forecasting 3 statictrendseason (1)

8/13/2019 Forecasting 3 StaticTrendSeason (1)

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Trend and Seasonality; Static 1Ardavan Asef-Vazir i

Chapter 7

Demand Forecasting

in a Supply Chain

Forecasting -3

Static Trend and Seasonality

Ardavan Asef-Vaziri

Based on Supply Chain Management

Chopra and Meindl


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Characteristics of Forecasts

Forecasts are rarely perfectbecause of

randomness.

Beside the average, we also need a measure ofvariationsStandard deviation.

Forecasts are more accurate for groups of items

than forindividuals.

Forecast accuracy decreasesas time horizon

increases.


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Forecasting Methods Qualitative: primarily subjective; rely on judgment and

opinion

Time Series: use historical demand only

Static

Adaptive

Causal: use the relationship between demand and some

other factor to develop forecast Simulation

Imitate consumer choices that give rise to demand

Can combine time series and causal methods


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Components of an Observation

Observed demand (O) =

Systematic component (S) + Random component (R)

Level(current deseasonalized demand)

Trend(growth or decline in demand)

Seasonali ty(predictable seasonal fluctuation)

Systematic component: Expected value of demandRandom component: The part of the forecast that deviates

from the systematic component


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Example: Tahoe Salt

Year Quarter Dema nd

2000 2 8000

2000 3 13000

2000 4 23000

2001 1 34000

2001 2 10000

2001 3 18000

2001 4 23000

2002 1 38000

2002 2 12000

2002 3 13000

2002 4 32000

2003 1 41000

Forecast demand for the next fou r quarters.

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 1 2 3 4 5 6 7 8 9 10 11 12 13


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Static Methods

Systematic component = (level + trend)(seasonal factor)

Ft+l= [L + (t + l)T]St+l

= forecast in period tfor demand in period t + l

L = estimate of level for period 0

T= estimate of trend

St= estimate of seasonal factor for period t

Dt= actual demand in period t

Ft

= forecast of demand in period t


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Static Methods

Estimating level and trend

Estimating seasonal factors


8/20Trend and Seasonality; Static 8Ardavan Asef-Vazir i

Estimating Level and Trend

Before estimating level and trend, demand data

must be deseasonalized

Deseasonalized demand = demand that would

have been observed in the absence of seasonal

fluctuations

Periodicity (p) the number of periods after which the seasonal cycle

repeats itself

for demand at Tahoe Salt p= 4



Seasonalized Time Series; Odd p

W D Y1 M 16.2

T 12.2

W 14.2

R 17.3

F 22.5

2 M 17.3

T 11.5

W 15.0R 17.6

F 23.5

3 M 14.6

T 13.1

W 13.0

R 16.9

F 21.9

4 M 16.1

T 11.8W 12.9

R 16.6

F 24.3

Y

0.0

5.0

10.0

15.0

20.0

25.0

30.0

1 3 5 7 9 11 13 15 17 19

Y

W D Y1 M 16.2

T 12.2

W 14.2 =(D3+D4+D5+D6+D7)/5

R 17.3

F 22.5

2 M 17.3

T 11.5

W 15

R 17.6F 23.5

3 M 14.6

T 13.1

W 13

R 16.9

F 21.9

4 M 16.1

T 11.8W 12.9

R 16.6

F 24.3



Seasonality Indices; Odd p

W D Y1 M 16.2

T 12.2

W 14.2 =(D3+D4+D5+D6+D7)/5

R 1 7.3 =(D4+D5+D6+D7+D8)/5

F 2 2.5 =(D5+D6+D7+D8+D9)/5

2 M 17.3 =(D6+D7+D8+D9+D10)/5

T 11.5 =(D7+D8+D9+D10+D11)/5

W 15 =(D8+D9+D10+D11+D12)/5

R 17.6 =(D9+D10+D11+D12+D13)/5

F 23.5 =(D10+D11+D12+D13+D14)/5

3 M 14.6 =(D11+D12+D13+D14+D15)/5

T 13.1 =(D12+D13+D14+D15+D16)/5

W 13 =(D13+D14+D15+D16+D17)/5

R 16.9 =(D14+D15+D16+D17+D18)/5

F 21.9 =(D15+D16+D17+D18+D19)/5

4 M 16.1 =(D16+D17+D18+D19+D20)/5

T 11.8 =(D17+D18+D19+D20+D21)/5W 12.9 =(D18+D19+D20+D21+D22)/5

R 16.6

F 24.3

W D Y

1 M 1 6.2

T 12.2

W 14.2 16.48

R 17.3 16.7

F 22.5 16.56

2 M 17.3 16.72

T 11.5 16.78

W 15.0 16.98

R 17.6 16.44F 23.5 16.76

3 M 14.6 16.36

T 13.1 16.22

W 13.0 15.9

R 16.9 16.2

F 21.9 15.94

4 M 16.1 15.92

T 11.8 15.86

W 12.9 16.34

R 16.6

F 24.3

W 14.2 16.48

R 17.3 16.7

F 22.5 16.56

M 17.3 16.72

T 11.5 16.78

W 15.0 16.98

R 17.6 16.44F 23.5 16.76

M 14.6 16.36

T 13.1 16.22

W 13.0 15.9

R 16.9 16.2

F 21.9 15.94

M 16.1 15.92

T 11.8 15.86W 12.9 16.34

1. In front of each number I have an average.

2. Averages do not contain seasonality. They are seasonality free data.

3. I can compare each day with the average of the 5 closest days and find the

seasonality of that day



Seasonality Indices; Even p

(8000+13000+23000+34000)/4 =1950But put it where(13000+23000+34000+10000)/4=20000But put it where

