Tahoe Salt

7/29/2019 Tahoe Salt

1/19

Period t Demand Dt

1 8,000 Historical Demand Data

2 13,000

3 23,000

4 34,000

5 10,000

6 18,0007 23,000

8 38,000

9 12,000

10 13,000

11 32,000

12 41,000

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

1 2 3 4 5 6 7 8 9 10


2/19

11 12

Series1


3/19

Period t Demand Dt Deseasonalized Demand

1 8,000

2 13,000 Dt = L + T*t

3 23,000 19,750

4 34,000 20,625

5 10,000 21,250

6 18,000 21,750

7 23,000 22,500

8 38,000 22,125

9 12,000 22,625

10 13,000 24,125

11 32,000

12 41,000

-

5,000

10,000

15,000

20,000

25,000

30,000

1 2 3 4


4/19

5 6 7 8

Series1


5/19

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.958065237

R Square 0.917888998

Adjusted R Square 0.90420383

Standard Error 414.5033124Observations 8

ANOVA

df SS MS F Significance F

Regression 1 11523810 11523810 67 0

Residual 6 1030878 171813

Total 7 12554688

Coefficients Standard Error t Stat P-value Lower 95%

Intercept 18439 441 42 0 17360

X Variable 1 524 64 8 0 367


6/19

Upper 95% Lower 95.0% Upper 95.0%

19518 17360 19518

680 367 680


7/19

Period

tDemand

Dt

Deseasonalized Demand

Dt

Seasonal Factors

St

Estimated Seasonal

Factor for corresponding

seasons

0

1 8,000 18,963 0.42 0.472

2 13,000 19,487 0.67 0.683

3 23,000 20,011 1.15 1.1714 34,000 20,535 1.66 1.664

5 10,000 21,059 0.47

6 18,000 21,583 0.83

7 23,000 22,107 1.04

8 38,000 22,631 1.68

9 12,000 23,155 0.52

10 13,000 23,679 0.55

11 32,000 24,203 1.32

12 41,000 24,727 1.66

13 11910 Forecast for next year14 17614

15 30787

16 44642

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000


8/19

Level Trend

18439 524

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Series1


9/19

Period

tDemand

Dt

Level

Lt

Forecast

Ft

Error

Et

Absolute Error

At

Mean Squared

Error

MSEt

MADt

1 8,000

2 13,000

3 23,000

4 34,000 19500

5 10,000 20000 19500 9,500 9,500 90,250,000 9,500

6 18,000 21250 20000 2,000 2,000 47,125,000 5,750

7 23,000 21250 21250 -1,750 1,750 32,437,500 4,417

8 38,000 22250 21250 -16,750 16,750 94,468,750 7,500

9 12,000 22750 22250 10,250 10,250 96,587,500 8,050

10 13,000 21500 22750 9,750 9,750 96,333,333 8,333

11 32,000 23750 21500 -10,500 10,500 98,321,429 8,643

12 41,000 24500 23750 -17,250 17,250 123,226,563 9,719

13 24500

14 24500

15 24500 12,148 is standard dev

16 24500

Estimate using Moving Average Method

Forecast error is very fairly high and hence this is not co

L0 = 1.25*MADt

Forecast


10/19

%Error MAPEt TSt

95 95 1

11 53 2

8 38 2

44 39 -1

85 49 0

75 53 2

33 50 0

42 49 -2

rect


11/19

Period

tDemand

Dt

Level

Lt

Forecast

Ft

Error

Et

Absolute Error

At

Mean Squared Error

MSEt

0 22,083

1 8,000 20,675 22,083 14,083 14,083 198,340,278

2 13,000 19,908 20,675 7,675 7,675 128,622,951

3 23,000 20,217 19,908 -3,093 3,093 88,936,486

4 34,000 21,595 20,217 -13,783 13,783 114,196,860

5 10,000 20,436 21,595 11,595 11,595 118,246,641

6 18,000 20,192 20,436 2,436 2,436 99,527,532

7 23,000 20,473 20,192 -2,808 2,808 86,435,714

8 38,000 22,226 20,473 -17,527 17,527 114,031,550

9 12,000 21,203 22,226 10,226 10,226 112,979,315

10 13,000 20,383 21,203 8,203 8,203 108,410,265

11 32,000 21,544 20,383 -11,617 11,617 110,824,074

12 41,000 23,490 21,544 -19,456 19,456 133,132,065

13 23,490 12760.5543

14 23,490

15 23,490

16 23,490

Estimate using Simple Exponential SmoothingL0 = 1.25*MADt

Standard deviation of forecasted demand error is fairly large rel

Forecast


12/19

MADt %Error MAPEt TSt

14,083 176 176 1.00

10,879 59 118 2.00

8,284 13 83 2.25

9,659 41 72 0.51

10,046 116 81 1.64

8,777 14 70 2.15

7,925 12 62 2.03

9,125 46 60 -0.16

9,247 85 62 0.95

9,143 63 63 1.86

9,368 36 60 0.58

10,208 47 59 -1.38

ethod

ative to the size of the forecasted demand.


