Data Envelopment Analysis. MSc in Regulation and DEA. What it is; Farrell measures of Efficiency. technical; allocative; scale. Running DEA; Dangers of DEA. 1, Data Envelopment Analysis for Students in a Hypothetical Class. 2. 3, Please note that cells with a red marker at the upper right-hand-side corner contain. In this paper, we demonstrate that Data Envelopment Analysis (DEA) can augment the Sorry, there is no online preview for this file type.
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OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research OR. They are now available for use by any students and teachers interested in OR subject to the following conditions.
A full list of the filetypw available in OR-Notes can be found here. Data envelopment analysis DEAoccasionally called frontier analysis, was first put forward by Charnes, Cooper and Rhodes in It is a performance measurement technique which, as we shall see, can be used for evaluating the relative efficiency of decision-making units DMU’s in organisations.
Here a DMU is a distinct unit within an organisation that has flexibility with respect to some of the decisions it makes, but not necessarily complete freedom with respect to these decisions. Examples of such units to which DEA has been applied are: Note here that one advantage of DEA is that it can be applied to non-profit making organisations. Since the technique was first proposed much theoretical and empirical work has been done.
Many studies have been published dealing with applying DEA in real-world situations. Obviously there are many more unpublished studies, e. We will initially illustrate DEA by means of a small example. More about DEA can be found here. Note here that much of what you will see below is a graphical pictorial approach to DEA.
This is very useful if you are attempting to explain DEA to those less technically qualified such as many you might meet in the management world. There is a mathematical approach to DEA that can be adopted however – this is illustrated later below. Consider a number of bank branches.
For each branch we have a single output measure number of personal transactions completed and a single input measure number of staff. For example, for the Dorking branch in one year, there were 44, transactions relating to personal accounts and 16 staff were employed. A commonly used method is ratios. Typically we take some output measure and divide it by some input measure. Note the terminology here, we view branches as taking inputs and converting them with varying degrees of efficiency, as we shall see below into outputs.
For our bank branch example we have a single input measure, the number of staff, and a single output measure, the number of personal transactions. Here we can see that Croydon has the highest ratio of personal transactions per staff member, whereas Reigate has the lowest ratio of personal transactions per staff member.
As Croydon qnalysis the highest ratio of 6. To do this we divide the ratio for any branch by 6. The other branches do not compare well with Croydon, so are presumably performing less well.
That is, they are relatively less efficient at using their given input resource staff members to produce output number of personal transactions. We could, if we wish, use this comparison with Croydon to set targets for the other branches. For example we could set filerype target for Reigate of continuing to process the same level of output but with one less member of staff.
Data Envelopment Analysis Tutorial | Datumbox
This is an example of an input target as it deals with an input measure. Plainly, in practice, we might well set a branch a mix of input and output targets which we want it to achieve. Typically we have more than one input and one output. For the bank branch example suppose now that we have two output measures number of personal transactions completed and number of business transactions completed and the same single input measure number of staff as before.
For example, for the Dorking branch in one year, there were 44, transactions relating to personal accounts, 20, transactions relating to business accounts and 16 staff were employed. As before, a commonly used method is ratiosjust as in the case considered before of a single output and a single input.
Typically we take one of the output measures and divide it by one of the input measures. For our bank branch example the input measure is plainly the number of staff as before and the two output measures are number of personal transactions and number of business transactions. Hence we have the two ratios:. Here we can see that Croydon has the highest ratio of personal transactions per staff member, whereas Redhill has the highest ratio of business transactions per staff member.
Dorking and Reigate do not compare so well with Croydon and Redhill, so are presumably performing less well.
That is, they are relatively less efficient at using their given input resource staff members to produce outputs personal and business transactions. One problem with comparison via ratios is that different ratios can give a different picture and it is difficult to combine the entire set of ratios into a single numeric judgement. For example consider Dorking and Reigate – Dorking is 2.
How would you combine these figures into a single judgement? For example given five extra branches A to E with ratios as below what can be said? One way around the problem of interpreting different ratios, at least for problems filefype just two outputs and a single input, is a simple graphical analysis. Suppose we plot the two envelooment for each branch as shown below. The positions on the graph represented by Croydon and Redhill demonstrate analyzis level of performance which is superior to all other branches.
