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8/6/2019 Project Prstn
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CONTENTSCONTENTS
y Abstract
y Review of Literature
y DEA Concept and LPP formulation
y Problem Example
y Efficiency
y Demonstration
y Conclusiony Reference
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ABSTRACTABSTRACT
y It links the nonparaeff package in Rand
tcl/tkscripting language, for computing
the efficiencies of an input file
y The Input and Output parameters with the
data are taken from Reserve Bank Of
India.
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Review Of LiteratureReview Of Literature
y R is a system for statistical computation and
graphics. It consists of a language plus a run-
time environment with graphics, a debugger,
access to certain system functions, and theability to run programs stored in script files.
y R can be extended via packages.
PACKAGE NAME PLATFOR
M UTILITY PR
ICE
DEA CRAN EFFICIENCYANALYSIS
FREE
NONPARAEFF CRAN MEASURINGNONPARAMETRICEFFICIENCY
FREE
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Contd..Contd..
y Tcl is commonly used for rapid prototyping, scripted
applications, GUIs and testing.
y The most popular Tcl extension is the Tk toolkit, which
provides a graphical user interface library for a variety
of operating systems.
y For Example:
y require(tcltk) ReturnVal
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DEA ConceptDEA Concept
y A linear programming method
y There are number of producers(DMU)
y
Used to determine efficiency of numberof Decision Making Units(DMU)
y It can handle multiple input and multiple
output models.
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LPP FormulationLPP Formulation
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Problem ExampleProblem Example
y Table : 2 inputs 1 output Case
D U A C D E F
nput 4 4 4 3 2 6
2 3 1 2 4 1
Output 1 1 1 1 1 1
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Table : Results ofTable : Results of
ff e y Reffe e e Set
8 167 167 8727 182 91 727
1 2 2 1
1 25 125 1
1 5 1
1 1 1 2
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0
igure1. : fficienc of
1
C
yx2
yx1
Efficienc rontier
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EfficiencyEfficiency
y Efficiency : Use of resources (inputs) so asto maximize the productivity.
y (For multiple input and output factors)
y Efficiency =weighted sum of
outputs/weighted sum of inputsy Economic efficiency is used in microeconomics
for producing a unit of good when that unit ofgood is produced at the lowest possible cost.
y Types of Efficiencies:y 1)Technical Efficiency
y 2) Allocative Efficiency
y 3) Scale Efficiency
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Software Demo
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ModelsModels
y FDH Model- enveloping the data, withoutimposing any uncertain parametric structure
y Additive Model- non-radial DEA model, which
moves an inefficient DMU to the efficientfrontier by reducing inputs and increasing
outputs concurrently.
y Dual-Dea- The dual model is constructed by
assigning a variable (dual variable) to eachconstraint in the primal model and constructing
a new model on these variables.
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OrientationsOrientations
y Under DEA: basically two types of orientationsusing which technical efficiency is calculated, i.e.Input Oriented and Output Oriented.
y In Input Oriented method, the inputs are ina reduced form keeping the outputs constantfor a particular problem.
y In Output Oriented method, the outputscould be increased without requiring extrainput.
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Return to ScaleReturn to Scale
y Constant Returns to Scale (CRS): scale theinputs and outputs linearly without increasing ordecreasing efficiency
y
IncreasingR
eturns to Scale (IR
S): changing allinputs by the same proportion changes the output bya greater extent than the proportional value
y Decreasing Returns to Scale (DRS) inputs are in
a reduced form such that the output remainsconstant. Combining the two extremes (IRS and DRS)would necessitate Variable Returns to Scale(VRS).
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ConclusionConclusion
y The developed software can be used by
various business entities to calculate their
efficiency in various fields and hence
improve their performance.
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ReferencesReferencesy http://cran.r-project.org/ ,
y http://www.tcl.tk/ ,
y Introduction to R,
y RBI Database
y An Introduction to Efficiency and Productivity Analysis by Timothy
J.Coeli,D.S.Prasada Rao, Christopher J.ODonnel,y Charnes, A., Cooper, W. W., and Rhodes, E. (1978), Measuring the
Efficiency of Decision Making Units,
y European Journalof Operational Research, 2, 429-444,
y Theory and Techniques for Economics and Optimal Research bySubhash C. Ray, University ofConnecticut,
y An introduction to data envelopment analysis: a tool forperformance measurement by Ramu Ramanathan,
y Data Envelopment Analysis: Models and Extensions
y By Srinivas Talluri, Silberman College of Business Administration,Fairleigh Dickinson University.
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