Case Study 5

Background The Glass Slipper restaurant has operated in a resort community near a popular ski area of New Mexico and busiest during the rst 3 months of the year. The Glass slipper oered the ultimate dining experience with breathtaking !iews of the surrounding mountains. "ames and #eena $eltee% the owner% place special attention in setting the perfect ambiance making dining a truly magnicent gourment experience. The Glass Slipper has de!eloped and maintained a reputation as one of the &must !isit& places in that region of New Mexico. Objective 'fter careful analysis of their nancial condition% the $eltee(s decided to sell the Glass Slipper and open a bed and breakfast on a beautiful beach in Mexico. 'lthough not retired yet% this would put them in the retirement setting they ha!e been longing for many years. They would ha!e to hire a manager that would allow them to begin a semi)retirement life in paradise. The Glass Slipper for the right price. The price of the business would be based on the !alue of the property and e*uipment% as well as pro+ections of future income. ' forecast of sales for the next year is needed to help in the determination of the calue of the restaurant. Monthly sales for each of the past 3 years are pro!ided below. Monthly ,e!enue -in /%000s1 Month  "anuary 6ebruary March 'pril May  "une  "uly 'ugust Septembe :ctober No!embe #ecember

222 34 /7 / 3/8 304 90 90 9/4 909 995 9;0 3/5

22 22 22 22 22 22 22 22 22 22 22 22 22

222 5 37 3 338 33/ 95 94 93/ 990 93 987 330

12-Month Moving Average Enter Enter the the past past demands demands in in the the data data area area

Forecasting Num pds !ata Month  "an)08 6eb)08 Mar)08 'pr)08 May)08  "un)08  "ul)08 'ug)08 Sep)08 :ct)08 No!)08 #ec)08  "an)07 6eb)07 Mar)07 'pr)07 May)07  "un)07  "ul)07 'ug)07 Sep)07 :ct)07 No!)07 #ec)07  "an)/0 6eb)/0 Mar)/0 'pr)/0 May)/0  "un)/0

Simple Linear egression /9

!emand 38 90 / 3/8 304 90 90 9/4 /78 995 9;0 3/5  95 93 33/ 3/8 95 955 993 9/0 933 9;8 399 50 38 3 338 33/ 95

Forecasts and "rror Anal#sis Forecast "rror Absolute

S$uared

Abs %ct "rr 500 400 300 Value

200 100 0

300.000 300.500 300.7/; 30/.44; 309.;50 303.;50 30./4; 305./; 304.000 30;.000 30;.44; 308.333 308.7/; 307./; 3/0.500 3//./; 3/9.000 3/3.083

/.000 /9.500 /99.083 97.333 /5.950 )58.;50 )7./4; )89./; )74.000 );.000 )97.44; /3.44; //.083 /98.583 /93.500 94.583 /7.000 )57.083

/.000 /9.500 /99.083 97.333 /5.950 58.;50 7./4; 89./; 74.000 ;.000 97.44; /3.44; //.083 /98.583 /93.500 94.583 /7.000 57.083

90;34.000 /5500.950 /70.30 840. 939.543 35/.543 9/;.34/ 4;79.50; 79/4.000 5;4.000 880./// /84.;;8 /770.50; /4533.4; /5959.950 ;04.4; 34/.000 370.80

0.39 0.973 0.987 0.087 0.08 0.90 0./73 0.3;0 0.5; 0.3/8 0./0; 0.09 0.3/ 0.97 0.985 0.0;7 0.05; 0.933

The lines abo!e the &forecast li the &forecast line& show their o sales as each New f thisisiscausal causalregression regression to toforecast forecasty. y.

Regression

15 mn B

20

25

30

35

40

Linear (Column B)

e is not. $hile the /9)month mo!ing a!erage plotted a ession plotted a negati!e trend line. ' trend line based on the *26 ich would indicate that sales are declining o!er time. The high trend line on the unad+usted data to appear to ha!e a

Multiplicative !ecomposition Enter Enterpast pastdemands demandsin inthe thedata dataarea. area.Do Donot notchange changethe thetime timeperiod period numbers! numbers! Forecasting !ecomposition: multiplicative

 /9 seasons !ata

Foreca

Month

!emand #3

;ime 03

Average

atio

Seasonal

Smoothed

2

Abs %ct "rr

/3.3/5

/3.3/5

/;;.985

0.030

7.8;5

7.8;5

7;.50;

0.09

4.45;

4.45;

.390

0.0/4

0.857

0.857

0.;3;

0.003

)/.45/

/.45/

9.;9

0.005

/.39/

/.39/

/.;5

0.004

)5.;4;

5.;4;

33.94

0.09

)/.50

/.50

9.949

0.00;

);.479

;.479

57./49

0.037

)3.;97

3.;97

/3.708

0.0/;

