Quantitative Techiniques (5)

7/23/2019 Quantitative Techiniques (5)

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Homework

John Nowell Diestro


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Problem 1Use quantitative forecast methods for the data shown below.

a. Compute for:

i. NAVE ME!"#

ii. !$EE %E$&"# M"V&N' AVE$A'E

iii. !$EE( %E$&"# )E&'!E# M"V&N' AVE$A'E

iv. *"U$ %E$&"# M"V&N' AVE$A'E

v. *"U$ %E$&"# )E&'!E# M"V&N' AVE$A'E

b. %lot the ori+inal time series and comment on the appropriateness of linear trend.

PERIOD 1 2 3 4 5 6 7

OBSERVATION 24 34 36 37 41 44 4


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PERIOD Demand NAVE

Forecast

TREE!PERIOD"OVIN#

AVERA#E

TREE!PERIOD%EI#TED

"OVIN#AVERA#E

FO&R!PERIOD"OVIN#

AVERA#E

F

1 24

2 34 24

3 36 34

4 37 36 31 33

5 41 37 36 36 33

6 44 41 3' 3( 37

7 45 44 41 42 4)


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o u on ree- er o oAverage,%eriod - /- 0 1- 0 12 3 1 4 /5

,%eriod 6 17 0 12 0 1- 3 1 4 12

,%eriod 2 -5 0 17 0 12 3 1 4 18

,%eriod 7 -- 0 -5 0 17 3 1 4 -5

Solution (!our-Period M

Av

,%eriod 6 /- 0 1- 0 1

,%eriod 2 -5 0 17 0 1

,%eriod 7 -- 0 -5 0 1


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o u on ree- er o"eighted Average,%eriod - 12,101-,/0/-,5 3 2 4 11

,%eriod 6 17,1012,/01-,5 3 2 4 12

,%eriod 2 -5,1017,/012,5 3 2 4 1

,%eriod 7 --,10-5,/017,5 3 2 4 -/

Solution (!our-Period M

Av

,%eriod 6 17,-012,101-,/

,%eriod 2 -5,-017,1012,/

,%eriod 7 --,-0-5,1017,/


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Demand Na*+e Forecast

T,ree!Per-od "o+-n. A+era.e T,ree!Per-od %e-.,ted A+era.e

Fo/r!Per-od "o+-n. A+era.e Fo/r!Per-od %e-.,ted A+era.e


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Problem #;uppose that the Universit< of the )est had the followin+ data of its +rowth of enro

/999(/998.

$equirements:a. *orecast the /99 enrollment usin+ three(


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0ear Enroment 3 ear e-.,ted

mo+-n. a+era.e 3) Forecast 1) Forecast Error

2))) 3)))

2))1 32)) 3))) 3))) 2))

2))2 36)) 3)6) 3)2) 5')

2))3 365) 3367 3222 3)7' 572

2))4 4))) 355' 335) 3135 '65

2))5 42)) 3'17 3545 3222 (7'

2))6 43)) 4)42 3742 332) (')

2))7 441) 4217 3()( 341' ((2

2))' 452) 433' 4)5( 3517 1))3

2))( 4447 41(7 3617

34'') 277'6 32)'4 2(327 617)


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o u on ree- ear e gAverage/991 > 1999 ,5 0 1/99 ,/ 0 1299 ,1 4 /9/99 3 2 4 1127

/99- > 1/99 ,5 0 1299 ,/ 0 1269 ,1 4 /5169 3 2 4 1668

/996 > 1299 ,5 0 1269 ,/ 0 -999 ,1 4 //99 3 2 4 1857

/992 > 1269 ,5 0 -999 ,/ 0 -/99 ,1 4 /-/69 3 2 4 -9-/

/997 > -999 ,5 0 -/99 ,/ 0 -199 ,1 4 /6199 3 2 4 -/57

/998 > -/99 ,5 0 -199 ,/ 0 --59 ,1 4 /2919 3 2 4 -118

/99 > -199 ,5 0 --59 ,/ 0 -6/9 ,1 4 /2289 3 2 4 ---7


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Solution (%&',/99/ 1999 0 .19 ,1/99 ( 1999 4 1999

,/991 1929 0 .19 ,1299 ( 1929 4 1///

,/99- 1/// 0 .19 ,1269 ( 1/// 4 1169

,/996 1169 0 .19 ,-999 ( 1169 4 16-6

,/992 16-6 0 .19 ,-/99 ( 16-6 4 17-/

,/997 17-/ 0 .19 ,-199 ( 17-/ 4 19

,/998 19 0 .19 ,--59 ( 19 4 -96

,/99 -96 0 .19 ,-6/9 ( -96 4 -57


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Solution (1&' rror,/99/ 1999 0 .5 ,1/99(1999 4 19/9

