Data Envelopment Analysis software

Frequent questions

Frontier Analyst® FAQs – General

Where can I get training?

A variety of places! Training in the use of Frontier Analyst® ranges from the basics – how to create a map and “which buttons to press”, through to advanced workshops which deal with “power user” applications – facilitating workshop, seamless use of Frontier Analyst® via the command line. There are a number of courses available. See our training pages for details.

Can I link to other software?

Yes! Frontier Analyst® allows you to copy results and maps to the clipboard for inclusion in other software.

You can also import data into Frontier Analyst® using the clipboard or ASCII text files. Direct support for a number of applications is also available – see thenew project wizard for details.

The install code doesn’t work

All install code problems are down to not typing the code in correctly, although this is usually because it’s not 100% clear whether a character is an ‘I’ or a ‘1’ (‘eye’ or ‘one’), or an ‘0’ or ‘O’ (zero or ‘oh’). The install codes are printed in a font which does differentiate, but unless you have two characters to compare it can be difficult. The ‘Oh’ is generally more rounded than the zero which is more oval. The ‘eye’ character has ‘serifs’ (extra little lines) on both sides at the top of the character, the one has only the left hand serif.

In general, the character will (as the software suggests), be a zero and not a letter ‘oh’. However, the letter ‘oh’ will appear in some codes, so you should try both combinations. Make sure that the user has entered the ‘-‘ characters in the right places too, nothing extra should be entered.

Can I run Frontier Analyst® on Windows 95, 98 and/or Windows NT or XP?


Windows compatibleFrontier Analyst® version 4 requires Windows 7, 8, 10 or 11. Version 3 is no longer available.

Can I run Frontier Analyst® on a Mac?

Yes, if you have a Windows emulator.

We know of many users who are using Frontier Analyst® on a Macintosh using a Windows emulator. If you want to see how well it works for you, then download the demonstration program. This is a fully working version of Frontier Analyst®, limited only in the number of concepts (ideas) that you can enter. If this program works with your Windows emulator, then the full program will.

At present there are no immediate plans to produce a Mac version of the software. Sorry – we cannot be more specific or give you any more details at this time, but this is a discussion which comes up from time to time. A Mac version has not been ruled out as a possibility.

Frontier Analyst® FAQs – Getting the best

How many ‘units’ do I need?

Q: What is the smallest number of units I can use DEA for?

A: Although it works best with larger numbers of units, DEA can successfully work with a very small number of units but you cannot use many input/output factors if it is to be useful. There is a simple rule of thumb: Multiply the number of inputs by the number of outputs – that is the number of units that are likely to be given a score of 100%. So, with four inputs and four outputs, you’ll probably get 16 efficient units. If you have 20 units, the discrimination will not be very good! If you have 200 units, then there is no problem.

Frontier Analyst® provides additional (non-DEA) analysis such as correlation displays so that you can view your data and select the input/output factors that you will use in the analysis. For example, if two inputs are highly correlated, then they perhaps represent the same thing and one could be excluded from the analysis.

Why do I get optimizations on both inputs and outputs?

Q: Choosing input minimization, the DEA solutions (results) sometimes also indicate the DMU can optimize their outputs too. I would expect that output is fixed and only input improvements can be made. The other way around, choosing for output maximization, some results say the DMU should change their input as well. What is the explanation for this?

A: The reason is due to the optimization that is done to show each unit in its best possible light. The linear program finds an optimal position relative to the efficient frontier which gives the unit its score. However, in doing so, it can also determine that to achieve that position, it does not need to use as much resource as it is using, or could produce more output (depending on the mode of operation). You could argue that such improvements should not be shown since that is not what you are looking for, but it is useful information and tells you a little more about your units, which is why we include it in the results information.

What do the Data Export Values mean?

The Data Export window introduced in Frontier Analyst® 3 allows you to get a lot of the core information from the analysis results and perform post-processing on them. The values available are described below.

The data for each unit is output as a separate line. For data items with multiple values, these are output in an appropriate number of columns. Data items that vary in number (efficient peers for example) use the number of columns to fit the maximum required, with either blank or zero values used for cells that are not needed.

Export item Data source
Score The score of the item, expressed as a percentage.
Actual values The values used as input into the calculation.
Target values The values that have been generated as targets – these would take the unit to the frontier.
Percentage actual->target The percentage difference between the actual and target.
Difference actual->target The difference between the actual value and the target generated.
Primal value (DEA core) The Primal Values are the raw weights assigned to the VARIABLES when solving the DEA model. They are most easily interpreted via the primal formulation of the DEA model.
Primal intercept (DEA core) The Primal Intercept is the constant term used in the BCC (varying returns to scale) version of the DEA formulation. This term can be used to determine “returns to scale” characteristics.
Lambda value (DEA core) The Lambda Values are the raw weights assigned to the peer UNITS when solving the DEA model. They are most easily interpreted via the dual formulation of the DEA model.
Lambda peer indicator This value is output either as a zero (no peer) or as a cell reference to the peer that the related lambda value relates to. Each Lambda value has an associated peer indicator. The cell reference is designed with the top left cell as “A1”. If you copy and paste into a spreadsheet, you should paste into an empty sheet first if you are not pasting to the A1 cell. The spreadsheet program will then adjust the references for you.
Returns to scale (-1, 0, 1) In the variable returns to scale model, this gives information about the returns to scale that the unit is displaying. This is output as a numeric value for easier post-processing. -1 indicates decreasing returns to scale, 0 indicates constant returns to scale, and +1 indicates increasing returns to scale.
IO Contributions The contributions, as a percentage, that each input and output gave to the final score (how much weight was applied to each input/output).
Peer Contributions The relative contribution towards the score given to each peer. The higher the contribution, the closer in performance the peer to the unit under consideration.
Number of peers The number of peers that the unit has, if any. Zero for units deemed efficient.
Number of references For efficient units, this is the number of references to this unit as a peer. For inefficient units, this is always zero.
Slacks This value is an internal calculation value, provided for users with specialist requirements. Interpretation is not supported by Banxia.

