$/.*& !+- ,&)*$ ( ,&’ % ,$ “# , !

RANKING EFFICIENT UNITS BY WEAKENED REFERENCES IN DATA ENVELOPMENT ANALYSIS

Mohammad Reza Alirezaee Abolfazl Keshvari

Iran University of Science and Technology Iran University of Science and Technology
mralirez@iust.ac.ir abkeshvari@iust.ac.ir

Abstract: This paper presents a model for ranking efficient units by a new approach. In the proposed method, the idea of excluding the unit being scored from the production possibility set is changed to the idea of weakening the unit being scored. We propose a model for ranking efficient DMUs that is more efficient and less problematic than the models based on excluding the under evaluation unit.

!” #
$ %&’ ()*’ +! ,

$! ” . ! “!# : %” (*2 )” $! ” .+ %” &'( ! #) ” *’+ $,-)/ )0 0 1 # 5 )” %”* .) 4, %” * # !” + ,3% ! B+ # C” )” )= > ? @A ” 89 :;< )” 67
> )” 67 ? ” ( $! . ;+ D *% E ? ! ++ F3 G! ) C”
1268732040128

Downloaded from ijiepm.iust.ac.ir at 16:22 IRST on Saturday November 4th 2017

Downloaded from ijiepm.iust.ac.ir at 16:22 IRST on Saturday November 4th 2017

. )/? 7 5 K@A #)” # &% HC I?) 8 %: ” 8J $,-)/ )0 0

)” 67 L%” * L :
– .)/ A R ) W) ! “!# ), + UV4 [T] MNSO + %= 5),’/ UV4 $! CCR -) # *0 >” ‘” ? $! >” 8J # X .)A+ . U<+ %# $! ‘” K -)/ )0 8(( # ( ” #” UV4 [Z] MNPY ) B+= >)A%” )” BCC ! #) .+)” ” BCC )2
%= 2 8J # X . <! )[, ( ” #” .[Y] ),% ” , K\(

Decision Making Units (DMU)
Farrell 8 Banker
9 Returns to scale

.
“!# )” CCR [M] MNOP # ) >B+= Q! CCR .+ D !
‘!( ” 8J ! #) ! “!# )” ), +

/ / :
// :
!”
mralirez@iust.ac.ir
#$% &'()*+*
abkeshvari@iust.ac.ir
Charnes
Cooper
Rhodes
Efficiency frontier
.
3 B! +)” Q! ” BCC ) 2)f *) > ) )” ” !J ” # (E *) ” U j . -) 8J I?) 8 %: yj =(y1j, y2 j,…, ysj ) & 8+ uj =(yj,−xj ) PPS 9 ” DEA ‘ + C- . xj =(x1j, x2 j,…,xmj ) jR .& 8+ u=(y,−x) ” PPS ]:;< C: . u j ∈PPS (∀j =1,…,n) :% 0 CCR ”

⎛ ms⎞
min z =θ−ε⎜∑ s− +∑ s+ ⎟


s.t.
⎧⎪θxip −∑n λj xij − si− = 0 ∀i
⎪j=1 (CCR)
⎪⎪ n

yrp ∀r
⎪ j=1
13651733162



⎪⎩

)” ” ” >+ 8″ CCR )” )!# H!) .%,’ 8″ “0 B+ >BCC %+ >)a!
)” )” & 8+ θ* ” U p ] !
.(CCR) θ ]%V” ( ”
M ! 8J # 2(+ ]:;< PPS ! #)
.%”
# u l(+ ]:;< # ‘*: p ] _k C-
.u≥up PPS
& 8+ u(p) ” U p ] I?) ](+
$! )”%” >u( )

u j 8J _k C- # (+
j=1
.u( )p ≥up
& 8+ E(p) U p ] I? ) ]:;< .

” ! )” – #) # 4, ” H! $! .+ $* M A > ?)3 Q!

7
. 8
Productivity Possibility Set
Reference
1268732040128

Downloaded from ijiepm.iust.ac.ir at 16:22 IRST on Saturday November 4th 2017

Downloaded from ijiepm.iust.ac.ir at 16:22 IRST on Saturday November 4th 2017

) )” > ; )” !J ” ! ( 8 %: ” :
&'( + ], ” >8J
.+ Q! # ),; ! + \” 8 ) )” )0 >Q! 🙂 %,’ Q! )” )” ! ( ) 8 , ” > !
_ $! `* >)” ” 8J ? ” )a! *b
.( 8″ [M]
%” * dR ” [S] MNNZ 8), 8+ +) 4, ! $! # V+J .%,3 ) #) K )[ +) 67 8A :;< # C ” eT C 8″ eM ! .+ )0 %”* < “!# %* > /! $; ” %” * ” )a! K B+ 8J # X
)” 4,f 5 >K4, /! )” U<+
. )2 %” * )” 67 5 ( $! A%! ” ? ” 8J W@g V? %,-)/ )0 )” 8J K@A 5 )” !V :;< # D !?
8+ + V+ 8%” )” 67
K* /! $! ! 8 %: ” 8),
. 3 4, ( $! “!# . A 8),e8+ %” * %” * )” 8),e8+ 5 ( $!
W@g )” A%A W) 8J # + K@A
. D 8),e8+ UV4 -) ” if” : )!# Kg ” ( ,3 .% %” (*2 >I?) 3 U if” .+ D if” $! ;+ g H!) e8+ .+ 8″ 8J K@A 8),e8+ .% $ V+J * I?) 3 67 ” 8), 3 HC ” 8),e8+ >U if” if” . W@g (I?) 3 67 ? “) I?)
. 8″ ( W) _ ]<,+ UV=

Data Envelopment Analysis (DEA)
Efficiency
Efficient
Inefficient
Andersen
Petersen

E( ) { }p = p • E( ) { }p ≠ p •

l”) 3 B! +)” U .u( )p = up )
)a! ]%V” E ? +/%= ]%V” E ? p ”
. E( ) { }p = p 2 ” ?

355087492922

x
1

x
2



قیمت: تومان


دیدگاهتان را بنویسید