project prstn

8/6/2019 Project Prstn

1/18


2/18


3/18

CONTENTSCONTENTS

y Abstract

y Review of Literature

y DEA Concept and LPP formulation

y Problem Example

y Efficiency

y Demonstration

y Conclusiony Reference


4/18

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.


5/18

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


6/18

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


7/18

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.


8/18

LPP FormulationLPP Formulation

s,,rru

m,,iiv

r

i

.

.

21outputththetoassignedeightThe:

21inputththetoassignedeightThe:

!

!

0,,,,0,,,

2.1,,2,11subject to

Maximize

2121

11

11

2211

2211

uu

!e

!

sm

mjmj

sjsj

mkmkk

skskk

uuuvvv

njxvxv

yuyu

xvxvxv

yuyuyu

..

..

.

.

.U


9/18

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


10/18

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


11/18

0

igure1. : fficienc of

1

C

yx2

yx1

Efficienc rontier


12/18

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


13/18

Software Demo


14/18

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.


15/18

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.


16/18

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).


17/18

ConclusionConclusion

y The developed software can be used by

various business entities to calculate their

efficiency in various fields and hence

improve their performance.


18/18

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.

project prstn

Documents