Zhu J., Cook W.D. (Eds.) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis
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230
SETS
FM DMU / FM1 * FM3 /
R /
X0, X10, X20, X30, Y31, Y32, Y43, Y41, Y42, Y0
/
OUTPUTS(R) / Y31, Y32, Y41, Y42, Y43 /
INTERMED(R) / Y31, Y32 /
INPUTS(R) / X10, X20, X30, Y31, Y32 /
FSS(FM);
ALIAS (FM,OBS) ;
ALIAS (FM,J) ;
OPTION RESLIM=450000;
OPTION INTEGER1=2;
OPTION INTEGER2=2;
OPTION INTEGER3=2;
OPTION SOLPRINT = OFF;
OPTION LIMROW = 23;
OPTION LIMCOL = 23;
OPTION SYSOUT = OFF;
PARAMETER REPORT(*,*);
PARAMETER PPERACRE;
SCALAR TOTFERT
SCALAR TOTPROFIT
SCALAR RUNOFF
$INCLUDE FIG2.DAT
* PRICES: P = 2 W = 1
VARIABLES
ZE1(FM)
ZE2(FM)
ZE3(FM)
TH1
TH2
TH3
Chapter 12
231
THALL
YV(OUTPUTS) OUTPUT SOLUTION VECTOR
XV(INPUTS) INPUT SOLUTION VECTOR
;
POSITIVE VARIABLES ZE1,ZE2,ZE3,XV,YV,LAMBDA;
EQUATIONS
EQA
EQB
EQC
EQD
EQE
EQF
EQG
EQH
EQI
EQJ
EQK
EQL
OBJ1
OBJ2
OBJ3
OBJALL
;
*-------------------------------------------
* P. 22, (A) - (E) P(3)
*-------------------------------------------
EQA .. SUM(FM,(D(FM,‘Y43’))*ZE3(FM)) =G= YV(‘Y43’);
EQB .. SUM(FM,(D(FM,‘X30’))*ZE3(FM)) =G= XV(‘X30’);
EQC .. SUM(FM,(D(FM,‘Y31’))*ZE3(FM)) =G= YV(‘Y31’);
EQD .. SUM(FM,(D(FM,‘Y32’))*ZE3(FM)) =G= YV(‘Y32’);
EQE .. SUM(FM,ZE3(FM)) =L= 1;
*-------------------------------------------
* P. 22, (F) - (H) P(1)
*-------------------------------------------
EQF .. SUM(FM,(D(FM,‘Y31’)+D(FM,‘Y41’))*ZE1(FM)) =G= YV(‘Y31’) + YV(‘Y41’);
EQG .. SUM(FM,(D(FM,‘X10’))*ZE1(FM)) =L= XV(‘X10’);
EQH .. SUM(FM,ZE1(FM)) =L= 1;
*-------------------------------------------
* P. 22, (I) - (L) P(2)
*-------------------------------------------
EQI .. SUM(FM,(D(FM,‘Y32’)+D(FM,‘Y42’))*ZE2(FM)) =G= YV(‘Y32’) + YV(‘Y42’);
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232
EQJ .. SUM(FM,(D(FM,‘X20’))*ZE2(FM)) =L= XV(‘X20’);
EQK .. SUM(FM,ZE2(FM)) =L= 1;
EQL .. XV(‘X10’) + XV(‘X20’) + XV(‘X30’) =E= SUM(FSS,D(FSS,‘X0’)) ;
*-------------------------------------------
* OBJ PROFIT, HOLD OUTPUT FIXED, VARY INPUT
*-------------------------------------------
OBJ1 .. TH1 =E= (YV(‘Y31’) + YV(‘Y41’))*2 - (XV(‘X10’))*1.0;