,/991 19/9 0 .5 ,1299(19/9 4 1978

,/99- 1978 0 .5 ,1269(1978 4 1516

,/996 1516 0 .5 ,-999(1516 4 1///

,/992 1/// 0 .5 ,-/99(1/// 4 11/9,/997 11/9 0 .5 ,-199(11/9 4 1-58

,/998 1-58 0 .5 ,--59(1-58 4 1657

,/99 1657 0 .5 ,-6/9(1657 4 1257

,/995 1/99(1999 4 /9

,/99/ 1299(19/9 4 68

,/991 1269(1978 4 67

,/99- -999(1516 4 82

,/996 -/99( 1/// 4 7,/992 -199( 11/9 4 8

,/997 --59( 1-58 4

,/998 -6/9( 1657 4 59


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-Average4 2579

8

4 775./6 ,/99- 1999,501/99,/01299,10126

,/996 1/99,501299,/01269,10-99

,/992 1299,501269,/0-999,10-/9

,/997 1269,50-999,/0-/99,10-19

,/998 -999,50-/99,/0-199,10--5

,/99 -/99,50-199,/0--59,10-6/


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Problem %*or the /997(/998 %hilippine ?as@etball Association ,%?A season= %ure *oods Bame

scorin+ leader with an avera+e of 11 points per +ame. he followin+ data shows thenumber of points per +ame for the scorin+ leader from the /99/(/991 season to theseason.

a. Use eDponential smoothin+ to forecast this time series. Consider smoothin+ conand a = 0.30. )hat value of the smoothin+ provides the best forecastb. )hat is the forecast of the leadin+ scorin+ avera+e for the /998(/99 seasonc. 'raph the forecast at a = 0.30.

Season A+era.e

2))2!2))3 25

2))3!2))4 35

2))4!2))5 2(

2))5!2))6 34

2))6!2))7 35

2))7!2))' 33


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Season A+era.e Forecast

)2)Error)2)

Error8)2)

Forecast)3)

Error)3)

2))2!2))3 25

2))3!2))4 35 25 1) 1)) 25 7

2))4!2))5 2( 27 2 4 2' 1

2))5!2))6 34 27 7 4( 2' 4

2))6!2))7 35 2' 7 4( 3) 3

2))7!2))' 33 2( 4 16 32 1

2))'!2))( 3) 32

Tota 166 3) 21' 175 16


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Solution (#&'*orecast ,9./9:

/99-(/996:

* 4 /6 0 9./9,16(/6

4 /6 0 9./9,59

4 /7

/996(/992:

* 4 /7 0 9./9,/(/7

4 /7 0 9./9,/

4 /7

/992(/997:

* 4 /7 0 9./9,1-(/7 4 /7 0 9./9,7

4 /8

/997(/998:

* 4 /8 0 9./9,16(/8

4 /8 0 9./9,7

4 /

/998(/99:

* 4 / 0 9./9,11(/ 4 / 0 9./9,-

4 19


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rror) rror#) MAD)/99-(/996: 16 ( /6 4 59

/996(/992: / ( /7 4 /

/992(/997: 1- ( /7 47

/997(/998: 16 ( /8 4 7

/998(/99: 11 ( / 4 -

/99-(/996: 59F 4 599

/996(/992: /F 4 -

/992(/997: 7F 4 -

/997(/998: 7F 4 -

/998(/99: -F 4 52

1936 4 2


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Solution (%&'*orecast ,9.19:

/99-(/996:

* 4 /6 0 9.19,16(/6

4 /6 0 9.19,59

4 /8

/996(/992:

* 4 /8 0 9.19,/(/8

4 /8 0 9.19,5

4 /8

/992(/997:* 4 /8 0 9.19,1-(/8

4 /8 0 9.19,2

4 19

/997(/998:

* 4 19 0 9.19,16(19

4 19 0 9.19,6

4 1/

/998(/99:* 4 1/ 0 9.19,11(1/

4 1/ 0 9.19,5

4 1/


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rror) rror#) MAD)/99-(/996: 16(/8 4 7

/996(/992: /(/8 4 5

/992(/997: 1-(19 4 -

/997(/998: 16(1/ 4 1/998(/99: 11(1/ 4 5

/99-(/996: 7F4 -

/996(/992: 5F4 5

/992(/997: -F4 52

/997(/998: 1F4

/998(/99: 5F4 5

5236 4 1./


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A+era.e Forecast 2 Forecast 3


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Problem **ill(up the vacant table. 'iven is as follows:

%ee9 Saes 1))) Fo/r!%ee9 "o+-n.