Does Frontier Analyst® Support “Weight restrictions”?

Q: One DEA facility that is discussed in academic papers is “weight restriction”. This allows the user to limit the emphasis placed on a particular input or output factor in the analysis. Does Frontier Analyst® support this facility?

A: Yes! The Since version 2, Frontier Analyst® has provided for user-specified weight restrictions without compromising the ease of use.

Q: How does Weighting help my work?

In data envelopment analysis, “weighting” allows a level of control over the efficiency scores. It allows you to ensure that at least some part of the efficiency score of every unit takes account of a particular input/output variable. For example, if the primary business is retail, the number of transactions is going to be important. Without weighting, a unit may be judged as efficient because it is doing well on stock levels per member of staff. That may be acceptable – it depends on your data – but if you want to ensure that transactions are considered, you need to add a weighting.

The Analysis Options window controls the way that the analysis is performed, and the weighting options are obtained by clicking on the Advanced button to show the bottom part.

The weighting grid allows you to enter the weights that are associated with each input/output variable. It is recommended that you add weights to only one or two variables, and that they are small. In general terms, the way DEA works is that the analysis tries to optimize the units’ score by varying the weights it applies to each input and output. It has 100% to allocate across all the variables. The weighting facility allows you to tell the analysis that it is not allowed to put less than a certain percentage on a particular variable. A problem will arise if you tell the analysis that it cannot put less than 60% on one variable and less than 60% on another. That totals 120%, which is impossible. Frontier Analyst® will tell you the problem is insolvable, and you will have to change the weights. Even weights close to 100% will cause problems – the ideal is to give Frontier Analyst® 100% freedom to optimize, and to tweak a weight or two if you are not happy with the results.

The maximum weight is similar to the minimum, except that it prevents all the weight being put on a particular input/output variable. In this case, the total of the maximums must be at least 100%, and preferably much more.

Is Weighting Appropriate?

Some people think that by allowing you to control the analysis to add bias it undermines the theoretical basis of DEA – which is to provide a method of comparing peers without higher level influence clouding the judgments.

However, the real world has a different emphasis – if you are to implement an improvement process, you have to be able to justify the basis for it. If a unit has been judged efficient on a ratio that is meaningless to the business, it may be a problem. The weighting facility allows you to ensure that every unit is judged at least to some extent on something that is critical to your business, for example transactions processed. However, don’t over-use the facility or the analysis will have its scope for optimization severely reduced.

Q: What is the mathematical model behind weighting?

The weight restriction model used in Frontier Analyst® is based on the use of proportions (Wong and Beasley 1990). These proportions determine how “prominently” a particular (input or output) variable must feature in the efficiency ratings of the units.

Consider a DEA analysis that includes the output variable “Profit”. If the user specifies that the weight assigned to profit must be between 0.3 and 0.8, then she is stating that “Profit” must contribute at least 0.3 and at most 0.8 of the total weighted output used to determine a unit’s efficiency.

Staff Input 100
Profit Output $500,000
Sales Output $10,000,000

Table 1: Data for DEA model

In a typical DEA analysis (Charnes et al 1978), the efficiency of a DMU is determined using the ratio of a weight sum of the output variables to a weighted sum of the input variables. So, for the unit described in Table 1, its efficiency would be determined by a weighted sum of “Profit” and “Sales”, over a weighted sum of “Staff” . Using the weight restrictions given earlier, the normalized value for “Profit”, multiplied by its assigned weight, would have to account for at least 30%, and at most 80%, of the combined, normalized, weighted values of “Profit” and “Sales”.

This metric was adopted as it is (relatively) easy to interpret – “output (or input) variable X must contribute at least, or at most, Y% to the efficiency ratings”. Unfortunately, a complete understanding of any weighting mechanisms require an comprehensive understanding of the DEA model. The interested reader should consult the references for further information.

Wong and Beasley 1990 Wong Y-H; Beasley J E, “Restricting Weight Flexibility in Data Envelopment Analysis”, 1990, Journal of the Operational Research Society 41 9, 829-835.

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

Q: How can you discriminate 100% score units?