)3.;78

3.;78

/.98

0.0/

)3.;45

3.;45

/./;

0.0/9

4.0;0

4.0;0

34.850

0.0/

9.//;

9.//;

.83

0.005

3.0/7

3.0/7

7.//;

0.00;

.05

.05

/4.357

0.0/9

0.85

0.85

0.;97

0.003

)/.09;

/.09;

/.055

0.00

/.484

/.484

9.8/

0.00;

)/./44

/./44

/.340

0.005

)/.7;4

/.7;4

3.70

0.007

)9.;00

9.;00

;.988

0.0/9

)./9/

./9/

/4.789

0.0/5

)4.30

4.30

/.39

0.090

)/./;

/./;

/.3;8

0.003

9.340

9.340

5.5;0

0.005

/.38/

/.38/

/.708

0.003

/.93/

/.93/

/.5/

0.00

.358

.358

/8.770

0.0/3

0.495

0.495

0.370

0.009

3./37

3./37

7.85/

0.0/9

0./;9

0./;9

0.030

0.00/

5.;0

5.;0

39.7;

0.094

0.330

0.330

0./07

0.00/

)/.3

/.3

9.08

0.005

)3.075

3.075

7.5;;

0.007

/8.//

/90./70

488./;5

0.373

0.503

3.337

/7.//4

0.0//

=ias

M'#

MSB

M'@B

SB

5.573

Season /0

Season //

Season /9

0.;9;

0.8;3

/.0/8

0.;53

0.877

/.0/

0.;85

0.73

/.083

0.;55

0.709

/.0;

 onal

!

10 &d$us ted

11

12

Forecasting  /9 seasons

!ata @eriod

!ecomposition: multiplicative

Enter Enterpast pastdemands demandsin inthe thedata dataarea. area.Do Donot notchange changethe thetime time period numbers! period numbers!

#emand -y1 Time -x1

 "an)08

38

6eb)08

90

Mar)08

/

'pr)08

3/8

May)08

304

 "un)08

90

 "ul)08

90

'ug)08

9/4

Sep)08

/78

:ct)08

995

No!)08

9;0

#ec)08

3/5

 "an)07



6eb)07

95

Mar)07

93

'pr)07

33/

May)07

3/8

 "un)07

95

 "ul)07

955

'ug)07

993

Sep)07

9/0

:ct)07

933

No!)07

9;8

#ec)07

399

 "an)/0

50

6eb)/0

38

Mar)/0

3

'pr)/0

338

May)/0

33/

 "un)/0

95

 "ul)/0

94

'ug)/0

93/

Sep)/0

99

:ct)/0

93

/ 9 3  5 4 ; 8 7 /0 // /9 /3 / /5 /4 /; /8 /7 90 9/ 99 93 9 95 94 9; 98 97 30 3/ 39 33 3

'!erage ,atio

300 300.5 300.7/4; 30/.444; 309.;5 303.;5 30./44; 305./4; 304 30; 30;.444; 308.3333 308.7/4; 307./4; 3/0.5 3//./4; 3/9 3/3.0833 3/3.8333 3/.5833 3/5.95 3/4./4; 3/;.95 3/8./44; 3/7.95

300.95 300.;083 30/.97/; 309.9083 303.95 303.7583 30.;7/; 305.;083 304.5 30;.3333 308 308.495 307./44; 307.7583 3/0.7583 3//.;083 3/9.5/; 3/3.583 3/.9083 3/.7/4; 3/5.8333 3/4.8333 3/;.;083 3/8.;083

Seasonal Smoothe Anad+uste /.59 303.9979 975.38; /.370597 309.033 974.95/ /.3;;/9 300.49; 97;./054 /.0;/70; 974.44;4 97;.744 /.03;/59 975.0388 978.8945 0.;7505 30/.;33 977.48; 0.;7733 0.8/9044 975.595 300.5; 0.;/830 0.;/88;8 300.483 30/.0;7 0.45;/;/ 0.44495/ 97;./853 309.948 0.;59 0.;400; 30/.4057 303./988 0.87035 0.8877/8 303.3788 303.7873 /.034394 /.03/;88 305.9753 30.87; /.54;33 /.59 30;.383/ 305.;/09 /.3709/ /.370597 305.437/ 304.5;0; /.380078 /.3;;/9 30;./49; 30;.3// /.0;;00; /.0;/70; 308.;755 308.97/4 /.03948 /.03;/59 304.4087 307./59/ 0.;738 0.;7505 308.0/7/ 3/0.0/95 0.89;78 0.8/9044 3/.0/37 3/0.8;3 0.;/759 0.;/88;8 3/0.905; 3//.;33 0.4;5339 0.44495/ 3/5./745 3/9.5737 0.;;7 0.;400; 3/9.397; 3/3.5 0.8878/ 0.8877/8 3/9.388 3/.3/8 /.09;95 /.03/;88 3/9.0;74 3/5./;53 /.39/;/ /.59 3//.5347 3/4.0358 /.3708 /.370597 3/.788 3/4.8749 /.3;/9 /.3;;/9 3/5./50 3/;.;54; /.04480; /.0;/70; 3/5.3957 3/8.4/;/ /.0/834 /.03;/59 3/7./33 3/7.;;4 0.;7474; 0.;7505 3/7.33/ 390.338/ 0.8/9044 395.0748 39/./785 0.;/88;8 39/.339 399.057 0.44495/ 334.9074 399.7/75 0.;400; 395.;3 393.;;77

