1. Forecasting A. A. Elimam
The presentation covers the quantitative material in Chapter 10 - Forecasting. The graphic is from Figure 10.1 on the components of demand.. 1

2. Components of Demand Quantity Time
(a) Average: Data cluster about a horizontal line. 3

3. Components of Demand Quantity Time
(b) Linear trend: Data consistently increase or decrease. 4

4. Components of Demand Year 1 Quantity | | | | | | | | | | | | Months
| | | | | | | | | | | |
J F M A M J J A S O N D
Months
(c) Seasonal influence: Data consistently show peaks and valleys.
Year 1
This slide and the next automatically build the two years of data for this example, reinforcing the longitudinal nature of the data collection. 5

5. Components of Demand Year 1 Quantity Year 2 | | | | | | | | | | | |
| | | | | | | | | | | |
J F M A M J J A S O N D
Months
(c) Seasonal influence: Data consistently show peaks and valleys.
Year 1
Year 2 6

6. Components of Demand Quantity | | | | | | Years
| | | | | |
Years
(d) Cyclical movements: Gradual changes over extended periods of time. 7

7. Forecasting Elements: Time Horizon
Short-range:
immediate future - 3 months
Medium-range:
several months to a year
Long range:
More than one year

8. Forecasting Applications: Examples
Short-range:
Weekly staffing
Medium-range:
Production Planning
Long range:
Plant Capacity

9. (A):The Forecasting Process
1. Identify the
purpose of forecast
2. Collect historical
data
3. Plot data and
identify patterns
4. Select a forecast
model
(A):The Forecasting Process
5. Develop/compute
forecast
6. Check forecast
accuracy

10. (B): The Forecasting Process
8b. Select new
forecast model
7. Is
accuracy
acceptable?
8a. Forecast
over planning horizon
9. Adjust forecast
(B): The Forecasting Process
10. Monitor results
and measure accuracy

11. Data Patterns Flat Average: Up and Down Trend: Gradual up or down
Seasonal Pattern: periodic, oscillating & repetitive
Cyclic: Undulating, repetitive movement up and down

12. Causal Methods Linear Regression
Dependent variable
Independent variable X Y
Actual
value
of Y
Estimate of
Y from
regression
equation
Value of X used
to estimate Y
Regression
equation:
Y = a + bX
This slide advances automatically. 12

13. Causal Methods Linear Regression
Dependent variable
Independent variable X Y
Actual
value
of Y
Estimate of
Y from
regression
equation
Value of X used
to estimate Y
Deviation,
or error {
Regression
equation:
Y = a + bX
And clearly illustrates the frequent difference between estimates and actual values. 13

14. Causal Methods Linear Regression
Sales Advertising
Month (000 units) (000 $)
a = Y - bX
b =
XY - nXY
X 2 - nX 2
These are the two equations we will use to compute values for a and b. 15

15. Causal Methods Linear Regression
a = Y - bX
b =
XY - nXY
X 2 - nX 2
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2
Total
Y = 171 X = 1.64 17

16. Causal Methods Linear Regression
a = Y - bX
b =
(1.64)(171)
(1.64)2
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2
Total
Y = 171 X = 1.64
Substituting in the equations, we will obtain the value for b first. This slide advances automatically. 18

17. Causal Methods Linear Regression
a = Y - bX
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2
Total
Y = 171 X = 1.64 19

18. Causal Methods Linear Regression
b =
Sales, Y Advertising,
Month (000 units) (000 $) XY X 2
Total
Y = 171 X = 1.64
Substituting in for a, we solve this equation as well. This slide advances automatically. 20

19. Causal Methods Linear Regression
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2
Total
Y = 171 X = 1.64
Y = (X)
We now have the full model of the relationship between advertising expenditure and sales. 22

20. Causal Methods Linear Regression
300 —
250 —
200 —
150 —
100 — 50
a =
b =
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
Y = (X)
Sales (000s)
| | | |
Advertising (000s) 24

21. Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2
Total
Y = 171 X = 1.64
r = r 2 = YX = 15.61
We can also compute r2 and , other useful measures of model accuracy. The coefficient of determination, r2, is especially useful as it directly shows the amount of the change in the dependent variable explained by changes in the independent variable. 28

22. Causal Methods Linear Regression
Sales, Y Advertising, X
Month (000 units) (000 $) XY X 2 Y 2
,696
,456
,225
,201
,681
Total ,259
Y = 171 X = 1.64
r = r 2 = YX = 15.61
Forecast for Month 6:
Advertising expenditure = $1750
Y = or 183,015 hinges 30

23. Time Series Methods Simple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient arrivals
| | | | | |
Actual patient
arrivals
We now move on to time series forecasting where there is no assumption of causality between the variables. Of course, time series is simply replacing unknown (or too difficult to gather) independent variables with the surrogate of time.
Week 31

24. Time Series Methods Simple Moving Averages
Actual patient
arrivals
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
Patient
Week Arrivals
1 400
2 380
3 411
For a three period moving average, we use the actual values from the first three periods. 33

25. Time Series Methods Simple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient
Week Arrivals
1 400
2 380
3 411
Patient arrivals 3
F4 =
Substituting the values in the equation.
Actual patient
arrivals
| | | | | |
Week 34

26. Time Series Methods Simple Moving Averages
Actual patient
arrivals
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
Patient
Week Arrivals
1 400
2 380
3 411
F4 =
We find the value of A3 (which in this terminology is also F4). 35

27. Time Series Methods Simple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient
Week Arrivals
1 400
2 380
3 411
Patient arrivals
And we plot this point on the graph.
F4 =
Actual patient
arrivals
| | | | | |
Week 36

28. Time Series Methods Simple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient
Week Arrivals
2 380
3 411
4 415
Patient arrivals 3
F5 =
We will do the same for the next three data points.
Actual patient
arrivals
| | | | | |
Week 37

29. Time Series Methods Simple Moving Averages
Actual patient
arrivals
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
Patient
Week Arrivals
2 380
3 411
4 415
F5 =
And plot that point as well. 38

30. Time Series Methods Simple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
Actual patient
arrivals
3-week MA
forecast
If we did this for all the data we have, we would have this graph of the 3-week moving average forecast. 39

31. Time Series Methods Simple Moving Averages
450 —
430 —
410 —
390 —
370 —
Patient arrivals
| | | | | |
Actual patient
arrivals
3-week MA
forecast
6-week MA
If we did the same for a 6-week moving average, we would develop this graph. Obviously, the longer the averaging period, the slower the forecast will be to react to changes in demand resulting in a ‘smoother’ forecast.
Week 40

32. Time Series Methods Weighted Moving Average
450 —
430 —
410 —
390 —
370 —
Patient arrivals
| | | | | |
Actual patient
arrivals
3-week MA
forecast
6-week MA
Weighted Moving Average
Assigned weights
t 0.70 t t
We can also use a variation of the moving average technique where different weights are assigned to the data to emphasize more recent data.
Week 41

33. Time Series Methods Weighted Moving Average
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
Actual patient
arrivals
3-week MA
forecast
6-week MA
Weighted Moving Average
Assigned weights
t 0.70 t t
F4 = 0.70(411) (380) +
0.10(400)
After the calculations. 42

34. Time Series Methods Weighted Moving Average
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
Actual patient
arrivals
3-week MA
forecast
6-week MA
Weighted Moving Average
Assigned weights
t 0.70 t t
F4 =
We will plot the data. 43

35. Time Series Methods Weighted Moving Average
450 —
430 —
410 —
390 —
370 —
6-week MA
forecast
3-week MA
forecast
Weighted Moving Average
Assigned weights
t 0.70 t t
Patient arrivals
F4 = F5 =
Actual patient
arrivals
| | | | | |
Week 44

36. Time Series Methods Weighted Moving Average
450 —
430 —
410 —
390 —
370 —
6-week MA
forecast
3-week MA
forecast
Weighted Moving Average
Assigned weights
t 0.70 t t
Patient arrivals
F4 = F5 =
Notice that for these two points, the graph will be quite different than for either of the simple moving average forecasts. By emphasising the more recent data, the forecast will be much more responsive.
Actual patient
arrivals
| | | | | |
Week 45