OBJ2 .. TH2 =E= (YV(‘Y32’) + YV(‘Y42’))*2 - (XV(‘X20’))*1.0;
OBJ3 .. TH3 =E= (YV(‘Y43’))*2 - (XV(‘X30’) - YV(‘Y31’) - YV(‘Y32’))*1.0;
OBJALL .. THALL =E= (YV(‘Y41’) + YV(‘Y42’) + YV(‘Y43’))*2 - (XV(‘X10’) + XV(‘X20’) +
XV(‘X30’))*1.0;
MODEL SUBP1 /
EQF
EQG
EQH
OBJ1
/;
MODEL SUBP2 /
EQI
EQJ
EQK
EQL
OBJ2
/;
MODEL SUBP3 /
EQA
EQB
EQC
EQD
EQE
OBJ3
/;
MODEL OVERALL /
EQA
EQB
EQC
EQD
EQE
EQF
Chapter 12
233
EQG
EQH
EQI
EQJ
EQK
EQL
OBJALL
/;
* SET OUTPUT FILE & FORMAT
FILE RES1 /SUBP1.RES / ;
FILE RES2 /SUBP2.RES / ;
FILE RES3 /SUBP3.RES / ;
FILE RESALL /SUBPALL.RES / ;
PUT RES1;
* COLUMN LABELS
PUT @10,“TH1”
@20,“XV(‘X10’)”
@30,“XV(‘X20’)”
@40,“XV(‘X30’)”
@50,“YV(‘Y31’)”
@60,“YV(‘Y41’)”
@70,“YV(‘Y42’)”
@80,“YV(‘Y43’)”
@90,“MODELSTAT”
/;
PUT RES2;
* COLUMN LABELS
PUT @10,“TH1”
@20,“XV(‘X10’)”
@30,“XV(‘X20’)”
@40,“XV(‘X30’)”
@50,“YV(‘Y31’)”
@60,“YV(‘Y41’)”
@70,“YV(‘Y42’)”
@80,“YV(‘Y43’)”
@90,“MODELSTAT”
/;
PUT RES3;
* COLUMN LABELS
PUT @10,“TH1”
@20,“XV(‘X10’)”
@30,“XV(‘X20’)”
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@40,“XV(‘X30’)”
@50,“YV(‘Y31’)”
@60,“YV(‘Y41’)”
@70,“YV(‘Y42’)”
@80,“YV(‘Y43’)”
@90,“MODELSTAT”
/;
PUT RESALL;
* COLUMN LABELS
PUT @10,“TH1”
@20,“XV(‘X10’)”
@30,“XV(‘X20’)”
@40,“XV(‘X30’)”
@50,“YV(‘Y31’)”
@60,“YV(‘Y41’)”
@70,“YV(‘Y42’)”
@80,“YV(‘Y43’)”
@90,“MODELSTAT”
/;
LOOP (OBS,
FSS(FM) = NO; FSS(OBS) = YES;
*************************************************
SOLVE SUBP1 USING LP MAXIMIZING TH1 ;
PUT RES1;
PUT @1, OBS.TL;
PUT @8,TH1.L:10:4;
PUT @18,XV.L(‘X10’):10:4;
PUT @28,XV.L(‘X20’):10:4;
PUT @38,XV.L(‘X30’):10:4;
PUT @48,YV.L(‘Y31’):10:4;
PUT @58,YV.L(‘Y41’):10:4;
PUT @68,YV.L(‘Y42’):10:4;
PUT @78,YV.L(‘Y43’):10:4;
PUT @88,SUBP1.MODELSTAT:10:4
/;
***********************************************
SOLVE SUBP2 USING LP MAXIMIZING TH2 ;
PUT RES2;
PUT @1, OBS.TL;
PUT @8,TH1.L:10:4;
PUT @18,XV.L(‘X10’):10:4;
Chapter 12
235
PUT @28,XV.L(‘X20’):10:4;
PUT @38,XV.L(‘X30’):10:4;
PUT @48,YV.L(‘Y31’):10:4;
PUT @58,YV.L(‘Y41’):10:4;
PUT @68,YV.L(‘Y42’):10:4;
PUT @78,YV.L(‘Y43’):10:4;
PUT @88,SUBP2.MODELSTAT:10:4
/;
********************************************************
SOLVE SUBP3 USING LP MAXIMIZING TH3 ;
PUT RES3;
PUT @1, OBS.TL;