Q: A branch that excels in only 1 dimension among the 10 and is worst in some or all other dimensions will be efficient using DEA. Further scope for improvements is reported as NIL for all the outputs from DEA. As the branch (e.g. branch A) is efficient, how should it be rewarded? Compared to other branches which may have 90% as efficiency and at the same time are not worst in any dimension, should branch A be rewarded? Is there any known technique in DEA which quickly detect all situations as described above where a branch may excel in only one dimension and are worst in all others?”

A: It is indeed the case that if a branch is found to be the best performer on one particular dimension then it will be found to be 100% efficient. Such an efficient branch, as you say, may well be performing poorly on the other dimensions in the analysis. There is thus a need to determine which of the efficient branches truly reflect good overall performance. There are two procedures in Frontier Analyst® which help to discriminate between branches found to be 100% efficient.

(1) Reference Set Frequency. All inefficient branches have their efficiency score calculated by comparing them with the 100% efficient branches most similar to them in terms of their input/output profile. These efficient branches will appear in an inefficient branches Reference Set. The number of times a 100% efficient branch appears in inefficient branches reference sets is a indicator of whether the efficient branch is largely a self evaluator or whether it is a role model for other inefficient units to emulate. The higher the frequency with which an 100% efficient unit appears in reference sets the more likely it is that it is an exemplar of good performance. Once the efficiency scores have been calculated, in Frontier Analyst®, the Reference Set Frequency can be obtained by clicking the icon labeled “Freq”.

(2) Virtual Inputs/Outputs A virtual input or output describes the importance attached to inputs and outputs in determining the branches efficiency rating.

“A branch whose efficiency rating is based fairly evenly on all its outputs and inputs can be said to show well-rounded performance. A 100% efficient unit with well-rounded performance is relatively efficient when all aspects of its performance are taken into account rather than just a small subset of them.” Thanassoulis et al, JORS 1987.

For a 100% efficient branch the virtual outputs will add up to 100%. In the analysis you are considering, with 10 outputs, if an efficient branch has all its virtual outputs around 10% then its efficiency rating will be based fairly evenly on all its outputs. If, by contrast, all 100% of the virtual output has been placed on one output then its efficiency rating will have been determined solely on its performance on that dimension. The Virtual Input/Output contributions for an efficient unit can be obtained from the “Unit Details” in Frontier Analyst® (not shown in the rolling demo at time of writing). These two methods will assist you in discriminating between the efficient units and hopefully will help in determining the policy you wish to adopt for awarding the branches.

Q: What does “greater than 8 orders of magnitude” mean?

Q: When I analyse my project data, Frontier Analyst® shows a message that says the data varies by more than 8 orders of magnitude. What does this mean?

A: This situation occurs when you have a range of numbers for one of your input or output variables that are very different. For example, you may have one unit with a value of “1”, and another with a value of “1,000,000,000”. The difference between these two numbers is too big to allow proper operation of the software – for the first unit to match
the second it would have to improve by over a million percent, and that will cause a problem.

This situation most often occurs when you have zero values in your data, and you have used the zero substitution facility to replace zeros. The default replacement value is “0.01”, so this is very small. In this example, with values of many millions, you could set this value to 100 perhaps, and it would perform the appropriate role. It is important to note though that the zero-substitution facility was designed as a quick help to get started, and you will have problems if
you have another variable with data ranging from, say, 1 to 10. The zero changed to 100 would then be much larger than the rest, and not close to zero at all. This is why we recommend fixing the source data for real projects.

Q: When the program calculates an efficiency, is that based upon a zero origin?

Q: When the program calculates an efficiency, is that based upon a zero origin? In other words, if you have lots of points positioned very near the frontier, will the scoring result in lots of high scores, or, rather, is the scoring relative to the least and most efficient points in the set?

A: Yes, it is based on a zero origin. If you look at the frontier plot, the score is obtained by drawing a line from the origin to the frontier through the points representing the unit of interest. The percentage position on that line is the score given to the unit. Of course when it gets “n-dimensional” the frontier is a lot more complicated, but the principle is the same.

Q: Do we need to ensure that the polarity of the inputs and outputs is uniform?

Q: Do we need to ensure that the polarity of the inputs and outputs is uniform? In other words, are all the inputs considered “good” when they are numerically smaller and conversely all the outputs are considered good when they are numerically greater?

A: Yes. Some inversion may be needed for sensible operation, but this will depend on the data. For example, you may have a percentage of people complaining, and in that case more is bad. So you’d invert it by making it the percentage of people who didn’t complain to get more is good. In some cases, you may have to use other mathematical methods to invert them – it is obviously important that it makes sense in the real world which is why we don’t do anything automatically.

Q: My data has negative numbers – is that okay?

Q: My data has negative numbers – is that okay? What will FA Pro do in this instance?

A: Data envelopment analysis cannot operate with negative numbers, for the same reason it cannot handle zeroes. Essentially the analysis is trying to multiply the actual value to match the values of other units. If a value is negative, then the greater the multiplier the further away the value ends up, so it obviously isn’t going to work. Again, this is a matter of changing the values to something small, adding a constant or picking an average – only the end user can know what makes sense in their case.