供應(yīng)鏈管理英文Chapter7-Exerciseanswers

Chapter7:DemandForecastinginaSupplyChain

ExerciseSolutions:

Problem7-1:

Weutilizeastaticmodelwithlevel,trend,andseasonalitycomponentstoevaluatetheforecastsforyear6.Initially,wedeseasonalizethedemandandutilizeregressioninestimatingthetrendandlevelcomponents.Wethenestimatetheseasonalfactorsforeachperiodandevaluateforecasts.EXCELWorksheet7-1providesthesolutiontothisproblem.

Themodelutilizedforforecastingis:F=[L+(t+l)T]S

t+lt+l

Thedeseasonalizedregressionmodelis:

t

D_=5997.261+70.245t

Theseasonalindicesforeachofthetwelvemonthsare:

Month

JAN

FEB

MAR

APR

MAY

JUN

JUL

AUG

SEP

OCT

NOV

DEC

S.I

0.427

0.475

0.463

0.398

0.621

0.834

0.853

1.151

1.733

1.778

2.124

1.095

Forexample,theforecastforJanuaryofYear6isobtainedbythefollowingcalculation:F61=[5997.261+(61)*70.245]*0.4266=4386

Thequalityoftheforecastingmethodisquitegoodgiventhattheforecasterrorsarenottoohigh.

Problem7-2:

Worksheet7-2comparesthefour-weekmovingaverageapproachwiththeexponentialsmoothingmodel(alpha=0.1).Inafour-weekmovingaveragemodeltheweightassignedtothemostrecentdatais0.25whereasinthecaseoftheexponentialsmoothingmodeltheweightassignedis0.1.Thefollowinggraphsdepicttheresultsfromthetwomodels.

MtlgDmvaenrdageForecastedDemand

130

125

120

115

110

105

100

95

90

85

80

123456789

Periods

10111213141516

U

D

i

e

EXPONENTIALSMOOTHING

ActualDemandForecastedDemand

130

125

120

115

110

105

100

95

90

85

80

12345678910111213141516

Periods

U

D

i

e

Forthisspecificproblem,itisevidentthatthemovingaveragemodelismoreresponsivethantheexponentialsmoothingapproachduethedifferenceinweightsallocation(0.25and0.1).UsingMADasameasureforforecastaccuracyitcanbeconcludedthatthemovingaveragemodel(MAD=9)isslightlymoreaccuratethantheexponentialsmoothingmodel(MAD=10)inevaluatingforecasts.

Problem7-3:

Thesimpleexponentialsmoothingmodelonlyconsidersthelevelcomponentanddoesnotincludeatrendcomponentintheanalysis.However,Holt’smodelallowsfortheincorporationofthetrendcomponentintotheanalysis.Worksheet7-3providestheresultsofthetwoapproaches.

200

180

160

140

120

100

80

60

40

20

0

P1P2P3P4P5P6P7P8P9

Period

S

P10

P11

P12

P13

P14

P15

P16

s

Byinvestigatingtherelationshipbetweensalesandperiod(shownintheabovegraph)itisevidentthatthedataexhibitsbothrandomfluctuationandtrend.Thus,itisnotsurprisingintheanalysisthatHolt’smodel(alpha=0.1,beta=0.1,MAD=8)isabetterapproachthanthesimpleexponentialsmoothingmodel(alpha=0.1,MAD=21).

Problem7-4:

Worksheet7-4evaluatesdemandforecastsfortheABCCorporationusingmovingaverage,simpleexponentialsmoothing,Holt’smodel,andWinter’smodel.Notethatsolverisutilizedforsimpleexponentialsmoothing,Holt’sandWinter’smodelsindeterminingtheoptimalvaluesforthesmoothingconstantsbyminimizingtheMAD

subjecttotheconstraintthatthesmoothingconstantvaluesare<1.

ItisevidentthatWinter’smodelispreferableinthiscasewiththelowestMADvalue,i.e.,lowestforecasterror.ItisalsoimportanttonotethatWinter’smodelallowsfortheincorporationoflevel,trendandseasonality,whichareevidentinthedemanddataforthiscase.

Problem7-5:

Worksheet7-5comparesthetwoexponentialsmoothingforecastswithanalphaof.1andandalphaof.9.

Fromthedataandthegraphs,itisevidentthatthealphaof.9isabettertrackeroftheforecast.

Problem7-6:

Worksheet7-6looksattheforecastforA&DElectronicsandcomparestheresultsofsimpleexponentialsmoothingmodelwiththeHolt’smodel.Inlookingattheresultsofthesetwomodels,itisevidenttheHolt’smodelisabetterf