$OnText
This file contains the DEA–MBP model program code to measure�eco-efficiency.
This model developed by Arabi et al (2016).

Table of contents:
         1- Sets
         2- Data
         3- Calculations & post Parameter definition
         4- Variables
         5- Equations
         6- Bounds
         7- Models & solution
         8- Display & Table generation


$offtext


option solprint=on;
Option nlp=conopt4;
*$OnText
$set commandfile commands.txt
$onecho > %commandfile%
I=DATA.xlsx
O=Data.GDX
$offecho
$call gdxxrw Index=Index!a1 @commands.txt
*$OffText

$gdxin 'Data.GDX'


Sets

l   set of Low  pollutant inputs
h   set of High pollutant inputs
m   set of NON- pollutant inputs

j   set of NON- pollutant outputs
k   set of     pollutant outputs

n   set of Decision making units

$Load l,h,m,j,k,n

Alias (n,o)
Parameters

XL(n,l) Amount of Low  pollutant inputs
XH(n,h) Amount of High pollutant inputs
XM(n,m) Amount of NON- pollutant inputs
Y(n,j)  Amount of NON- pollutant outputs
Z(n,k)  Amount of      pollutant outputs
b(j,k)
al(l,k)
ah(h,k)
eff(o) Eficiency Score;


$Load  XL,XH,XM,Y,Z,b,al,ah
Display l,h,m,j,k,n,XL,XH,XM,Y,Z,b,al,ah
*$Exit
Parameters
XLO(l) Amount of Low  pollutant inputs  for under-assessment of DMU
XHO(h) Amount of High pollutant inputs  for under-assessment of DMU
XMO(m) Amount of NON- pollutant inputs  for under-assessment of DMU
YO(j)  Amount of NON- pollutant outputs for under-assessment of DMU
ZO(k)  Amount of      pollutant outputs for under-assessment of DMU
RXL(l)
RXH(h)
RXM(m)
RY(j)
RZ(k);

XLO(l)=XL("2",l);
XHO(h)=XH("2",h);
XMO(m)=XM("2",m);
YO(j) =Y ("2",j);
ZO(k) =Z ("2",k);

RXL(l)=Smax(n,XL(n,l))-Smin(n,XL(n,l));
RXH(h)=Smax(n,XH(n,h))-Smin(n,XH(n,h));
RXM(m)=Smax(n,XM(n,m))-Smin(n,Xm(n,m));
RY(j)=Smax(n,Y(n,j))-Smin(n,Y(n,j));
RZ(k)=Smax(n,Z(n,k))-Smin(n,Z(n,K));
Positive variable
Lambda_V(n)
AlphaL_V(l)
AlphaH_V(h)
AlphaM_V(m)
Beta_V(j)
Gama_V(k)


Variable
D_V

Equations
obj
XLCon(l)
XHCon(h)
XMCon(m)
YCon(j)
ZCon(k)
Balance1
Balance2(k)
*Equal1
;

Obj..   D_V=e=Sum(l,AlphaL_V(l))
                 +Sum(h,AlphaH_V(h))+Sum(m,AlphaM_V(m))
                 +Sum(j,Beta_V(j)) +Sum(k,Gama_V(k));

XLCon(l).. Sum(n,Lambda_V(n)*XL(n,l))=l=XLO(l)+AlphaL_V(l);

XHCon(h).. Sum(n,Lambda_V(n)*XH(n,h))=l=XHO(h)-AlphaH_V(h);

XMCon(m)..Sum(n,Lambda_V(n)*XM(n,m))=l=XMO(m)-AlphaM_V(m);

YCon(j)..Sum(n,Lambda_V(n)*Y(n,j))=g=YO(j)+Beta_V(j);
ZCon(k)..Sum(n,Lambda_V(n)*Z(n,k))=e=ZO(k)-Gama_V(k);

Balance1.. sum(l,AlphaL_V(l))-Sum(h,AlphaH_V(h))=e=0;
Balance2(k)..Gama_V(k)-Sum(j,b(j,k)*Beta_V(j))=e= Sum(h,ah(h,k)*AlphaH_V(h))-sum(l,al(l,k)*AlphaL_V(l));

model EcoEFF /all/;

Parameters

Lambda_P(o)
AlphaL_P(o,l)
AlphaH_P(o,h)
AlphaM_P(o,m)
Beta_P(o,j)
Gama_P(o,k)

*$Exit
loop(o,XLO(l)=XL(o,l);XHO(h)=XH(o,h);XMO(m)=XM(o,m);YO(j) =Y (o,j);ZO(k) =Z (o,k);

solve EcoEFF using nlp maximizing D_V;

Eff(o)=1-(1/(Card(l)+Card(h)+card(m)+card(j)+card(k)))*(Sum(l,AlphaL_V.l(l)/RXL(l))
                 +Sum(h,AlphaH_V.l(h)/RXH(h))+Sum(m,AlphaM_V.l(m)/RXM(m))
                 +Sum(j,Beta_V.l(j)/RY(j)) +Sum(k,Gama_V.l(k)/RZ(k)));

Lambda_P(o)=Lambda_V.l(o);
AlphaL_P(o,l)=AlphaL_V.l(l);
AlphaH_P(o,h)=AlphaH_V.l(h);
AlphaM_P(o,m)=AlphaM_V.l(m);
Beta_P(o,j) =Beta_V.l(j);
Gama_P(o,k)=Gama_V.l(k);
)

Display Eff;

execute_unload "results.gdx"
Eff
Lambda_P
AlphaL_P
AlphaH_P
AlphaM_P
Beta_P
Gama_P

$onecho > gdxxrwout1.txt
I=results.gdx
O=results.xlsx

par = Eff             rng=Eff!a1               Rdim=1 Cdim = 0

par = Lambda_P        rng=Lambda_P!a1          Rdim=1 Cdim = 0

par = AlphaL_P        rng=AlphaL_P!a1          Rdim=1 Cdim = 1

par = AlphaH_P        rng=AlphaH_P!a1          Rdim=1 Cdim = 1

par = AlphaM_P        rng=AlphaM_P!a1          Rdim=1 Cdim = 1

par = Beta_P          rng=Beta_P!a1            Rdim=1 Cdim = 1

par = Gama_P          rng=Gama_P!a1            Rdim=1 Cdim = 1



$offecho
execute 'gdxxrw.exe @gdxxrwout1.txt trace=2';