PUT @8,TH1.L:10:4;
PUT @18,XV.L(‘X10’):10:4;
PUT @28,XV.L(‘X20’):10:4;
PUT @38,XV.L(‘X30’):10:4;
PUT @48,YV.L(‘Y31’):10:4;
PUT @58,YV.L(‘Y41’):10:4;
PUT @68,YV.L(‘Y42’):10:4;
PUT @78,YV.L(‘Y43’):10:4;
PUT @88,SUBP3.MODELSTAT:10:4
/;
**************************************************************
SOLVE OVERALL USING LP MAXIMIZING THALL ;
PUT RESALL;
PUT @1, OBS.TL;
PUT @8,TH1.L:10:4;
PUT @18,XV.L(‘X10’):10:4;
PUT @28,XV.L(‘X20’):10:4;
PUT @38,XV.L(‘X30’):10:4;
PUT @48,YV.L(‘Y31’):10:4;
PUT @58,YV.L(‘Y41’):10:4;
PUT @68,YV.L(‘Y42’):10:4;
PUT @78,YV.L(‘Y43’):10:4;
PUT @88,OVERALL.MODELSTAT:10:4
/;
);
Output:
Färe, Grosskopf & Whittaker, Network DEA
236
Appendix II
This appendix contains a program listing and output using the General
Algebraic Modeling System (GAMS) for the network shown in Figure 12-4.
The example data are called from separate file, which is listed first. The
variables are named to follow the nomenclature in Figure 12-4, i.e.,
1
0
x
is
X10 in the program.
Example data, FIG4.DAT:
Listing of GAMS program:
* NETWORK MODEL FOR FIGURE 12-4
*
*
$TITLE NETWORK FIGURE 12-4
$OFFSYMXREF
$OFFSYMLIST
subp1.res
TH1 XV('X10') XV('X20') XV('X30') YV('Y31') YV('Y41') YV('Y42') YV('Y43') MODELST
A
FM1 930060001
FM2 935206631
FM3 9340065.3333 3 1
subp2.res
TH1 XV('X10') XV('X20') XV('X30') YV('Y31') YV('Y41') YV('Y42') YV('Y43') MODELST
A
FM1 955060001
FM2 925006631
FM3 965006631
subp3.res
TH1 XV('X10') XV('X20') XV('X30') YV('Y31') YV('Y41') YV('Y42') YV('Y43') MODELST
A
FM1 955040031
FM2 925046631
FM3 965046631
subpall.res
TH1 XV('X10') XV('X20') XV('X30') YV('Y31') YV('Y41') YV('Y42') YV('Y43') MODELST
A
FM1 935206631
FM2 9340065.3333 3 1
FM3 936206631
X1 X2 X3 Y1F Y2F Y3F Y1I Y2I
FM1 34425511
FM2 45636612
FM3 56747622
TABLE D(FM,R)
Chapter 12
237
SETS
FM DMU / FM1 * FM3 /
R /
X1, X2, X3, Y1F, Y2F, Y3F, Y1I, Y2I
/
OUTPUTS(R) / Y1F, Y2F, Y3F, Y1I, Y2I /
INTERMED(R) / Y1I, Y2I /
INPUTS(R) / X1, X2, X3, Y1I, Y2I /
FSS(FM);
ALIAS (FM,OBS) ;
ALIAS (FM,J) ;
OPTION RESLIM=450000;
OPTION INTEGER1=2;
OPTION INTEGER2=2;
OPTION INTEGER3=2;
OPTION SOLPRINT = OFF;
OPTION LIMROW = 23;
OPTION LIMCOL = 23;
OPTION SYSOUT = OFF;
