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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Data Envelopment Analysis, also known as DEA, is a non-parametric method for performing frontier analysis. It uses linear programming to estimate the efficiency of multiple decision-making units and it is commonly used in production, management and economics.
The technique was first proposed by Charnes, Cooper and Rhodes in and since then it became a valuable tool for estimating production frontiers. The Datumbox Machine Learning Framework is now open-source and free to download.
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When I first encountered fjletype method years ago, I was amazed by the originality of the algorithm, its simplicity and the cleverness of the ideas that fileetype used. I was even more amazed to see that the technique worked well outside of its usual applications financial, operation research etc since it could be successfully applied in Online Marketing, Search Engine Ranking and for creating composite metrics.
Despite this, today DEA is almost exclusively discussed within the context of business. That is why, in this article, I will cover the basic ideas and mathematical framework behind DEA and in the next post I will show you some novel applications of the algorithm on web applications. Data Envelopment Analysis is a method that enables us compare and rank records stores, employees, factories, webpages, marketing campaigns etc based on their features weight, size, cost, revenues and other metrics or KPIs without making any prior assumptions about the importance or weights of the features.
The most interesting part of this technique is that it allows us to compare records comprised of multiple features that have totally different units of measurement.
As we discussed earlier, DEA is a method which was invented to measure productivity in business. Thus several dqta its ideas come from the way that productivity is measured in this context.
One of the core characteristics of the method is the separation of the record features into two categories: For example if we measure the efficiency of a car, we could say that the input is the liters of petrol and the output is the number of kilometers that it travels. Additionally Data Envelopment Analysis assumes that the features can be combined linearly as a weighted sum of non-negative weights and form a ratio between input and output that will measure the efficiency of each record.
The efficiency is measured by the ratio between output and input and then compared to the ratio of the other records. We use input and outputs, weighted sums and ratios to rank our records. The clever idea of DEA is in the way that the weights of the features are calculated. Instead of having to set the weights of the features and deciding on their importance before we run the analysis, the Data Envelopment Analysis calculates them from the data.
Moreover the weights are NOT the same for every record! Here is how DEA selects the weights: We try to maximize the ratio of every record by selecting the appropriate feature weights; at the same time though we must ensure that if we use the same weights to calculate the ratios of all the other records, none of them will become larger than 1. The idea sounds a bit strange at the beginning. The answer is yes. Does not this mean that we actually calculate differently the ratios for every record?
The answer is again yes. So how does this work? The answer is simple: So the main idea of DEA can be summed in the following: Suppose that we are interested in evaluating the efficiency of the supermarket stores of a particular chain based on a number of characteristics: It becomes obvious that finding the most efficient stores requires us to compare records with multiple features.
To apply DEA we must define which is our input and output. In this case the output is obviously the amount of sales and the number of customers that they serve. The input is the number of employees and the size of the store. If we run DEA, we will estimate the output to input ratio for every store under the ideal weights as discussed above.
Once we have their ratios we will rank them according to their efficiency. The efficiency ratio of a particular record i with x input and y output both feature vectors with positive values is estimated by using the following formula:.
Where u and v are the weights of each output and input of the record, s is the number of output features and m is the number of input features.
Data envelopment analysis – Wikipedia
To solve this problem we must use linear programming. Unfortunately linear programming does not allow us to use fractions and thus we need to transform the formulation of the problem as following:. We should stress that the above linear programming problem will gives us the best weights for record i and calculate its efficiency under those optimal weights. The same must be repeated for every record in our dataset.
So if we have n records, we have to solve n separate linear problems. Here is the pseudocode of how DEA works:. DEA is a great technique but it has its limitations. You must understand that DEA is like a black box. Since the weights that are used in the effectiveness ratio of each record are different, trying to explain how and why each score was calculated is pointless. Usually we focus on the ranking of the records rather than on the actual values of the effectiveness scores.
Also note that the existence of extremums can cause the scores to have very low values. Have in mind that DEA uses linear combinations of the features to estimate the ratios. Thus if combining them linearly is not appropriate in our application, we must apply transformations on the features and make them possible to be linearly combined. Another drawback of this technique is that we have to solve as many linear programming problems as the number of records, something that requires a lot of computational resources.
Another problem that DEA faces is that it does not work well with high dimensional data. Running DEA when d is very close or larger than n does not provide useful results since most likely all the records will be found to be optimal.
Note that as you add a new output variable dimensionall the records with maximum value in this dimension will be found optimal. This means that DEA can be a good solution when it is not possible to make any assumptions about the importance of the features but fieltype we do have any prior information or we can quantify their importance then using alternative techniques is advised.
In the next article, I will show you how to develop an implementation of Data Envelopment Analysis in JAVA and we will use the method to estimate the popularity of web pages and articles in social media networks. My name is Vasilis Vryniotis. Such an example could be the evaluation of the efficiency of hospitals where the input is doctors and nurses and the output is patients. What those weights represent? Basically the importance of each feature.
So what we have at the end of the analysis is a score for each record under different conditions aka different weights. In each case, those weights are selected envelopmrnt maximize the efficiency of the record and thus it can be considered as the upper analyais of the efficiency of the record. Since the score is the maximum value of the Linear Programming Problem, it is not always simple to explain why the record received the score.
If you want to interpret it, you must check the weights that maximized its score and try to understand in which sense and under what condition this record receives the score. DEA is used in cases when you have no idea about the importance of the features or when it does not make sense to make assumptions about their weights.
Data envelopment analysis
For example in the context of the hospital, what is more important input the nurses or the doctors? Or when you evaluate the performance of a store, what is more important the revenues or the number of served customers? I hope this clarifies the matter a bit and not the opposite.
BTW in the article, I dat to the original article. The math that I provide in the article envelpoment the same, but for more details you can refer to it.
Data envelopment analysis
Why Data Envelopment Analysis is interesting? The description and assumptions of Data Envelopment Analysis As we discussed earlier, DEA is a method which was invented to measure productivity in business.
The efficiency ratio of a particular record i fletype x input and y output both feature vectors with positive values is estimated by using the following formula: Unfortunately linear programming does not allow us to use fractions and thus we need to transform the formulation of the problem as following: Here is the pseudocode of how DEA works: If you like the article, take a moment to share it on Twitter or Facebook.
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