供应链管理英文Chapter9answerstoexercises

Chapter9:SalesandOperationsPlanning

Wedefineacomprehensivesetofdecisionvariablesthatareutilizedinproblems9-1to9-3dependingontheproblemcontext.

DecisionVariables:

Ht=#ofworkershiredinmontht(t=1,..,12)

Lt=#ofworkerslaid-offinmontht(t=1,..,12)

Wt=#ofworkersemployedinmontht(t=1,..,12)

Ot=#ofhoursofovertimeinmontht(t=1,..,12)

It=#ofunitsheldininventoryattheendofmontht(t=1,..,12)

Ct=#ofunitssubcontractedinmontht(t=1,..,12)

Pt=#ofunitsproducedinmontht(t=1,..,12)

Parameters:

Dt=#ofunitsdemandedintimeperiodt(t=1,…12)

Problem9-1:

Minimize240012W+2212O+312I+4012P

tttt

t=1i=1i=1i=1

Subjectto:

Inventoryconstraints:

I+PI=D,t=1,..,12

t1ttt

I=I=4000

012

Overtimeconstraints:

O20W0,t=1,...,12

tt

Productionconstraints:

2PO160W0,t=1,...12

ttt

Workforceconstraints:

W=250,t=0,...,12

t

(a)Worksheet9-1providesthesolutiontothisproblemandthecorrespondingaggregate

plan.Thetotalcostoftheplanis$16,820,000

2PO160W0,t=1,...12

ttt

(b)FromthetablebelowwecanseethatitisbettertopromoteinAprilthaninJuly,astheprofitisslightlyhigher.

TotalCost

Promotion

Nopromotion(April)$16,820,000$17,059,400$28,500,000$28,916,625$11,680,000$11,857,225

$177,225

Price=$125

TotalCost=TotalRevenue=Profit=

Profitincrease=

Promotion

(July)

$17,367,300$29,198,750$11,831,450$151,450

(c)Ifasinkissoldat$250,thentheprofitassociatedwithpromotioninJulyishigherthaninApril.So,astheproductmarginincreasesitismorebeneficialtoofferthediscountinhighdemandperiod.

Promotion(April)Promotion(July)

$17,059,399.94 $57,833,250$40,773,850.06$593,850.06

$17,367,299.95 $58,397,500$41,030,200.05$850,200.05

Price=$250

TotalCost=TotalRevenue=Profit=

Profitincrease=

TotalCost

Nopromotion$16,820,000$57,000,000$40,180,000

Problem9-2:

Wenowincludehiringandlayoffcostsinthemodel.Notethattheworkforcelevel

constraintsalsochange.

Minimize100012H+200012F+240012W+2212O+312I+4012PSubjectto:

tttttt

t=1t=1t=1i=1i=1i=1

Inventoryconstraints:

I+PI=D,t=1,..,12

t1ttt

I=I=4000

012

Overtimeconstraints:

O20W0,t=1,...,12

tt

Productionconstraints:

Workforceconstraints:

WWH+L=0,t=1,...,12

tt1tt

W=250

0

(a)

TotalCost=TotalRevenue=Profit=

$L9‘gLL‘000

$Z8‘g00‘000

$LL‘6Z6‘000

PeriodProduction

0LZ0‘000ZZ0‘000CZ0‘000

v

g

9

L

8

6

L0

LL

LZ

Z0‘000Z0‘000Z0‘000Z0‘000Z0‘000Z0‘000L8‘000Lg‘000Lg‘000

(b)PromotioninJulyisbetter.Profitincreasesto$218,900.1

Promotion

(April)

$16,794,500$28,916,625$12,122,125$193,125.1

Promotion

(July)

$17,050,850$29,198,750$12,147,900$218,900.1

TotalCost

No

promotion

$16,571,000$28,500,000$11,929,0000

TotalCost=TotalRevenue=Profit=

Profitincrease=

(c)Iftheholdingcostincreasesto$5/unit/month,thenpromotionshouldbeheldinApril.PromotioninJulywillresultinproducingmoreunitsofproduct,whichinturnresultsinahighercarryingcost.Although,thesalesamountisalsohigherifpromotionisinJuly,theincurredprofitislowerduetothehighercarryingcost.

