# An Introduction to Data Envelopment Analysis - A Tool for by R Ramanathan

By R Ramanathan

From the Foreword: 'This e-book is a wonderful instrument for practitioners who're attracted to the benefits and pitfalls of the techniqueâ€¦. (The author's) learn is an instance of inventiveness, diligence and accuracy' - Freerk A. Lootsma, Delft Institute of expertise information envelopment research is a Mathematical Programme for measuring functionality potency of organizational devices. The organizational devices, termed as decision-making devices (DMU) might be of any variety: production devices, a suite of colleges, banks, hospitals, strength vegetation, police stations, prisons, a suite of agencies and so forth. DEA has been unsuccessfully utilized to degree the functionality potency of those other forms of DMUs which proportion a typical attribute - that they're non-profit association the place size of functionality potency is hard. DEA has been hired for assessing the relative functionality of a suite of businesses that use quite a few exact inputs-say in relation to a faculty: caliber of scholars, lecturers, gives you etc.,-to produce quite a few exact outputs-number of scholars who go the ultimate 12 months, regular grades bought via the scholars within the ultimate yr and so on. DEA assumes the functionality of the DMUs through the use of the techniques of potency or productiveness that is measured because the ratio of overall outputs to overall inputs. additionally, the efficiencies anticipated are relative to the easiest appearing DMU or DMUs. the easiest appearing DMU is given a rating of a hundred% and the functionality of different DMUs range among zero -100%.

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**Sample text**

As we do not know which ratio is more crucial, we cannot say Firm A is more efficient than Firm C or otherwise. , value added to capital or value added to employees) are lower. 3 Graphical DescriptionFrontier Analysis One way to tackle the problem of interpreting different ratios, for problems involving two inputs and one output, is through graphical analysis. 1. 1. 5. 6. The firms that are more efficient consume lower levels of input per unit of output and hence lie closer to the origin. As discussed previously, Firms A and C are more efficient than the others.

6 See Chapter 5 for further discussion on the computational features of DEA. 58 An Introduction to Data Envelopment Analysis The optimization models for Stages 1 and 2 are given below. 24) Note that this Stage 1 model is the same as the DEA model with no e constraints. 25) where q * is the optimal value of q A in stage 1. 4 Multiplier and Envelopment DEA Programs We know that the dual of a dual is primal. Hence, the terms primal DEA program and dual DEA program are relative. New terms are being increasingly used to represent DEA formulations.

The general matrix representations of the four programs are given below. 7 This section requires knowledge of matrix algebra, and can be skipped without any loss of continuity. Mathematical Programming Aspects of DEA 63 Multiplier Versions Output Maximizing Envelopment Versions Input Oriented z = VmT Ym max U, V such that UmT Xm = 1 VmTY − UmT X ≤ 0 VmT , UmT ≥ 0 or VmT , UmT ≥ ε θm min θ ,λ such that Yλ ≥ Ym Xλ ≤ θ m Xm λ ≥ 0; θ m free ( ) Input Minimizing Output Oriented z′ = Um′T Xm min U′, V′ φm max φ, µ such that Yµ ≥ φ mYm Xµ ≤ Xm µ ≥ 0; φ m free such that Vm′ TYm = 1 Vm′ TY − Um′T X ≤ 0 Vm′ T, Um′T ≥ 0 or Vm′ T, Um′T ≥ ε ( ) Using the theory of duality, we can make certain observations regarding the relationships among the optimal values of these programs.