13/19

Period

tDemand

Dt

Level

Lt

Trend

Tt

Forecast

Ft

Error

Et

Absolute Error

At

0 12,015 1,549

1 8,000 13,008 1,438 13,564 5,564 5,564

2 13,000 14,301 1,409 14,445 1,445 1,445

3 23,000 16,439 1,555 15,710 -7,290 7,290

4 34,000 19,594 1,875 17,993 -16,007 16,007

5 10,000 20,322 1,645 21,469 11,469 11,469

6 18,000 21,570 1,566 21,967 3,967 3,967

7 23,000 23,123 1,563 23,137 137 137

8 38,000 26,018 1,830 24,686 -13,314 13,314

9 12,000 26,262 1,513 27,847 15,847 15,847

10 13,000 26,298 1,217 27,775 14,775 14,775

11 32,000 27,963 1,307 27,515 -4,485 4,485

12 41,000 30,443 1,541 29,270 -11,730 11,730

13 31,985

14 33,526

15 35,067

16 36,609

Forecast Estimate using Trend Corrected ExThough tracking signal is within range and indic

Standard deviation is = 1.25 X 8836 i.e. 11,045


14/19

Mean Squared Error

MSEtMADt %Error MAPEt TSt

30,958,096 5,564 70 70 1.00

16,523,523 3,505 11 40 2.00

28,732,318 4,767 32 37 -0.06

85,603,146 7,577 47 40 -2.15

94,788,701 8,355 115 55 -0.58

81,613,705 7,624 22 49 -0.11

69,957,267 6,554 1 42 -0.11

83,369,836 7,399 35 41 -1.90

102,010,079 8,338 132 52 0.22

113,639,348 8,981 114 58 1.85

105,137,395 8,573 14 54 1.41

107,841,864 8,836 29 52 0.04

ponential Smoothing Methodate better estimates, MAD is fairly large.

s still fairly large.


15/19

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.481327197

R Square 0.23167587

Adjusted R Square 0.154843457

Standard Error 10666.88337Observations 12

ANOVA

df SS MS F Significance F

Regression 1 343092657.3 343092657.3 3.015340286 0.113127023

Residual 10 1137824009 113782400.9

Total 11 1480916667

Coefficients Standard Error t Stat P-value Lower 95%

Intercept 12015.15152 6565.012894 1.830179424 0.09714727 -2612.608777

X Variable 1 1548.951049 892.0095994 1.73647352 0.113127023 -438.5701958


16/19

Upper 95% Lower 95.0% Upper 95.0%

26642.91181 -2612.608777 26642.91181

3536.472294 -438.5701958 3536.472294


17/19

Period

tDemand

Dt

Deseasonalize

D_bar

Level

Lt

Trend

Tt

Seasonal Factor

St

Forecast

Ft

Error

Et

0 18,439 524

1 8,000 18,862 514 0.472 8,951 951

2 13,000 19,359 512 0.683 13,234 234

3 23,000 19,750 19,860 511 1.171 23,269 269

4 34,000 20,625 20,374 511 1.664 33,897 -103

5 10,000 21,250 20,911 514 0.467 9,758 -242

6 18,000 21,750 21,674 539 0.682 14,609 -3,391

7 23,000 22,500 22,085 526 1.170 25,983 2,983

8 38,000 22,125 22,622 527 1.664 37,636 -364

9 12,000 22,625 23,273 540 0.468 10,841 -1,159

10 13,000 24,125 23,555 514 0.697 16,591 3,591

11 32,000 24,248 532 1.157 27,845 -4,155

12 41,000 24,772 531 1.666 41,284 284

13 11969 0.473

14 17624 0.682

15 30930 1.173

16 44778 1.665

1.25 X MAD

= 1846.34959

Estimate using Trend Corrected Exponential SmoothingForecast

Standard Deviation =

Tracking signal is within range as well as standard deviation.


18/19

Absolute Error

At

Mean Squared Error

MSEtMADt %Error MAPEt TSt

951 903,519 951 11.88 11.88 1.00

234 479,131 592 1.80 6.84 2.00

269 343,599 485 1.17 4.95 3.00

103 260,343 389 0.30 3.79 3.47

242 219,996 360 2.42 3.52 3.08

3391 2,099,992 865 18.84 6.07 -2.64

2983 3,070,760 1167 12.97 7.05 0.60

364 2,703,466 1067 0.96 6.29 0.32

1159 2,552,289 1077 9.66 6.67 -0.76

3591 3,586,376 1329 27.62 8.76 2.08

4155 4,829,951 1586 12.99 9.15 -0.87

284 4,434,173 1477 0.69 8.44 -0.75

ethod


19/19

ComparisonForecasting Method MAD MAPE TS Range

Moving Average 9,719 49.00 -1.52 to 2.21

Simple Exponential Smoothing 10,208 59.00 -1.38 to 2.15

Holt's Model 8,836 52.00 -2.15 to 2.00

Winter's Model 1,477 8.44 -2.64 to 3.47

So, Winter's model is most suitable.

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Tahoe Salt