The Basis of Data Envelopment Analysis
- 1. The basis of Data Envelopment Analysis Skarleth Carrales 1
- 2. What is DEA? DEA stands for Data Envelopment Analysis DEA is a data-driven, non-parametric, frontier-based methodology originally designed for the evaluation of the relative performance of a set of entities commonly referred to as decision- making units (DMUs). Within a DEA framework, benchmarking is done with respect to the best or the worst peers rather than the average performers, which is the case for other methodologies such as Stochastic Frontier Analysis. In other words, DEA is one of the most used methods for measuring the relative efficiency of a group of similar entities in transforming selected inputs into outputs.
- 3. Before using DEA model Before using DEA model, we need to take several decisions such as: 1. DUMs 2. Inputs 3. Outputs 4. Scale 5. Orientation 6. Model 7. Static or Dynamic
- 4. DUMs Inputs Outputs Scale Orientation Model Stat / Dynamic What is a DMU? o DMU stands for Decision Making Units and is a set of peer units. o DMUs are the units under evaluation, for example: Universities, Banks, Hospital, cities, companies, basketball teams, etc. o These entities, known as DMUs, are assumed homogenous. For example if we want to asses the relative efficiency of Banks (DMUs) we need to group the DMUs accordingly to ownership (e.g. public or cooperative), location (e.g. domestic or foreign), size (e.g. big, medium, small), or market condition, in order to have an homogenous set of peer units. Note: Avoid Outliers
- 5. DUMs Inputs Outputs Scale Orientation Models Stat / Dynamic Inputs and Outputs In DEA the measures/metrics are classified as Inputs and Outputs An important feature of DEA is its capability to provide efficiency scores, while taking account of both multiple common inputs and common multiple outputs, without assuming any relationship between them. DMUs The inputs are the resources used to produce the outputs The outputs are the products and/or services produced by the units. *The inputs and outputs used in DEA define the basis to be used for assessing the units concerned, and so they must be determined with great care. Note: the number of DMUs should be at least three times the total number of inputs plus outputs used in the models. Inputs Outputs
- 6. DUMs Inputs Outputs Scale Orientation Models Stat / Dynamic Types of Scale The basic DEA models are Constant Return to Scale (CRS) used in the CCR model, and Variable Return to Scale (VRS) used in the BCC model. CCR BCC Yields an objective evaluation of overall efficiency Estimates pure technical efficiency at the given scale of operation Identifies the sources and estimates the amounts of thus-identified inefficiencies Identifies whether increasing decreasing, or constant returns to scale possibilities are presented for further exploitation Results in a piecewise linear, constant returns-to-scale (CRS) envelopment surface. Yields in a piecewise linear, variable returns-to-scale (VRS) envelopment surface. Mehdi Toloo and Soroosh Nalchigar (2009) suggest that “CCR models are a specific type of BCC models” because “identifies whether a DMU is operating in increasing, decreasing or constant returns to scale”.
- 7. DUMs Inputs Outputs Scale Orientation Models Stat / Dynamic Orientation To select the orientation of the model depends on the objective of the evaluation Input-oriented o To minimize the inputs at the same time that we are producing at least the same output level given Output-oriented o To maximize the outputs at the same time that we are using no more than the inputs observed. Non-oriented o To reduce at the same time inputs and increase outputs. In this type of orientation, we assume that are able to control the inputs and outputs and thus change them simultaneously.
- 8. DUMs Inputs Outputs Scale Orientation Models Stat / Dynamic DEA models With the passing of the years, DEA has been developed and becoming a “body of concepts and methodologies that have now been incorporated in a collection of models” (Cooper et al. 1994). These developments have emerged by the necessity of covering certain areas that the usual DEA method do not cover by itself. We can see a sample of the developed models In Cook and Seaford’s survey (2009).
- 9. Static or Dynamic? DUMs Inputs Outputs Scale Orientation Models Stat / Dynamic The main objective is to measure the efficiency of the DMU Do we want to consider one period or more in the analysis? Do we want to consider the DMU as a whole unit or we want to take into account the internal structure?
- 11. Network Period t Sub DMU 1 Sub DMU 2 Sub DMU 3 Input 1 Input 2 Input 3 Link 1 - 2 Link 2 - 3 Output 1 Output 2 Output 3
- 12. Dynamic Period t DMU 1 Input 1 Output 1 Carry Over Period t+1 DMU 1 Input 1 Output 1
- 13. Dynamic-Network Period t Sub DMU 1 Sub DMU 2 Sub DMU 3 Input 1 Input 2 Input 3 Link 1 - 2 Link 2 - 3 Output 1 Output 2 Output 3 Carry Over Carry Over Carry Over Period t+1 Sub DMU 1 Sub DMU 2 Sub DMU 3 Input 1 Input 2 Input 3 Link 1 - 2 Link 2 - 3 Output 1 Output 2 Output 3