精品数据模型与决策运筹学课后习题和案例答案009Word文件下载.docx
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9.2-4ThemutuallyexclusivealternativesaretobuildawarehouseinLosAngelesorbuildawarehouseinSanFrancisco.Theformoftheresultingconstraintisthatthesumofthesevariablesmustbelessthanorequalto1（x3+x4≤1）.
9.2-5Thecontingentdecisionsarethedecisionstobuildawarehouse.Theformsoftheseconstraintsarex3≤x1andx4≤
x2.
9.2-6Theamountofcapitalbeingmadeavailabletotheseinvestments（$10million）isamanagerialdecisiononwhichsensitivityanalysisneedstobeperformed.
9.3-1Avalueof1isassignedforchoosingyesandavalueof0isassignedforchoosingno.
9.3-2Yes-or-nodecisionsforcapitalbudgetingwithfixedinvestmentsarewhetherornottomakeacertainfixedinvestment.
9.3-3Yes-or-nodecisionsforsiteselectionsarewhetherornotacertainsiteshouldbeselectedforthelocationofacertainnewfacility.
9.3-4Whendesigningaproductionanddistributionnetwork,yes-or-nodecisionslikeshouldacertainplantremainopen,shouldacertainsitebeselectedforanewplant,shouldacertaindistributioncenterremainopen,shouldacertainsitebeselectedforanewdistributioncenter,andshouldacertaindistributioncenterbeassignedtoserveacertainmarketareamightarise.
9.3-5Shouldacertainroutebeselectedforoneofthetrucks.
9.3-6ItisestimatedthatChinaissavingabout$6.4billionoverthe15years.
9.3-7Theformofeachyes-or-nodecisionisshouldacertainassetbesoldinacertaintimeperiod.
9.3-8TheairlineindustryusesBIPforfleetassignmentproblemsandcrewschedulingproblems.
9.4-1Abinarydecisionvariableisabinaryvariablethatrepresentsayes-or-nodecision.Anauxiliarybinaryvariableisanadditionalbinaryvariablethatisintroducedintothemodel,nottorepresentayes-or-nodecision,butsimplytohelpformulatethemodelasaBIPproblem.
9.4-2Thenetprofitisnolongerdirectlyproportionaltothenumberofunitsproducedsoalinearprogrammingformulationisnolongervalid.
9.4-3Anauxiliarybinaryvariablecanbeintroducedforasetupcostandcanbedefinedas1ifthesetupisperformedtoinitiatetheproductionofacertainproductand0ifthesetupisnotperformed.
9.4-4Mutuallyexclusiveproductsexistwhenatmostoneproductcanbechosenforproductionduetocompetitionforthesamecustomers.
9.4-5Anauxiliarybinaryvariablecanbedefinedas1iftheproductcanbeproducedand0iftheproductcannotbeproduced.
9.4-6Aneither-orconstraintarisesbecausetheproductsaretobeproducedateitherPlant3orPlant4,notboth.
9.4-7Anauxiliarybinaryvariablecanbedefinedas1ifthefirstconstraintmustholdand0ifthesecondconstraintmusthold.
9.5-1Restriction1issimilartotherestrictionimposedinVariation2exceptthatitinvolvesmoreproductsandchoices.
9.5-2Theconstrainty1+y2+y3≤2forceschoosingatmosttwoofthepossiblenewproducts.
9.5-3ItisnotpossibletowritealegitimateobjectivefunctionbecauseprofitisnotproportionaltothenumberofTVspotsallocatedtothatproduct.
9.5-4ThegroupsofmutuallyexclusivealternativeinExample2arex1=0,1,2,or3,x2=0,1,2,or3,andx3=0,1,2,or3.
9.5-5Themathematicalformoftheconstraintisx1+x4+x7+x10≥
1.Thisconstraintsaysthatsequence1,4,7,and10includeanecessaryflightandthatoneofthesequencesmustbechosentoensurethatacrewcoverstheflight.
Problems
9.1a）LetT=thenumberoftowbarstoproduce
S=thenumberofstabilizerbarstoproduce
MaximizeProfit=$130T+$150S
subjectto3.2T+2.4S≤16hours
2T+3S≤15hours
andT≥0,S≥0
T,Sareintegers.
b）Optimalsolution:
（T,S）=（0,5）.Profit=$750.
c）
9.2a）
b）LetA=thenumberofModelA（high-speed）copierstobuy
B=thenumberofModelB（lower-speed）copierstobuy
MinimizeCost=$6,000A+$4,000B
subjecttoA+B≥6copiers
A≥1copier
20,000A+10,000B≥75,000copies/day
andA≥0,B≥
A,Bareintegers.
c）Optimalsolution:
（A,B）=（2,4）.Cost=$28,000.
