LINGO软件程序.docx
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LINGO软件程序
LINGO软件程序
程序一：
MODEL:
SETS:
!
Dynamicprogrammingillustration（seeAnderson,
Sweeney&Williams,AnIntrotoMgtScience,
6thEd.）.Wehaveanetworkof10cities.We
wanttofindthelengthoftheshortestroute
fromcity1tocity10.;
!
Hereisourprimitivesetoftencities,where
F（i）representstheshortestpathdistance
fromcityitothelastcity;
CITIES/1..10/:
F,CONPATH;
!
ThederivedsetROADSliststheroadsthat
existbetweenthecities（note:
notallcity
pairsaredirectlylinkedbyaroad,androads
areassumedtobeoneway.）;
ROADS（CITIES,CITIES）/
1,21,31,4
2,52,62,7
3,53,63,7
4,54,6
5,85,9
6,86,9
7,87,9
8,109,10/:
D,RONPATH;
!
D（i,j）isthedistancefromcityitoj;
ENDSETS
DATA:
!
Herearethedistancesthatcorrespondtothe
abovelinks;
D=
152
131211
6104
1214
39
65
810
52;
ENDDATA
!
Ifouarealreadyinlastcity,thenthecostto
traveltoitis0;
F（@SIZE（CITIES））=0;
!
Thefollowingistheclassicdynamicprogramming
recursion.Inwords,theshortestdistancefrom
Cityitolastcityistheminimumoverall
citiesjreachablefromiofthesumofthe
distancefromitojplustheminimaldistance
fromjtolastcity;
@FOR（CITIES（i）|i#LT#@SIZE（CITIES）:
F（i）=@MIN（ROADS（i,j）:
D（i,j）+F（j））;
）;
!
SetCONPATH（j）>0ifcityjisonanycriticalpath,
i.e.,ifgoingtojfromsomeionthecriticalpath,
stillallowsustogettolastcityinoptimaltime;
CONPATH
（1）=1;
@FOR（CITIES（j）|j#GT#1:
CONPATH（j）=@MAX（ROADS（i,j）:
CONPATH（i）*（（F（I）-F（j）#EQ#D（i,j））））;
）;
!
SetRONPATH（i,j）=1ifarci,jisonanycriticalpath,
i.e.,bothiandjareonpathand（i,j）isshortestpath
fromitoj.Note,wedonotassumedistancessatisfy
triangleinequality;
@FOR（ROADS（i,j）:
RONPATH（I,J）=
@SMIN（CONPATH（i）,CONPATH（j））*（（F（i）-F（j））#EQ#D（i,j））;
）;
END
程序二：
MODEL:
!
TheMexicanSteelproblem;
SETS:
!
Steelplants;
PLANT/AHMSAFUNDIDASICARTSAHYLSAHYLSAP/:
RD2,MUE;
!
Markets;
MARKET/MEXICOMONTEGUADA/:
DD,RD3,MUV;
!
Finalproducts;
CF/STEEL/:
PV,PE,EB;
!
Intermediateproducts;
CI/SPONGEPIGIRON/;
!
Rawmaterials;
CR/PELLETSCOKENATGASELECTRICSCRAP/:
PD;
!
Processes;
PR/PIGIRON1SPONGE1STEELOHSTEELELSTEELBOF/;
!
Productiveunits;
UNIT/BLASTFUROPENHEARBOFDIRECTELECARC/;
!
;
CRXP（CR,PR）:
A1;CIXP（CI,PR）:
A2;
CFXP（CF,PR）:
A3;UXP（UNIT,PR）:
B;
UXI（UNIT,PLANT）:
K;
PXM（PLANT,MARKET）:
RD1,MUF;
PXI（PR,PLANT）:
Z;
CFXPXM（CF,PLANT,MARKET）:
X;
CRXI（CR,PLANT）:
U;CFXI（CF,PLANT）:
E;
CFXM（CF,MARKET）:
D,V;
ENDSETS
!
Demandequations;
@FOR（CFXM（C,J）:
D（C,J）=5.209*（1+40/100）*DD（J）/100）;
!
Transportrateequations;
@FOR（PXM（I,J）|RD1（I,J）#GT#0:
MUF（I,J）=2.48+.0084*RD1（I,J））;
@FOR（PXM（I,J）|RD1（I,J）#LE#0:
MUF（I,J）=0）;
@FOR（PLANT（I）|RD2（I）#GT#0:
MUE（I）=2.48+.0084*RD2（I））;
@FOR（PLANT（I）|RD2（I）#LE#0:
MUE（I）=0）;
@FOR（MARKET（J）|RD3（J）#GT#0:
MUV（J）=2.48+.0084*RD3（J））;
@FOR（MARKET（J）|RD3（J）#LE#0:
MUV（J）=0）;
!