A horizontal line can be drawn, from the y-axis to Croydon, from Croydon to Redhill, and a envelopent line from Redhill to the x-axis.
This line is called the efficient frontier sometimes also referred to as the efficiency frontier. Mathematically the efficient frontier is the convex hull of the data. The efficient frontier, derived from the examples of best practice contained in the data we have considered, represents a standard of performance that the branches not on the efficient frontier could try to achieve. You can see therefore how the name data envelopment analysis arises – the efficient frontier envelopes encloses all the data we have.
Whilst a picture is all very well a number is often easier to interpret. It may, or analysiz not, be possible to do that. However we enveelopment say that, on the evidence data available, we have no idea of the extent to which their performance can be improved. Consider now Dorking and Reigate in the figure above. We can see that, with respect to both of the ratios Croydon for example dominates both Dorking and Reigate.
Can we assign an appropriate numerical value? For Reigate the ratio personal transactions: Consider the diagram below. You can see Reigate plotted on it. It can be shown that any branch with a ratio personal transactions per staff member: You can see that line below. If you are geometrically minded then the slope gradient of this line is 1.
Hence if Filetye were to retain the same business mix i. It might seem reasonable to suggest therefore that the best possible performance that Reigate could be expected to achieve is given by the point labelled Best in the diagram above. This is the point where the line from the origin through Reigate meets the efficient frontier. The logic here is to compare the current performance of Reigate the length enelopment the line from the origin to Reigate to the best possible performance that Reigate could reasonably be expected to achieve the length of the line from the origin through Reigate to the efficient frontier.
The diagram below shows the same diagram as before but with these five extra branches A to E added as in the above list of ratios. Plainly we could easily find their efficiencies from the diagram. This issue of looking at data in a different way is an important practical issue.
Many mangers without any technical expertise are happy with ratios. Showing them that their ratios can be viewed differently and used to obtain new filetypf is often an eye-opener to them. On a technical issue note that the scale used for the x-axis and the y-axis in plotting positions for each branch is irrelevant. Had we used a different scale above we would have had envelopmebt different picture, but the efficiencies of each branch would be exactly the same.
If you need convincing of this note that if we rescale the x-axis by a factor of k dattaand the y-axis by a factor of k 2then the coordinates of any point x,y change to k 1 x,k 2 y. The point labelled Best on the efficient frontier is considered to represent the best possible performance that Reigate can reasonably be expected to achieve.
Whilst we have talked above of Reigate varying the number of staff to achieve Best in fact there are a number of ways by which Reigate can move towards that point. In fact the same diagram as we used to calculate the efficient of Reigate can be used to set targets in a graphical manner. It is important to be clear about the appropriate use of the relative efficiencies we have calculated. This does NOT automatically mean that Reigate is only approximately one-third as efficient as the best branches.
Rather the efficiencies here would usually be taken as indicative analysiss the fact that other branches are adopting practices and procedures which, if Reigate were to adopt them, would enable it to filstype its performance.
In DEA the concept of the reference set can be used to identify best performing branches with which to compare a poorly performing branch. The Best point associated with Reigate lies on the efficient frontier. A branch at this point would be analysiz best possible branch to compare Reigate with as it would have the same business mix. No such branch exists however so we go to the two efficient branches either side of this Best point.
These branches, Croydon and Redhill, are the reference set for Reigate. Broadly put this means that the branches in the reference set have a “similar” mix of inputs and output.
What other reasons can you think of for the apparently low relative efficiency score for Reigate? Consider the diagram above with branches A to E included.
Data envelopment analysis
What would be the efficiencies and reference sets for branches A to E? What changes as a result of this extra branch being included in the analysis? Note that the efficient frontier now excludes Redhill. We do not draw that efficient frontier xata Croydon to Redhill and from Redhill to F for two reasons:.
The example below, where we have added a branch G, illustrates that a branch can be efficient even if it is not a top performer. In the diagram below G is efficient since under DEA it is judged to have “strength with respect to both ratios”, even though it is not the top performer in either.
Let us recap what we have done here – we have shown how a simple graphical analysis of data on inputs and outputs can be used to calculate efficiencies.