Holding=

$5/unit/month

TotalCost=TotalRevenue=Profit=

Profitincrease=

Promotion

(April)

$17,038,361$28,916,625$11,878,264$206,889

Promotion

(July)

$17,353,188$29,198,750$11,845,562$174,187.4

TotalCost

No

promotion

$16,828,625$28,500,000$11,671,3750

Problem9-3:

Inthiscaseweaddthesubcontractoptiontoprobleminformationgivenin9-1

Minimize240012W+2212O+312I+4012P+7412C

ttttt

t=1i=1i=1i=1i=1

Subjectto:

Inventoryconstraints:

I+P+CI=D,t=1,..,12

t1tttt

I=I=4000

012

Overtimeconstraints:

O20W0,t=1,...,12

tt

Productionconstraints:

2PO160W0,t=1,...12

ttt

Workforceconstraints:

W=250,t=0,...,12

t

Fromworksheet9-3,nounitsshouldbeoutsourcedfromthesubcontractor.Butwith

promotion,thesubcontractingoptionshouldbeused.Specifically,ifthepromotionisin

April,2600unitsand1000unitsshouldbeoutsourcedfromthesubcontractorinAugust

andSeptember,respectively.IfthepromotionisinJuly,then1000unitsand6100units

shouldbeoutsourcedinJulyandAugust,respectively.Theneedforsubcontractingis

becausepromotioninducesadditionaldemand,whichwillnotbecosteffectivefor

Lavaretoproducebyitself,asthecarryingcostwilloutweighthecostspaidtothe

subcontractor.

O20W0,t=1,...,12

tt

TotalCost

Promotion

(April)

$17,000,100

$28,916,625$11,916,525

Promotion

(July)

$17,251,400

$29,198,750$11,947,350

TotalCost=TotalRevenue=

Profit=

9-4~9-6

Wedefineacomprehensivesetofdecisionvariablesthatareutilizedinproblems9-4to9-6dependingontheproblemcontext.

DecisionVariables:

Ht=#ofworkershiredinmontht(t=1,..,12)

Lt=#ofworkerslaid-offinmontht(t=1,..,12)

Wt=#ofworkersemployedinmontht(t=1,..,12)

Ot=#ofhoursofovertimeinmontht(t=1,..,12)

It=#ofunitsheldininventoryattheendofmontht(t=1,..,12)

Ct=#ofunitssubcontractedinmontht(t=1,..,12)

Pt=#ofunitsproducedinmontht(t=1,..,12)

Parameters:

Dt=#ofunitsdemandedintimeperiodt(t=1,…12)

Problem9-4:

Minimize160012W+1512O+412I+3512P

tttt

t=1i=1i=1i=1

Subjectto:

Inventoryconstraints:

I+PI=D,t=1,..,12

t1ttt

I=I=4000

012

Overtimeconstraints:

Productionconstraints:

2PO160W0,t=1,...12

ttt

Workforceconstraints:

W=250,t=0,...,12

t

(a)

TotalCost=TotalRevenue=

Profit=

$12,013,000

$15,920,000

$3,907,000

Pt

Production

0

19,000

220,000

320,000

420,000

520,000

620,000

720,000

820,000

915,000

1010,000

1111,000

1214,000

Period

(b)Profit(Jumbonopromotion,ShrimpypromotesinApril)=$3,615,000

Profit(Jumbonopromotion,ShrimpypromotesinJune)=$3,594,600

Profit(JumbopromotesinApril,Shrimpynopromotion)=$4,103,000

Profit(JumbopromotesinJune,Shrimpynopromotion)=$4,008,400

Also,from(a),profit(bothnopromotion)=$3,907,000.

SincebothJumboandShrimpyhavesimilardemandpatterns,andmaybesimilarcoststructure,itisreasonabletothinkthattheprofitgainedbyoneparty’spromotionisthecompetitor’slosscausedbynotpromoting.Oftenthemarketsizeforaspecificproductissteady.So,onefirm’sgainislikelycomingfromitscompetitors’loss.

