The document discusses three methods for trend projection in demand forecasting: 1) graphic method of fitting a trend line visually to data, 2) least squares method of fitting a trend line algebraically, and 3) smoothing methods such as moving averages that predict values based on averages of past data. It provides examples of applying a three-period and five-period moving average to sample time series data and calculating the root-mean-square error to evaluate forecast accuracy. Finally, it introduces exponential smoothing, which forecasts the next period as a weighted average of the actual current value and previous forecast.

1. DEMAND FORECASTING II

2. 2
TREND PROJECTION METHOD
1. Graphic method (fitting trend line by observation)
2. Algebric (least squares)
3. Smoothing methods
 Moving average method
 Exponential smoothing

3. 3
Time
ValuesofDependentVariable
(I) GRAPHIC METHOD
Random Influences
Cyclical Fluctuation
Secular Trend

4. 4
Time
ValuesofDependentVariable
Actual
observation
GRAPHIC METHOD

5. 5
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Time
ValuesofDependentVariable
Point on
the line
Actual
observation
GRAPHIC METHOD

6. 6
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Deviation
Time
ValuesofDependentVariable
bxaYˆ
Point on
the line
Actual
observation
GRAPHIC METHOD

7. 7
(II) LEAST SQUARES METHOD
• Fitting a trend line to the data
• Constant Rate of Change
St = So + bt
• Where:
– St value of time series to be forecasted for period t
– So estimated value of time series in the base period
– b is the absolute amount of growth per period
– t time period for which series is to be forecasted
S = nSo + b t
S*t = So t + b t2

8. 8
Period
Year (t) Sales (S) S * t t^2
1991 1 300 300 1
1992 2 305 610 4
1993 3 315 945 9
1994 4 340 1360 16
1995 5 346 1730 25
1996 6 352 2112 36
1997 7 364 2548 49
1998 8 390 3120 64
1999 9 397 3573 81
2000 10 404 4040 100
2001 11 418 4598 121
2002 12 445 5340 144
EXAMPLE
Assuming the present trend continues, in which year would you
expect 1992 sales to be doubled?

9. 9
Period
Year (t) Sales (S) S * t t^2
1991 1 300 300 1
1992 2 305 610 4
1993 3 315 945 9
1994 4 340 1360 16
1995 5 346 1730 25
1996 6 352 2112 36
1997 7 364 2548 49
1998 8 390 3120 64
1999 9 397 3573 81
2000 10 404 4040 100
2001 11 418 4598 121
2002 12 445 5340 144
n = 12 78 4376 30276 650
St = So + bt
S = nSo + b t
S*t = So t + b t2
St = 281.39 + 12.81t
SOLUTION
Double of 1992 sales = 610
So t = 25.65
i.e. in 2017

10. 10
(III) SMOOTHING TECHNIQUES
• Predicting values of a time series on the basis of some
average of its past values
• Used when time series exhibit irregular or random variation
– Moving Averages
– Exponential Smoothing

11. 11
Quarter Actual Market 3 Quarter Moving
Share (A) Average(F)
1 20
2 22
3 23
4 24 21.67
5 18 23.00
6 23 21.67
7 19 21.67
8 17 20.00
9 22 19.67
10 23 19.33
11 18 20.67
12 23 21.00
MOVING AVERAGE: EXAMPLE

12. 12
Year Actual Market 3 Quarter Moving A - F (A - F)^2 5
Share (A) Average(F) Av
1 20
2 22 21.67 0.33 0.1089
3 23 23 0 0
4 24 21.67 2.33 5.43
5 18 21.67 -3.67 13.47
6 23 20.00 3.00 9.00
7 19 19.67 -0.67 0.45
8 17 19.33 -2.33 5.43
9 22 20.67 1.33 1.77
10 23 21.00 2.00 4.00
11 18 21.33 -3.33 11.09
12 23
50.63
RMSE 2.05
MOVING AVERAGE

13. 13
Year Actual Market 3 Quarter Moving A - F (A - F)^2 5 Quarter Moving A - F (A - F)^2
Share (A) Average(F) Average(F)
1 20
2 22 21.67 0.33 0.1089
3 23 23 0 0 21.4 1.6 2.56
4 24 21.67 2.33 5.43 22.00 2.00 4.00
5 18 21.67 -3.67 13.47 21.40 -3.40 11.56
6 23 20.00 3.00 9.00 20.20 2.80 7.84
7 19 19.67 -0.67 0.45 19.80 -0.80 0.64
8 17 19.33 -2.33 5.43 20.80 -3.80 14.44
9 22 20.67 1.33 1.77 19.80 2.20 4.84
10 23 21.00 2.00 4.00 20.60 2.40 5.76
11 18 21.33 -3.33 11.09
12 23
50.63 51.64
RMSE 2.05 2.07
MOVING AVERAGE

14. 14
n
FA tt
2
)(
RMSE =
To decide on the better moving average forecast calculate the
root-mean-square error(RMSE) of each forecast and use the
moving average which results in the smallest RMSE

15. 15
EXPONENTIAL SMOOTHING
• Forecast for next period (ie, t) is a weighted average of
the actual value in that period and forecasted values of
the time series in period (t - 1)
0 1w
St = w Y t + (1 – w) S t-1

16. 16
Year Demand (000 units)
1 48
2 42
3 20
4 48
5 38
6 34
7 46
8 50
9 48
10 54
11 40
12 44
Find the exponentially
smoothened time series using
smoothing constant w = 0.1
and w = 0.4

17. 17
Year Demand
(000 units) (A)
Exponentially
Smoothened
values
(w = 0.1)
(f t+1)
A – (Ft +
1)
{A – (Ft + 1)}2
1 48 48
2 42 47.4
3 20 44.66
4 48 45
5 38 44.3
6 34 43.28
7 46 43.56
8 50 44.2
9 48 44.58
10 54 45.52
11 40 44.96
12 44 44.86
Find
RMSE