Year Quarter Dema nd

2000 2 8000

2000 3 13000

2000 4 23000

2001 1 34000

2001 2 10000

2001 3 18000

2001 4 230002002 1 38000

2002 2 12000

2002 3 13000

2002 4 32000

2003 1 41000



Seasonalized Time Series; Even p

Q12 1 8000

Q13 2 13000

Q14 3 23000

Q21 4 34000

Q13 2 13000

Q14 3 23000

Q21 4 34000

Q22 5 10000

Q14 3 23000

Q21 4 34000

Q22 5 10000

Q23 6 18000

Q21 4 34000

Q22 5 10000

Q23 6 18000

Q24 7 23000

=(C1+C2+C3+C4)/4

=(C2+C3+C4+C5)/4

=(C3+C4+C5+C6)/4

=(C4+C5+C6+C7)/4

Q12 1 8000

Q13 2 13000

Q14 3 23000

Q21 4 34000

Q22 5 10000Q23 6 18000

Q24 7 23000

Q31 8 38000

Q32 9 12000

Q33 10 13000

Q34 11 32000

Q41 12 41000

=(C1+C2+C3+C4)/4

=(C2+C3+C4+C5)/4

=(C3+C4+C5+C6)/4

=(C4+C5+C6+C7)/4=(C5+C6+C7+C8)/4

=(C6+C7+C8+C9)/4

=(C7+C8+C9+C10)/4

=(C8+C9+C10+C11)/4

=(C9+C10+C11+C12)/4

=(C1+2*(C2+C3+C4)+C5)/8

=(C2+2*(C3+C4+C5)+C6)/8

=(C3+2*(C4+C5+C6)+C7)/8

=(C4+2*(C5+C6+C7)+C8)/8

=(C5+2*(C6+C7+C8)+C9)/8

=(C6+2*(C7+C8+C9)+C10)/8

=(C7+2*(C8+C9+C10)+C11)/8

=(C8+2*(C9+C10+C11)+C12)/8



Seasonalized Time Series; Even p

Q12 1 8000

Q13 2 13000

Q14 3 23000 =(C1+2*(C2+C3+C4)+C5)/8

Q21 4 34000 =(C2+2*(C3+C4+C5)+C6)/8

Q22 5 10000 =(C3+2*(C4+C5+C6)+C7)/8

Q23 6 18000 =(C4+2*(C5+C6+C7)+C8)/8

Q24 7 23000 =(C5+2*(C6+C7+C8)+C9)/8

Q31 8 38000 =(C6+2*(C7+C8+C9)+C10)/8

Q32 9 12000 =(C7+2*(C8+C9+C10)+C11)/8

Q33 10 13000 =(C8+2*(C9+C10+C11)+C12)/8

Q34 11 32000

Q41 12 41000

19750

20625

21250

21750

22500

22125

22625

24125



Deseasonalizing Demand

pDDDDEvenisp

pDDOddisp

Dpt

pti

iptptt

pt

pti

it

2/)](2[

/)(

1)2/(

1)2/(

2/2/

2/

2/

For the example, p = 4 is even. For t = 3:

D3 = {D1 + D5 + 2Sum(i=2 to 4) [Di]}/8={8000+10000+2(13000+23000)+34000)}/8 = 19750

D4 = {D2 + D6 + 2Sum(i=3 to 5) [Di]}/8

={13000+18000+2(23000+34000)+10000)}/8 = 20625



Deseasonalizing Demand

Then include trend

Dt= L + tT

where Dt= deseasonalized demand in period t

L = level (deseasonalized demand at period 0)

T = trend (rate of growth of deseasonalized demand)

Trend is determined by linear regression using deseasonalized

demand as the dependent variable and period as the independent

variable (can be done in Excel)



Linear Regression on the Deseasonalized Demand

3 19750

4 20625

5 212506 21750

7 22500

8 221259 22625

10 24125

Data/Data Analysis/Regression



Liner Regression

L = 18,439 and T = 523.81Ft = 18,439 + 523.81 t

Replace t with 1,2, 3, .., 12

05000

1000015000200002500030000350004000045000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Period

Dt

Dt-bar



Final Estimation of the Seasonal Factors

Use the previous equation to calculate

deseasonalized demand for each period

St= Dt/ Dt = seasonal factor for period t

In the example,

D2= 18439 + (524)(2) = 19487 D2= 13000

S2= 13000/19487 = 0.67

The seasonal factors for the other periods are

calculated in the same manner



Final Estimation of the Seasonal Factors

t Dt Re gDe sDe ms

Q12 1 8000 18963

Q13 2 13000 19487

Q14 3 23000 20010Q21 4 34000 20534

Q22 5 10000 21058

Q23 6 18000 21582

Q24 7 23000 22106

Q31 8 38000 22629

Q32 9 12000 23153

Q33 10 13000 23677

Q34 11 32000 24201

Q41 12 41000 24725

Seas

0.42

0.67

1.151.66

0.47

0.83

1.04

1.68

0.52

0.55

1.32

1.66

SeasIndx

0.47

0.68

1.171.66

0.47

0.68

1.17

1.66

0.47

0.68

1.17

1.66

Q1 1.66

Q2 0.47

Q3 0.68

Q4 1.17


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forecasting 3 statictrendseason (1)

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