37. Time Series Methods Exponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
 = 0.10
Ft = Ft - 1 +(Dt-1 - Ft - 1 )
Patient arrivals
Exponential smoothing is another technique that will result in a ‘smoothed’ forecast. This is not the most common expression of the exponential smoothing equation, but is used here because it makes the transition to the trend-adjusted equation easier.
| | | | | |
Week 46

38. Exponential Smoothing
Ft = Ft-1 +  ( Dt-1 - Ft-1 )
Ft = the forecast for next period
Dt-1 = actual demand for present period
Ft-1 = forecast for period t
 = weighting factor - smoothing constant

39. Time Series Methods Exponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
 = 0.10
F4 = ( )
Ft - 1 = ( )/2
D3 = 411
Ft = Ft - 1 +(Dt-1 - Ft - 1 )
Patient arrivals
Substituting in the basic equation.
| | | | | |
Week 47

40. Time Series Methods Exponential Smoothing
450 —
430 —
410 —
390 —
370 —
F4 = ( )
Ft - 1 = ( )/2
D3 = 411
Ft = Ft - 1 +(Dt-1 - Ft - 1 )
Patient arrivals
We can calculate and plot the first point (in this case, for Week 4).
F4 =
| | | | | |
Week 48

41. Time Series Methods Exponential Smoothing
450 —
430 —
410 —
390 —
370 —
Exponential Smoothing
 = 0.10b
Ft = Ft - 1 +(Dt-1 - Ft - 1 )
Patient arrivals
F4 = 392.1
D4 = 415
We do this again for the following week.
F4 = F5 = 394.4
| | | | | |
Week 49

42. Time Series Methods Exponential Smoothing
450 —
430 —
410 —
390 —
370 —
Patient arrivals
Week
| | | | | |
This graph is not shown in the text, but using the original data from the problem (as derived from Figure 10.4) and applying the exponential smoothing model to the entire data set, this is the graph that would result. Clearly this smooths more than even the 6 period moving average. It is important to emphasize that such ‘smoothing’ techniques must be used only when a smoothed forecast is viable for an organization. For example, this technique may be viable for a manufacturing organization that can inventory items. 50

43. Time Series Methods Linear Regression Analysis
| | | | | | | | | | | | | | |
80 —
70 —
60 —
50 —
40 —
30 —
Patient arrivals
Week
Yn = a + bXn
where
Xn = Weekn
Though not covered in the text, regression analysis can also be used in a time series analysis and is especially valuable when there is a strong trend component. The form of the basic linear equation is the same as in the door hinge example earlier in the presentation, but now the independent variable is time and we are no longer assuming causality. 58

44. Time Series Methods Linear Regression Analysis
| | | | | | | | | | | | | | |
80 —
70 —
60 —
50 —
40 —
30 —
Patient arrivals
Week
Yn = a + bXn
where
Xn = Weekn
Substituting in the values from the CMOM printout on page 476, we can calculate the values for a and b (an exercise left for the student) and plot the resulting function, which will look like this slide. 59

45. Time Series Methods Seasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
Total
Average
Seasonal Index =
Actual Demand
Average Demand
This slide presents the data and the various totals. 61

46. Time Series Methods Seasonal Influences
Quarter Year 1 Year 2 Year 3 Year 4
1 45/250 =
Total
Average
Seasonal Index = = 0.18 45
250
We place the index in the data set (along with the complete calculation to replicate Example 10.6 on page 478). 63

47. Time Series Methods Seasonal Influences
Quarter Year Year Year Year 4
1 45/250 = /300 = /450 = /550 = 0.18
2 335/250 = /300 = /450 = /550 = 1.32
3 520/250 = /300 = /450 = /550 = 2.11
4 100/250 = /300 = /450 = /550 = 0.39
Quarter Average Seasonal Index
1 ( )/4 = 0.20
2 ( )/4 = 1.30
3 ( )/4 = 2.00
4 ( )/4 = 0.50
This is the complete set of indices. 66

