three) icons on the Data Editor Window. The first is the type of mathematical model you wish to use in the analysis. Frontier Analyst will run under two "returns to scale" models. The constant return to scale (CRS) model assumes that one unit of input results in one unit of output. The variable returns to scale (VRS) model assumes that one unit of input can result in one unit of output, less than one unit of output (diseconomies of scale), or more than one unit of output (economies of scale). In the VRS model, Frontier Analyst determines the relationship (positive or negative) as well as the size of the returns to scale. This provides flexibility for the user to test different scenarios of performance based on differing assumptions. Additionally, under the VRS model the user can explore the impact of input minimization or output maximization by clicking the corresponding icon. Input minimization allows the user to determine the extent to which a DMU can reduce inputs while maintaining the current level of outputs. This might occur in a situation where competition limits the market for finished goods. Output maximization might be used when the inputs are constrained, such as by a fixed allocated budget, and the emphasis is increasing the outputs. Once the mathematical model is chosen, the efficiency analysis can be initiated by clicking the "Recalc" icon.
One of the strongest features of Frontier Analyst is the variety of outputs it produces. It supports all standard output information provided by DEA plus some excellent graphic representations of the relationships among DMUs.
The first output screen of Frontier Analyst is an efficiency score for each DMU, as shown in Figure 2. DEA assigns mathematically optimal weights to all input and output variables on the basis of the decision rule that maximum weight is placed on those variables where a DMU compares favorably and minimum weight on those variables where a DMU compares unfavorably. Frontier Analyst generates a table of DMUs with scalar measures that ranges from 0 to 1.00. A DEA score of 0 would mean that a DMU is maximally inefficient in comparison to all the other DMUs being compared, while a score of 1.00 would mean that a DMU is 100 percent, relatively efficient by comparison. The screen can be copied to a clipboard and inputted directly into word processing software.
Figure 2 - Efficiency scores
Reference set information
Frontier Analyst computes a reference set, or comparison group, for any DMU found to be relatively inefficient. The reference set represents the other DMUs that constitute "best practices" and to which the relatively inefficient DMU is being compared. Frontier Analyst provides a series of graphic and tabular information to support analysis of both efficient and inefficient DMUs.
Among the most useful are:
A series of 12 tests were run under Frontier Analysis. The data sets ranged from 3 x 20 (input/output x DMU) to 13 x 155. The response from Frontier Analyst was immediate. In each case, the solution sets were verified as accurate. All output options were accessed. No problems were encountered during any of the test runs.
Opportunities for Improvement
Frontier Analyst is a significant investment, even for large commercial users. At the equivalent of $2,500 per copy, it has a relatively small market. For academic users, the price is still high at approximately $700 (see Vendor Comments). As DEA becomes a more mainstream analytical tool, competition from other software manufacturers should bring the price down considerably.
From a technical standpoint, one enhancement that should be forthcoming is the ability for the user to limit the "weight" that is applied to each input and output variable. Information from the manufacturer indicates that they are currently considering this feature and have already added a capability to view the weights that Frontier Analyst applies to each input and output variable. Additionally, several new DEA models are appearing in the literature [c.f., the additive model, Charnes, et al., 1995 and the free disposal hull model, Tulkens, 1993].
Finally, if Frontier Analyst, or any PC-based software, is to compete for the market now serviced by mainframe applications, it will need to increase its input parameters and processing speed.
Public policy makers and business managers need improved analytic tools to enhance decision making. There is a continued, growing need to find ways to increase efficiency in both the public and private sectors. DEA represents a promising method of addressing this need. The availability of specific DEA software applications, like Frontier Analyst, will help to de-emphasize the mathematics of the analysis while hopefully increasing its conceptual understanding and usefulness as a decision making tool.
1. Banker, R. D., Charnes, A., Cooper, W., Swarts, J. and Thomas, D. (1989), "An Introduction to Date Envelopment Analysis With Some Models and Their Uses," Research in Government And Non-Profit Accounting, Vol. 5, pp. 125-164.
2. Banker, R. D., Charnes, A., and Cooper, W. (1984), "Models for Estimation of Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, Vol. 30, pp. 1078-1092.
3. Charnes, A., Cooper, W. and Rhodes, E. (1978), "Measuring the Efficiency of Decision Making Units," European Journal of Operations Research, Vol. 2, pp. 429-444.
4. Charnes, A., Cooper, W., Golany, B. Seiford, L. and Shutz, J. (1995), "Foundations of Data Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions," Journal of Econometrics, Vol. 30, pp. 91-107.
5. Farrell, M. J. (1957), "The Measurement of Productive Efficiency," Journal of the Royal Statistical Society, Vol. 120, pp. 253-290.
6. Norman, M. and Stoker. B. (1991), "Data Envelopment Analysis: The Assessment of Performance," John Wiley and Sons.
7. Seiford, L. (1996), "Data Envelopment Analysis: The Evolution of the State of the Art (1978- 1995)," The Journal of Productivity Analysis, Vol. 7, pp. 99-137.
8. Tulkens, H. (1993). "On FHD Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Journal of Productivity Analysis, Vol. 4, pp. 183-210.
Ronald C. Nyhan is on the faculty the College of Urban and Public Affairs at Florida Atlantic University. Dr. Nyhan was previously a principal with Booz, Allen & Hamilton, and CEO of an international management consulting firm. His primary areas of specialization include organizational development, performance measures design and productivity enhancement.
Reader Service Form
OR/MS Today copyright © 1998 by the Institute for Operations Research and the Management Sciences. All rights reserved.
Lionheart Publishing, Inc.
506 Roswell Street, Suite 220, Marietta, GA 30060, USA
Phone: 770-431-0867 | Fax: 770-432-6969
Web Site © Copyright 1998 by Lionheart Publishing, Inc. All rights reserved.