No!)/0

987

35

0.8877/8

#ec)/0

335

34

/.03/;88 39.4;7/ 395.5008 '!erage

39.;7 39.40

>ntercept 97.599 Slope 0.84043

atios Season /

'!erage

Season 9 Season 3 Season  Season 5 Season 4 Season ; Season 8 0.;7733 0.;/830 /.54;39; /.3709/ /.380078 /.0;;00; /.03948 0.;738 0.89;78 0.;/759 /.39/;08 /.3708 /.3;/9 /.04480; /.0/834 0.;7474; /.5/8 /.370597 /.3;;/9 /.0;/70; /.03;/59 0.;7505 0.8/9044 0.;/88;8

Forecasts @eriod Anad+usted Seasonal 'd+usted 3; 394.34/3/ /.59 ;/./39 38 39;.99/;; /.370597 55.0// 37 398.0899 /.3;;/9 5/.808; 0 398.79; /.0;/70; 359.5757 / 397.803/4 /.03;/59 39.0557 9 330.44349 0.;7505 943.0//4 3 33/.5907 0.8/9044 947.9/7  339.3855 0.;/88;8 938.737 5 333.950/ 0.44495/ 999.098 4 33./05; 0.;400; 97.97 ; 33.7457 0.8877/8 978.0799 8 335.894 /.03/;88 34.50/;

Forecasts and "rror Anal#sis 'd+usted Brror CBrrorC BrrorD9 'bs @ct Brr 94.4487 //.33// //.33// /98.3737 09.57E //.73;5 8.04958 8.04958 45.0048 0/.79E 07./50/ .87703 .87703 93.59/54 0/./;E 3/7.37/8 )/.37/8/ /.37/8/ /.73;/34 00.E 307.7985 )3.7985 3.79853 /5.39; 0/.98E 938.3;94 /.49;374 /.49;374 9.48/; 00.48E 9.043 ).043/ .043/3 /4.5/84 0/.47E 9/4.4;5 )0.4;5 0.4;538 0.549/4 00.3/E 90/.3844 )3.38449 3.38449 //.479 0/.;/E 994./34/ )/./34/ /./34074 /.970;/5 00.50E 9;0.5955 )0.59559 0.59559/ 0.9;4/;9 00./7E 3/.503 0.57484 0.57484 0.9//3// 00./5E /.583; 9./434 9./434 5.838;94 00.5E 94.975 )/.9753 /.9753 /.4;8/37 00.30E 93.3474 )0.34749 0.34749 0./344/7 00.07E 330.578 0.50/43 0.50/43 0.97/;;4 00./4E 390.43;4 )9.43;49 9.43;4/4 4.75;0/4 00.83E 94.5854 )/.5854 /.58540/ 9.5//39 00.45E 959.73 9.55044 9.55044 4.505844 0/.00E 99.0789 )/.07895 /.07894 /.904/5 00.7E 908.944 /.;337;/ /.;337;/ 3.004455 00.83E 933.837 )0.83709 0.837095 0.;03749 00.34E 9;7.;/ )/.;// /.;//3 9.7379/3 00.49E 395./7/ )3./707 3./7073 /0.90993 00.77E 54.78 )4.78/ 4.78/ 9.99738 0/.E 0.453 )9.453/ 9.4530; ;.005;/ 00.4/E 3;.587/ )3.587/ 3.587/ /9.88/75 00.83E 3/.59;7 )3.59;84 3.59;84 /9.589 0/.0E 33/.348 )0.34;8 0.34;;7 0./90955 00./0E 95.;784 )0.;784 0.;78577 0.43;;4 00.3/E 940.83 3./45433 3./45433 /0.09/93 0/.90E 93/.59// )0.59/05 0.59/055 0.9;/78 00.93E 9/5./5 8.85549 8.85549 ;8.039; 03.75E 9/.59 /.580; /.580; 9./9570/ 00.40E