(c)Profit(bothpromoteinApril/44)=$3,871,000Profit(bothpromoteinJune/66)=$3,760,600

Profit(JumboJune,ShrimpyApril/64)=$3,498,400

Profit(JumboApril,ShrimpyJune/46)=$3,513,800

Theproductionplanisshownasfollows:

44664664

PeriodProductionProductionProductionProduction

0

9,000

20,000

20,000

20,000

20,000

20,000

20,000

20,000

15,000

10,000

11,000

14,000

8,000

15,000

20,000

20,000

20,000

20,000

20,000

18,000

15,000

10,000

11,000

14,000

8,000

12,700

20,000

20,000

20,000

17,500

20,000

20,000

15,000

10,000

11,000

14,000

12,000

20,000

20,000

20,000

20,000

20,000

20,000

17,000

15,000

10,000

11,000

14,000

1

2

3

4

5

6

7

8

9

10

11

12

(d)TherearethreestrategiesforbothJumboandShrimpy,whichleadstoatotalof9combinationsofstrategies,asshowninthetablebelow.JumbowouldachievethehighestprofitifitpromotedinJuneandShirmpydidnotpromoteatall,anditwouldreceivethelowestprofitifitpromotedinJuneandShrimpypromotedinApril.Inordertoachieveamiddleground,itwouldbebeneficialforJumbotocoordinatewithShirmpysothattheyeitherdon’tpromoteatallorpromoteinthesamemonth.

Jumbo\ShrimpyNopromotionApril

June

NopromotionAprilJune

$3,907,000$3,615,000$3,594,600$4,103,000$3,871,000$3,513,800$4,008,400$3,498,400$3,760,600

Note:numberineachcellrepresentsJumbo’sprofit

(e)WefirstidentifytheminimumprofitforeachstrategyforJumbo,asindicatedbythenumbersinboldinthetablebelow.Themaximumofthesethreeminimumprofitsis$3,594,600.So,Jumboshouldnotundertakeanypromotionatallthroughouttheyear.

Jumbo\ShrimpyNopromotionApril

June

NopromotionAprilJune

$3,907,000$3,615,000$3,594,600$4,103,000$3,871,000$3,513,800$4,008,400$3,498,400$3,760,600

Problem9-5:

Re-definetwovariables:

W:workforce,intermsof#ofshifts(pershift=100employees)

t

O:overtime(hourspershift)

t

Minimize160*100012W+15*10012O+10012I+100012P

tttt

t=1i=1i=1i=1

Subjectto:

Inventoryconstraints:

I+PI=D,t=1,..,12

t1ttt

I=I=150(tons)

012

I100,t=1,…,11

t

Overtimeconstraints:

O20W0,t=1,...,12

tt

Productionconstraints:

PO160W0,t=1,...12

ttt

Workforceconstraints:

W=2,t=0,...,12

t

(a)

TotalCost=TotalRevenue=Profit=

$7,453,150

$9,061,000

$1,607,850

Pt

Production

230

301

277

302

285

278

291

277

304

291

320

329

Period

0

1

2

3

4

5

6

7

8

9

10

11

12

(b)Profit(Q&Hnopromotion,UnilockpromotesinApril)=$1,362,250

Profit(Q&Hnopromotion,UnilockpromotesinJune)=$1,385,450

Profit(Q&HpromotesinApril,Unilocknopromotion)=$1,520,174

Profit(Q&HpromotesinJune,Unilocknopromotion)=$1,611,294

Also,from(a),profit(bothnopromotion)=$1,607,850.

Fromtheresults,ifQ&HdoesnotpromoteintherightmonthittendstoloseevenifUnilockdoesnotpromote.Ontheotherhand,ifUnilockdoespromote,thenQ&Hwouldexpectlossofprofit.

(c)Profit(bothpromoteinApril/44)=$1,466,410Profit(bothpromoteinJune/66)=$1,477,050Profit(Q&HApril,UnilockJune/46)=$1,259,774

Profit(Q&HJune,UnilockApril/64)=$1,253,614

Theproductionplanisshownasfollows:

44664664

Period

ProductionProductionProductionProduction

0

1291230263230

2320305320301

3320320320277

4320320320188

5214320228320

620932083320

7291218291233

8277208277222

9304304304304

10291291291291

11320320320320

12329329329329

(d)TherearethreestrategiesforbothQ&HandUnilock,whichleadstoatotalof9combinationsofstrategies,asshowninthetablebelow.Q&HwouldachievethehighestprofitifitpromotedinJuneandUnilockdidnotpromoteatall,anditwouldreceivethelowestprofitifitpromotedinJuneandUnilockpromotedinApril.Inordertoachieveamiddleground,itwouldbebeneficialforQ&Htocoordinatewit