ForeachplantI1;
@FOR（PLANT（I1）:
!
Sources>=uses,finalproducts;
@FOR（CF（CF1）:
[MBF]
@SUM（PR（P1）:
A3（CF1,P1）*Z（P1,I1））>=
@SUM（MARKET（J1）:
X（CF1,I1,J1））+
E（CF1,I1））;
!
Intermediateproducts;
@FOR（CI（CI1）:
[MBI]
@SUM（PR（P1）:
A2（CI1,P1）*
Z（P1,I1））>=0）;
!
Rawmaterials;
@FOR（CR（CR1）:
[MBR]
@SUM（PR（P1）:
A1（CR1,P1）*
Z（P1,I1））+U（CR1,I1）>=0）;
!
CapacityofeachproductiveunitM1;
@FOR（UNIT（M1）:
[CC]
@SUM（PR（P1）:
B（M1,P1）*Z（P1,I1））<=
K（M1,I1））;
）;
!
ForeachfinalproductCF1;
@FOR（CF（CF1）:
!
DemandrequirementsforeachmarketJ1;
@FOR（MARKET（J1）:
[MR]
@SUM（PLANT（I1）:
X（CF1,I1,J1））+V（CF1,J1）
>=D（CF1,J1））;
!
Upperlimitonexports;
[ME]@SUM（PLANT（I1）:
E（CF1,I1））<=EB（CF1）;
）;
!
Componentsofobjective;
PHIPSI=@SUM（CR（CR1）:
@SUM（PLANT（I1）:
PD（CR1）*U（CR1,I1）））;
PHILAM=@SUM（CF（CF1）:
@SUM（PLANT（I1）:
@SUM（MARKET（J1）:
MUF（I1,J1）*
X（CF1,I1,J1）））+@SUM（MARKET（J1）:
MUV（J1）*V（CF1,J1））+@SUM（PLANT（I1）:
MUE（I1）*E（CF1,I1）））;
PHIPI=@SUM（CFXM（CF1,I1）:
PV（CF1）*V（CF1,I1））;
PHIEPS=@SUM（CFXP（CF1,I1）:
PE（CF1）*E（CF1,I1））;
[OBJROW]MIN=PHIPSI+PHILAM+PHIPI-PHIEPS;
DATA:
A1=-1.58,-1.38,0,0,0,
-0.63,0,0,0,0,
0,-0.57,0,0,0,
0,0,0,-0.58,0,
0,0,-0.33,0,-0.12;
A2=1,0,-0.77,0,-0.95,
0,1,0,-1.09,0;
A3=0,0,1,1,1;
B=10000
00100
00001
01000
00010;
K=3.25,1.40,1.10,0,0,
1.50,0.85,0,0,0,
2.07,1.50,1.30,0,0,
0,0,0,0.98,1,
0,0,0,1.13,0.56;
RD1=12042181125
101701030
8191305704
101701030
1851085760;
RD2=739,521,0,521,315;
RD3=428,521,300;
PD=18.7,52.17,14,24,105;
PV=150;
PE=140;
EB=1;
DD=55,30,15;
ENDDATA
END
程序三：
MODEL:
!
TheVehicleRoutingProblem（VRP）;
!
************************************;
!
WARNING:
Runtimesforthismodel;
!
increasedramaticallyasthenumber;
!
ofcitiesincrease.Formulations;
!
withmorethanadozencities;
!
WILLNOTSOLVEinareasonable;
!
amountoftime!
;
!
************************************;
SETS:
!
Q（I）istheamountrequiredatcityI,
U（I）istheaccumulateddeliversatcityI;
CITY/1..8/:
Q,U;
!
DIST（I,J）isthedistancefromcityItocityJ
X（I,J）is0-1variable:
Itis1ifsomevehicle
travelsfromcityItoJ,0ifnone;
CXC（CITY,CITY）:
DIST,X;
ENDSETS
DATA:
!
city1representthecommondepo;
Q=063771845;
!
distancefromcityItocityJissamefromcity
JtocityIdistancefromcityItothedepotis
0,sincethevehiclehastoreturntothedepot;
DIST=!
ToCity;
!
ChiDenFrsnHousKCLAOaklAnahFrom;
099621621067499205421342050!
Chicago;
0011671019596105912271055!
Denver;
01167017471723214168250!
Fresno;
0101917470710153819041528!
Houston;
059617237100158918271579!
K.City;
0105921415381589037136!
L.A.;
01227168190418273710407!
Oakland;
0105525015281579364070;!
Anaheim;
!
VCAPisthecapacityofavehicle;
VCAP=18;
ENDDATA
!