48. Time Series Methods Seasonal Influences
Quarter Year Year Year Year 4
1 45/250 = /300 = /450 = /550 = 0.18
2 335/250 = /300 = /450 = /550 = 1.32
3 520/250 = /300 = /450 = /550 = 2.11
4 100/250 = /300 = /450 = /550 = 0.39
Quarter Average Seasonal Index Forecast
1 ( )/4 = 0.20
2 ( )/4 = 1.30
3 ( )/4 = 2.00
4 ( )/4 = 0.50
Projected Annual Demand = 2600
Average Quarterly Demand = 2600/4 = 650
To use these for a forecast, we need to estimate the average quarterly demand, in this case by dividing the annual estimate by four. 67

49. Time Series Methods Seasonal Influences
Quarter Year Year Year Year 4
1 45/250 = /300 = /450 = /550 = 0.18
2 335/250 = /300 = /450 = /550 = 1.32
3 520/250 = /300 = /450 = /550 = 2.11
4 100/250 = /300 = /450 = /550 = 0.39
Quarter Average Seasonal Index Forecast
1 ( )/4 = (0.20) = 130
2 ( )/4 = 1.30
3 ( )/4 = 2.00
4 ( )/4 = 0.50
Projected Annual Demand = 2600
Average Quarterly Demand = 2600/4 = 650
Substituting the average seasonal value and index in the equation, we find the seasonal forecast for quarter 1. 68

50. Time Series Methods Seasonal Influences
Quarter Year Year Year Year 4
1 45/250 = /300 = /450 = /550 = 0.18
2 335/250 = /300 = /450 = /550 = 1.32
3 520/250 = /300 = /450 = /550 = 2.11
4 100/250 = /300 = /450 = /550 = 0.39
Quarter Average Seasonal Index Forecast
1 ( )/4 = (0.20) = 130
2 ( )/4 = (1.30) = 845
3 ( )/4 = (2.00) = 1300
4 ( )/4 = (0.50) = 325
This slide completes the calculations. 69

51. Choosing a Method Forecast Error
Measures of Forecast Error
Et = Dt - Ft
Bias
CFE = Et
Mean Square Error
MSE =  = MSE
Five basic types of error terms are introduced.
Et2 n 74

52. Choosing a Method Forecast Error
Measures of Forecast Error
Et = Dt - Ft
Mean Absolute Deviation
MAD =
Mean Absolute Percent Error
MAPE =
|Et | n
Five basic types of error terms are introduced.
[ |Et | (100) ] / Dt n 74

53. Selecting a Forecast Error Measurement
Bias: When Consistently over or under- forecasting.
MSE: To avoid canceling out (+ve and -ve) Error.
Penalizes large Errors
MAD: To avoid canceling out (+ve and -ve) without
Penalizing large Errors
MAPE: To consider error relative to the order of
magnitude of forecast value
Five basic types of error terms are introduced. 74

54. Choosing a Method Forecast Error
Absolute
Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error,
t Dt Ft Et Et |Et| (|Et|/Dt)(100) %
Total %
This data set is quite busy, but it duplicates the data in Example 10.7. 75

55. Choosing a Method Forecast Error
Absolute
Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error,
t Dt Ft Et Et |Et| (|Et|/Dt)(100) %
Total %
MSE = = 659.4
5275 8
CFE = - 15
Measures of Error
MAD = = 24.4
195
MAPE = = 10.2%
81.3%
The true benefit of any of these error terms lies more in the comparison of alternative techniques (or coefficients) than in the analysis of any single application. However, it can be quickly seen that this forecast has an average percent error of a little over ten. At an absolute level, an organization may make a decision on this factor alone. 81

56. 模型比較的標準 MAPE (Mean Absolute Percentage Error) ：
RMSPE (Root Mean Square Percentage Error) ：
評估準則
<10%
10%~20%
20%~50%
>50%
預測能力
高精確度 良好 合理
不正確

57. 總生育率的預測值比較