A+era.eFo/r!%ee9 %e-.,ted

"o+-n. A+era.e

1 23

2 36

3 45

4 46

5 55

6 64

7 55

' 5'

( 66


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%ee9 Saes Fo/r!%ee9 "o+-n.

A+era.eFo/r!%ee9 %e-.,t

"o+-n. A+era.e

1 23)))

2 36)))3 45)))

4 46)))

5 55))) 375)) 414))

6 64))) 455)) 4'4))

7 55))) 525)) 55'))

' 5'))) 55))) 56'))( 66))) 5'))) 5')))

1) 65))) 6)75) 612))

11 4'))) 61))) 62())

12 67))) 5(25) 577))

13 5'))) 615)) 6)')

14 6'))) 5(5)) 5(4))

o u on our ee ov n


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o u on our- ee ov nAverage)ee@ 6: /1999 0 12999 0 -6999 0 -2999 3 - 4 17699

)ee@ 2: 12999 0 -6999 0 -2999 0 66999 3 - 4 -6699

)ee@ 7: -6999 0 -2999 0 66999 0 2-999 3 - 4 6/699

)ee@ 8: -2999 0 66999 0 2-999 0 66999 3 - 4 66999

)ee@ : 66999 0 2-999 0 66999 0 68999 3 - 4 68999

)ee@ 59: 2-999 0 66999 0 68999 0 22999 3 - 4 29769

)ee@ 55: 66999 0 68999 0 22999 0 26999 3 - 4 25999)ee@ 5/: 68999 0 22999 0 26999 0 -8999 3 - 4 6/69

)ee@ 51: 22999 0 26999 0 -8999 0 27999 3 - 4 25699

)ee@ 5-: 26999 0 -8999 0 27999 0 68999 3 - 4 6699

o u on our ee e g


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o u on our- ee e gAverage)ee@ 6: /1999,5 0 12999,/ 0 -6999,1 0 -2999,- 3 59 4 -5-99

)ee@ 2: 12999,5 0 -6999,/ 0 -2999,1 0 66999,- 3 59 4 -8-99

)ee@ 7: -6999,5 0 -2999,/ 0 66999,1 0 2-999,- 3 59 4 66899

)ee@ 8: -2999,5 0 66999,/ 0 2-999,1 0 66999,- 3 59 4 62899

)ee@ : 66999,5 0 2-999,/ 0 66999,1 0 68999,- 3 59 4 68999

)ee@ 59: 2-999,5 0 66999,/ 0 68999,1 0 22999,- 3 59 4 25/99)ee@ 55: 66999,5 0 68999,/ 0 22999,1 0 26999,- 3 59 4 2/99

)ee@ 5/: 68999,5 0 22999,/ 0 26999,1 0 -8999,- 3 59 4 67799

)ee@ 51: 22999,5 0 26999,/ 0 -8999,1 0 27999,- 3 59 4 29899

)ee@ 5-: 26999,5 0 -8999,/ 0 27999,1 0 68999,- 3 59 4 6-99


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Use eDponential smoothin+ with G between 9.59 and 9.19 to +et t

one period ahead for the followin+ time series.Use the initial valuand identif< which value of G is the best

Problem +

PERIOD DE"AND FORE:AST1 25) 2))

2 265

3 3))

4 35)

5 25)

6 35)

7 265

' 3()


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1) 3)

Per-od Demand Forecast Error Forecast Error

1 25) 2)) 5) 2)) 5)

2 265 2)5 6) 215 5)

3 3)) 211 '( 23) 7)

4 35) 22) 13) 251 ((

5 25) 233 17 2'1 !31

6 35) 235 115 272 7'

7 265 247 1' 2(5 !3)

' 3() 24( 141 2'6 1)4

( 35) 263 '7 317 33

1) 4)) 272 12' 327 73

11 47) 2'5 1'5 34( 121

Tota 262) 1)2) 3)23 617


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Solution (1&'%eriod /:

*t4 /99 0 .59 ,/69(/99 4 /99 0 6 4 /96

%eriod 1:*t4 /96 0 .59 ,/26(/96 4 /96 0 2 4 /55

%eriod -:*t4 /55 0 .59 ,199(/55 4 /55 0 8. 4 //9

%eriod 6:

*t4 //9 0 .59 ,169(//9 4 //9 0 51 4 /11

%eriod 2:*t4 /11 0 .59 ,/69(/11 4 /11 0 5.7

4 /16

%eriod 7:*t4 /16 0 .59 ,169(/16 4 /16 0 55.6 4 /-7

%eriod 8:

*t4 /-7 0 .59 ,/26(/-7 4 /-7 0 5.8 4 /-

%eriod :*t4 /- 0 .59 ,19(/- 4 /- 0 5-.5

4 /21

%eriod 59:*t4 /21 0 .59 ,169(/21 4 /21 0 8.7 4 /7/

%eriod

*t4 /7/ 4 /7/ 4 /86


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Solution (%&'%eriod /:

*t4 /99 0 .19 ,/69(/99 4 /99 0 56 4 /56

%eriod 1:*t4 /56 0 .19 ,/26(/56 4 /56 0 56 4 /19

%eriod -:*t4 /19 0 .19 ,199(/19 4 /19 0 /5 4 /65

%eriod 6:

*t4 /65 0 .19 ,169(/65 4 /65 0 /.7 4 /85

%eriod 2:*t4 /85 0 .19 ,/69(/85 4 /85 0 (.1

4 /7/

%eriod 7:*t4 /7/ 0 .19 ,169(/7/ 4 /7/ 0 /1.- 4 /6

%eriod 8:

*t4 /6 0 .19 ,/26(/6 4 /6 0 ( 4 /82

%eriod :*t4 /82 0 .19 ,19(/82 4 /82 0 15./

4 157

%eriod 59:*t4 157 0 .19 ,169(157 4 157 0 . 4 1/7

%eriod

*t4 1/7 4 1/7 4 1-


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Problem ,ANV&C"$";E buildin+ contracts for a 5/(month period are ,in million pesos shown

a. Compare a four(month movin+ avera+e forecast with an eDponential smoothi

G 4 9.19. )hich of the two provides better forecastsb. )hat is the forecast for the neDt monthc. %lot the ori+inal data and the four(month movin+ avera+e on the same +raph.d. %lot the ori+inal data and the smoothin+ forecast on the same +raph.e. Compute the MA# and M;E.

"ont, 1 2 3 4 5 6 7 ' ( 1

Demand 35 27 37 41 45 3' 44 42 3( 4


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"ont, Demand4 "ont,"o+-n.

A+era.e

3)Forecast

Error Error8

1 35

2 27 35 !' 64

3 37 33 4 16

4 41 34 7 4(

5 45 35 36 ( '1

6 3' 3' 3( !1 1

7 44 4) 3( 5 25

' 42 42 41 1 1

( 3( 42 41 !2 41) 43 41 4) 3 (

11 3( 42 41 !2 4

12 4) 41 4) ) )

TOTA; 47) 361 41( 2) 254

o u on our- on ov


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o u on our- on ovAverage

Month 6

,-50170/70163- 4 16

Month 2,-60-50170/73- 4 18

Month 7

,180-60-50173- 4 -9Month 8,--0180-60-53- 4 -/

Month

,-/0--0180-63- 4 -/

Month 59,10-/0--0183- 4 -5

Month 55,-1010-/0--3- 4 -/

Month 5/,10-1010-/3- 4 -5


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Solution (%&'Month /:

*t4 16 0 .1 ,/7(16 4 11

Month 1:*t4 11 0 .1 ,17(11

4 1-

Month -:

*t4 1- 0 .1 ,-5(1- 4 12

Month 6:*t4 12 0 .1 ,-6(12

4 1

Month 2:

*t4 1 0 .1 ,18(1 4 1

Month 7:*t4 1 0 .1 ,--(1

4 -5

Month 8:*t4 -5 0 .1 ,-/(-5

4 -5

Month :*t4 -5 0 .1 ,1(-5

4 -9

Month 59:

*t4 -9 0 .1 ,-1(-94 -5

Month 55:*t4 -5 0 .1 ,1(-5

4 -9

Month 5/:*t4 -9 0 .1 ,-9(-9 4 -9


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MAD MS4 52 3 55 4 /-6 3 55

4 5.-6 4 /1.9


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ra.h (!our-Month

Moving Average

Demand 4 "ont, "o+-n. A+era.e


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ra.h (%&' Smoothing

!ore/ast

Demand 3) Forecast


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Problem 0he AHC"$ #epartment ;tore has recorded the followin+ numbers of cus

complaints each month.

a. Compute a three(month wei+hted movin+ avera+e.

b. %repare forecast for Bune= Bul< and Au+ust.

"ont, :omr/ar 4'

"arc, 55A


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"ONT :O"P;AINTS 3!"ONT %EI#TED"OVIN# AVERA#E

FORE:AS

=an/ar 6)

Fe>r/ar 4' 6)

"arc, 55 4'

A


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SolutionApril

29,5 0 -8,/ 0 66,1 3 2 4 6-

Ma

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Quantitative Techiniques (5)