PARAMETER REPORT(*,*);
PARAMETER PPERACRE;
SCALAR TOTFERT
SCALAR TOTPROFIT
SCALAR RUNOFF
$INCLUDE FIG4.DAT
* PRICES: P = 2 W = 1
VARIABLES
ZE1(FM)
ZE2(FM)
ZE3(FM)
TH1
TH2
TH3
Färe, Grosskopf & Whittaker, Network DEA
238
THALL
YV(OUTPUTS) OUTPUT SOLUTION VECTOR
XV(INPUTS) INPUT SOLUTION VECTOR
;
POSITIVE VARIABLES ZE1,ZE2,ZE3,XV,YV,LAMBDA;
EQUATIONS
EQA
EQB
EQC
EQD
EQE
EQF
EQG
EQH
OBJ1
;
*-------------------------------------------
* INPUTS
*-------------------------------------------
EQA .. SUM(FM,(D(FM,‘X1’))*ZE1(FM)) =L= SUM(FSS,D(FSS,‘X1’));
EQB .. SUM(FM,(D(FM,‘X2’))*ZE2(FM)) =L= SUM(FSS,D(FSS,‘X2’));
EQC .. SUM(FM,(D(FM,‘X3’))*ZE3(FM)) =L= SUM(FSS,D(FSS,‘X3’));
*-------------------------------------------
* INTERMEDIATE OUTPUTS
*-------------------------------------------
EQD .. SUM(FM,(D(FM,‘Y1I’))*ZE2(FM)) =L= YV(‘Y1I’);
EQE .. SUM(FM,(D(FM,‘Y2I’))*ZE3(FM)) =L= YV(‘Y2I’);
*-------------------------------------------
* OUTPUTS
*-------------------------------------------
EQF .. YV(‘Y1F’)+YV(‘Y1I’) =L= SUM(FM,(D(FM,‘Y1F’)+D(FM,‘Y1I’))*ZE1(FM));
EQG .. YV(‘Y2F’)+YV(‘Y2I’) =L= SUM(FM,(D(FM,‘Y2F’)+D(FM,‘Y2I’))*ZE2(FM));
EQH .. YV(‘Y3F’) =L= SUM(FM,D(FM,‘Y3F’)*ZE3(FM));
*-------------------------------------------
* OBJ PROFIT, HOLD OUTPUT FIXED, VARY INPUT
*-------------------------------------------
* PRICE OF ALL OUTPUTS = 1
OBJ1 .. TH1 =E= YV(‘Y1F’) + YV(‘Y2F’) + YV(‘Y3F’);
MODEL FIG4 /
Chapter 12
239
EQA
EQB
EQC
EQD
EQE
EQF
EQG
EQH
OBJ1
/;
* SET OUTPUT FILE & FORMAT
*FILE RES /SUB_TECH_P3.RES / ;
FILE RES1 /FIG4.RES / ;
PUT RES1;
* COLUMN LABELS
PUT @12,“TH1”
@30,“YV(‘Y1I’)”
@40,“YV(‘Y2I’)”
* @48,“YV(‘X3F’)”
@50,“YV(‘Y1F’)”
@60,“YV(‘Y2F’)”
@70,“YV(‘Y3F’)”
@80,“MODELSTAT”
/;
LOOP (OBS,
FSS(FM) = NO; FSS(OBS) = YES;
* OPTION LP=MPSWRITE;
* OPTION LP = CONVERT;
* UPPER.OPTFILE = 1;
*************************************************
SOLVE FIG4 USING LP MAXIMIZING TH1 ;
PUT RES1;
PUT @1, OBS.TL;
PUT @8,TH1.L:10:4;
PUT @28,YV.L(‘Y1I’):10:4;
PUT @38,YV.L(‘Y2I’):10:4;
PUT @48,YV.L(‘Y1F’):10:4;
PUT @58,YV.L(‘Y2F’):10:4;
PUT @68,YV.L(‘Y3F’):10:4;
PUT @78,FIG4.MODELSTAT :7:2
/;
Färe, Grosskopf & Whittaker, Network DEA