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

By R Ramanathan

From the Foreword: 'This publication is a superb software for practitioners who're drawn to the advantages and pitfalls of the technique…. (The author's) study 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) will be of any style: production devices, a collection of colleges, banks, hospitals, strength crops, police stations, prisons, a suite of businesses and so on. DEA has been unsuccessfully utilized to degree the functionality potency of those other kinds of DMUs which percentage a standard 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 agencies that use a number of exact inputs-say in terms of a faculty: caliber of scholars, academics, offers etc.,-to produce various exact outputs-number of scholars who cross the ultimate yr, typical grades got by means of the scholars within the ultimate yr and so on. DEA assumes the functionality of the DMUs by utilizing the suggestions of potency or productiveness that's measured because the ratio of overall outputs to overall inputs. additionally, the efficiencies anticipated are relative to the simplest appearing DMU or DMUs. the easiest appearing DMU is given a ranking of a hundred% and the functionality of different DMUs range among zero -100%.

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4) where Em is the efficiency of the mth DMU, yjm is jth output of the mth DMU, vjm is the weight of that output, xim is ith input of the mth DMU, uim is the weight of that input, and yjn and xin are jth output and ith input, respectively, of the nth DMU, n = 1, 2, …, N. Note that here n includes m. Consider the Firms A, B, C and D discussed in the first chapter. Let vVA, A be the weight associated with the only output (value Mathematical Programming Aspects of DEA 41 added, VA) when Firm A is the reference DMU.

Note that the techniques of frontier analysis has been described by Farrel in 1957, but a mathematical framework to handle frontier analysis could be established only after 20 years. This mathematical formulation was provided by Charnes et al. (1978). This seminal paper provided the fundamentals of the mathematical aspects of frontier analysis. The authors also coined the term Data Envelopment Analysis. 1 Mathematical Formulation Let us use x and y to represent inputs and outputs, respectively.

15: they represent the best achievable performance. 7q B* represents the best achievable value for employees. Together, these two values represent point E. 17). The dual objective function for a firm corresponding to point E is min θ E − ε s EMP, E , * which is less than 1 as e and sEMP, B are positive. 1. Firms P and R are efficient. They represent the best practice. This implies that no other firm or no linear combination5 of firms can be identified which produces the same level of output for less than either or both the inputs.

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