Minimizetotaltraveldistance;
MIN=@SUM（CXC:
DIST*X）;
!
Foreachcity,exceptdepot....;
@FOR（CITY（K）|K#GT#1:
!
avehicledoesnottravalinsideitself,...;
X（K,K）=0;
!
avehiclemustenterit,...;
@SUM（CITY（I）|I#NE#K#AND#（I#EQ#1#OR#
Q（I）+Q（K）#LE#VCAP）:
X（I,K））=1;
!
avehiclemustleaveitafterservice;
@SUM（CITY（J）|J#NE#K#AND#（J#EQ#1#OR#
Q（J）+Q（K）#LE#VCAP）:
X（K,J））=1;
!
U（K）isatleastamountneededatKbutcan't
exceedcapacity;
@BND（Q（K）,U（K）,VCAP）;
!
IfKfollowsI,thencanboundU（K）-U（I）;
@FOR（CITY（I）|I#NE#K#AND#I#NE#1:
U（K）>=U（I）+Q（K）-VCAP+VCAP*
（X（K,I）+X（I,K））-（Q（K）+Q（I））
*X（K,I）;
）;
!
IfKis1ststop,thenU（K）=Q（K）;
U（K）<=VCAP-（VCAP-Q（K））*X（1,K）;
!
IfKisnot1ststop...;
U（K）>=Q（K）+@SUM（CITY（I）|
I#GT#1:
Q（I）*X（I,K））;
）;
!
MaketheX'sbinary;
@FOR（CXC:
@BIN（X））;
!
Minimumno.vehiclesrequired,fractional
androunded;
VEHCLF=@SUM（CITY（I）|I#GT#1:
Q（I））/VCAP;
VEHCLR=VEHCLF+1.999-
@WRAP（VEHCLF-.001,1）;
!
Mustsendenoughvehiclesoutofdepot;
@SUM（CITY（J）|J#GT#1:
X（1,J））>=VEHCLR;
END
程序四：
MODEL:
MIN=10*W88+18*W87+23*W86+28*W85+33*W84+38*W83+43*W82+48*W81+16*W78+8*W77+16*W76+21*W75+26*W74+31*W73+36*W72+41*W71+19*W68+14*W67+6*W66+14*W65+19*W64+24*W63+29*W62+34*W61+22*W58+17*W57+12*W56+4*W55+12*W54+17*W53+22*W52+27*W51+25*W48+20*W47+15*W46+10*W45+2*W44+10*W43+15*W42+20*W41+28*W38+23*W37+18*W36+13*W35+8*W34+8*W32+13*W31+40*W28+35*W27+30*W26+25*W25+20*W24+15*W23+7*W22+15*W21+52*W18+47*W17+42*W16+37*W15+32*W14+27*W13+22*W12+14*W11;
!
Probabilitiessumto1;
W88+W87+W86+W85+W84+W83+W82+W81+W78+W77+W76+W75+W74+W73+W72+W71+W68+W67+W66+W65+W64+W63+W62+W61+W58+W57+W56+W55+W54+W53+W52+W51+W48+W47+W46+W45+W44+W43+W42+W41+W38+W37+W36+W35+W34+W33+W32+W31+W28+W27+W26+W25+W24+W23+W22+W21+W18+W17+W16+W15+W14+W13+W12+W11=1;
!
Prob{outofstate1}-Prob{intostate1}=0;
-.4*W82-.5*W81-.4*W72-.5*W71-.4*W62-.5*W61-.4*W52-.5*W51-.4*W42-.5*W41-.4*W32-.5*W31-.4*W22-.5*W21+W18+W17+W16+W15+W14+W13+.6*W12+.5*W11=0;
!
Intostate2;
-.4*W83-.1*W82-.5*W81-.4*W73-.1*W72-.5*W71-.4*W63-.1*W62-.5*W61-.4*W53-.1*W52-.5*W51-.4*W43-.1*W42-.5*W41-.4*W33-.1*W32-.5*W31+W28+W27+W26+W25+W24+.6*W23+.9*W22+.5*W21-.4*W13-.1*W12-.5*W11=0;
!
Intostate3;
-.4*W84-.1*W83-.5*W82-.4*W74-.1*W73-.5*W72-.4*W64-.1*W63-.5*W62-.4*W54-.1*W53-.5*W52-.4*W44-.1*W43-.5*W42+W38+W37+W36+W35+.6*W34+.9*W33+.5*W32+W31-.4*W24-.1*W23-.5*W22-.4*W14-.1*W13-.5*W12=0;
!
Intostate4;
-.4*W85-.1*W84-.5*W83-.4*W75-.1*W74-.5*W73-.4*W65-.1*W64-.5*W63-.4*W55-.1*W54-.5*W53+W48+W47+W46+.6*
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