988.7033 0.07447 0.07447

0.00735

00.03E

335.8;7 )0.8;8; 0.8;8;9 0.;/888; 00.95E Total 0.59/983 73.;;9/ ;4.0;/ 30.//E 0.0/8 9.40;89 /3.99353 00.8E =ias M'# MSB M'@B SB .45/;9/ Season 7 Season /0Season //Season /9 0.45;/;/ 0.;59 0.87035 /.034394 0.4;5339 0.;;7 0.8878/ /.09;95 0.44495/ 0.;400; 0.8877/8 /.03/;88

Forecasting

;rend adjusted e0ponential smoothing

Enter Enter alpha alpha and and beta beta (between (between 00 and and 1, 1, enter enter the the past past demands demands in in the the shaded shadedcolumn columnthen thenenter enter aa starting orecast. I the starting orecast is not in the irst period then delete the error anal"sis starting orecast. I the starting orecast is not in the irst period then delete the error anal"sisor or all allrows rowsabo#e abo#ethe the starting starting orecast. orecast.

'lpha =eta !ata

@eriod @eriod / @eriod 9 @eriod 3 @eriod  @eriod 5 @eriod 4 @eriod ;

Forecasts and "rror Anal#sis

#emand

@eriod 8 /e0t period

Smoothed Forecast Forecast, Smoothed Including Ft Trend, Tt Trend, FIT t Brror

0 0 0 0 0 0

0 0 0 0 0 0 0

'bsolute S*uared 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

0

0

0

0

0

 Total Average



 0 

0 

0 

0 0 0 0 0 0 0

Bias

MA! S"

MS" 

'bs @ct Brr 2#>F0H

Forecasting 1

2#>F0H ?!7@ MA%"

0'! 0' 0'7 0'6 Value

0'5 0'4 0'3 0'2 0'1 0 1

2

3

4

5

6

 Time Demand

%mooted Forecast Ft

7



I'TB $'JSK 'SS:L>'TBS

Forecasting

"0ponential smoothing

Enter Enter alpha alpha (between (between 00 and and 1, 1,enter enter the the past past demands demands in in the the shaded shaded column column then then enter enter aa starting starting orecast. orecast. II the the starting starting orecast orecast is is not not in in the the irst irst period period then then delete delete the the error error anal"sis anal"sisor orall allrows rows abo#e abo#ethe thestarting startingorecast. orecast.

'lpha !ata @eriod @eriod / @eriod 9 @eriod 3 @eriod  @eriod 5 @eriod 4

0./ #emand ;0 48.5 4.8 ;/.; ;/.3 ;9.8

Forecasts and "rror Anal#sis Forecast "rror Absolute S$uared Abs %ct "rr 45 5 5 95 0;./E 45.5 3 3 7 0.38E 45.8 )/ / / 0/.5E 45.; 4 4 34 08.3;E 44.3 5 5 95 0;.0/E 44.8 Total Average

4 4 9 94 , ,'(((((( Bias MA!

34 0.089/;589 /39 34.47E 22 *'11C MS" MA%"

S" &'),,&*( /e0t period #>SLASS>:N

*)',

5.97? Asing exponential smoothing forecast for 'ugust(s income is 4;%00.

Forecasting 74 72 70 6 Value

66 64 62 60 1

2

3  Time 70

65

4

5

DA;" EALS ASSO87A;"S Forecasting

'lpha !ata @eriod M:NTK / M:NTK 9 M:NTK 3 M:NTK  M:NTK 5 M:NTK 4

"0ponential smoothing

0.3 #emand ;0 48.5 4.8 ;/.; ;/.3 ;9.8

Forecasts and "rror Anal#sis Forecast "rror Absolute S$uared Abs %ct "rr 45 5 5 95 0;./E 44.5 9 9  09.79E 4;./ )9.3 9.3 5.97 03.55E 44./ 5.97 5.97 9;.78/ 0;.38E 4;.77; 3.303 3.303 /0.7078/ 0.43E 48.78;7 3.8/9/ 3.8/9/ /.539// 0.059340// Total /;./05/ 9/.;05/ 8;.;/409 30.84E Average 2'.&.& ('*1)&1) 1,'*1+(, &'1,C Bias MA! MS" MA%" S" ,'*.2.,1

/e0t period #>SLASS>:N

)'1(1&(

5.30? Asing alpha of 0./ %M'# !alue is .333 while using alpha of 0.3 %M'# !alue is 3.4/8. =ased on this using alpha of 0.3 pro!ides a better forecast since it has a lower M'# !alue.

En E or o ab a

Forecasting 74 72 70 6 Value

66 64 62 60 1

2

3  Time 70

65

4

5

ter teralpha alpha(between (between00and and 1, 1,enter enterthe thepast pastdemands demandsin inthe theshaded shadedcolumn columnthen thenenter enter aa starting starting ecast. IIthe recast. thestarting startingorecast orecastis isnot notin inthe theirst irstperiod periodthen thendelete deletethe theerror error anal"sis anal"sisor orall allrows rows o#e o#ethe thestarting startingorecast. orecast.