9.3a）Optimalsolution:
（x1,x2）=（2,3）.Profit=13.
b）TheoptimalsolutiontotheLP-relaxationis（x1,x2）=（2.6,1.6）.Profit=14.6.
Roundedtothenearestinteger,（x1,x2）=（3,2）.Thisisnotfeasiblesinceitviolatesthethirdconstraint.
RoundedSolution
Feasible?
ConstraintViolated
P
（3,2）
No
3rd
-
（3,1）
2nd&
3rd
（2,2）
Yes
12
（2,1）
11
Noneoftheseisoptimalfortheintegerprogrammingmodel.TwoarenotfeasibleandtheothertwohavelowervaluesofProfit.
9.4a）Optimalsolution:
（x1,x2）=（2,3）.Profit=680.
b）TheoptimalsolutiontotheLP-relaxationis（x1,x2）=（2.67,1.33）.Profit=693.33.
Roundedtothenearestinteger,（x1,x2）=（3,1）.Thisisnotfeasiblesinceitviolatesthesecondandthirdconstraint.
2nd
600
520
9.5a）
b）LetL=thenumberoflong-rangejetstopurchase
M=thenumberofmedium-rangejetstopurchase
S=thenumberofshort-rangejetstopurchase
MaximizeAnnualProfit（$millions）=4.2L+3M+2.3S
subjectto67L+50M+35S≤1,500（$million）
（5/3）L+（4/3）M+S≤40（maintenancecapacity）
L+M+S≤30（pilotcrews）
andL≥0,M≥
0,S≥
L,M,Sareintegers.
9.6a）Letxij=tonsofgravelhauledfrompititositej（fori=N,S;
j=1,2,3）
yij=thenumberoftruckshaulingfrompititositej（fori=N,S;
MinimizeCost=$130xN1+$160xN2+$150xN3+$180xS1+$150xS2+$160xS3+
$50yN1+$50yN2+$50yN3+$50yS1+$50yS2+$50yS3
subjecttoxN1+xN2+xN3≤18tons（supplyatNorthPit）
xS1+xS2+xS3≤14tons（supplyatSouthPit）
xN1+xS1=10tons（demandatSite1）
xN2+xS2=5tons（demandatSite2）
xN3+xS3=10tons（demandatSite3）
xij≤5yij（fori=N,S;
j=1,2,3）（max5tonspertruck）
andxij≥0,yij≥
0,
yijareintegers（fori=N,S;
b）
9.7a）LetFLA=1ifbuildafactoryinLosAngeles;
0otherwise
FSF=1ifbuildafactoryinSanFrancisco;
FSD=1ifbuildafactoryinSanDiego;
WLA=1ifbuildawarehouseinLosAngeles;
WSF=1ifbuildawarehouseinSanFrancisco;
WSD=1ifbuildawarehouseinSanDiego;
MaximizeNPV（$million）=9FLA+5FSF+7FSD+6WLA+4WSF+5WSD
subjectto6FLA+3FSF+4FSD+5WLA+2WSF+3WSD≤
$10million（Capital）
WLA+WSF+WSD≤1warehouse
WLA≤FLA（warehouseonlyiffactory）
WSF≤FSF
WSD≤FSD
andFLA,FSF,FSD,WLA,WSF,WSDarebinaryvariables.
9.8SeethearticlesinInterfaces.
9.9a）LetEM=1ifEvedoesthemarketing;
EC=1ifEvedoesthecooking;
ED=1ifEvedoesthedishwashing;
EL=1ifEvedoesthelaundry;
SM=1ifStevendoesthemarketing;
SC=1ifStevendoesthecooking;
SD=1ifStevendoesthedishwashing;
SL=1ifStevendoesthelaundry;
MinimizeTime（hours）=4.5EM+7.8EC+3.6ED+2.9EL+
4.9SM+7.2SC+4.3SD+3.1SL
subjecttoEM+EC+ED+EL=2（eachpersondoes2tasks）
SM+SC+SD+SL=2
EM+SM=1（eachtaskisdoneby1person）
EC+SC=1
ED+SD=1
EL+SL=1
andEM,EC,ED,EL,SM,SC,SD,SLarebinaryvariables.
9.10a）Letx1=1ifinvestinproject1;
x2=1ifinvestinproject2;
x3=1ifinvestinproject3;
x4=1ifinvestinproject4;
x5=1ifinvestinproject5;
Ma
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