1. 3. Forecasting
Homework problems: 2,4,5,6,7,11,12,14.

2. 3.1. Providing Appropriate Forecast Information
The forecasting process involves much more than just the estimation of future demand. The forecast also needs to take into consideration the intended use of the forecast, the methodology for aggregating and disaggregating the forecast, and assumptions about future conditions.
Selection of an appropriate forecast method is determined by different levels of aggregation, cost of data acquisition and processing, length of forecast (timeframe), top management involvement, forecast frequency, etc.
Figure 3.1

3. 3.1. Forecast Information
The forecast information and technique must match the intended application:
For strategic decisions such as capacity or market expansion highly aggregated estimates of general trends are necessary.
Sales and operations planning (SOP) activities require more detailed forecasts in terms of product families and time periods.
Master production scheduling (MPS) and control demand highly detailed forecasts, which only need to cover a short period of time.

4. 3.1.1 Forecasting for Strategic Business Planning
Forecast is presented in general terms (sales dollars, tons, hours)
Aggregation level may be related to broad indicators (gross national product (GNP), income)
Causal models and regression/correlation analysis are typical tools
Managerial insight is critical and top management involvement is intense
Forecast is generally prepared annually and covers a period of years

5. 3.1.2 Forecasting for Sales and Operations Planning
Forecast is presented in aggregate measures (dollars, units)
Aggregation level is related to product families (common family measurement)
Forecast is typically generated by summing forecasts for individual products.
Managerial involvement is moderate, and limited to adjustment of aggregate values
Forecast is generally prepared several times each year and covers a period of several months to a year.

6. 3.1.3 Forecasting for MPS and Control
Forecast is presented in terms of individual products (units, not dollars)
Forecast is typically generated by mathematical procedures, often using software
Projection techniques are common
Assumption is that the past is a valid predictor of the future
Managerial involvement is minimal.
Forecast is updated almost constantly and covers a period of days or weeks.

7. 3.2. Regression Analysis & Decomposition
Regression identifies a relationship between two or more correlated variables.
Linear regression is a special case where the relationship is defined by a straight line, used for both time series and causal forecasting.
Data should be plotted to see if they appear linear before using linear regression.
Y = a + bX
Y is value of dependent variable, a is the y-intercept of the line, b is the slope, and X is the value of the independent variable.

8. 3.2 Least Squares Method
Objective–find the line that minimizes the sum of the squares of the vertical distance between each data point and the line
Y – calculated dependent variable value
yi – actual dependent variable point
a – y intercept
b – slope of the line
x – time period
Y = a + bx
See Fig. 3.2

9. Least Squares Regression Line (Fig.3.2)
Regression errors are the vertical distance from the point to the line

10. Least Squares Equation (3.3)Or

11. Least Squares Example (Fig. 3.3)
Quarter (x)
Sales (y) xy x2 y2 Y 1
600
360,000
801.3 2
1,550
3,100 4
2,402,500
1,160.9 3
1,500
4,500 9
2,250,000
1,520.5
6,000 16
1,880.1 5
2,400
12,000 25
5,760,000
2,239.7 6
18,600 36
9,610,000
2,599.4 7
2,600
18,200 49
6,760,000
2,959.0 8
2,900
23,200 64
8,410,000
3,318.6
3,800
34,200 81
14,440,000
3,678.2 10
45,000
100
20,250,000
4,037.8 11
4,000
44,000
121
16,000,000
4,397.4 12
4,900
58,800
144
24,010,000
4,757.1
Sum 78
33,350
268,200
650
112,502,500

12. Least Squares Example (Fig. 3.2)

13. Least Squares Example Quarter Calculation Forecast 13
Y13= (13)
5,119.4 14
Y14= (14)
5,476.0 15
Y15= (15)
5,835.6 16
Y16= (16)
6,195.2
Standard Error of Estimate (Syx) – how well the line fits the data
=363.9

14. Regression Using Excel

15. Time Series Decomposition
A time series can consist of one or more components of demand
Trend–the long term growth (or decrease) of demand
Seasonal–Changes in demand associated with portions of the year (may be additive or multiplicative)
Cyclical–repetitive patterns not associated with seasonal demand
Autocorrelation–changes in demand associated with previous demand levels
Random–changes in demand that can’t be linked to a specific cause

16. Seasonality
Seasonality may or may not be relative to the general demand trend
Additive seasonal variation is constant regardless of changes in average demand
Multiplicative seasonal variation maintains a consistent relationship to the average demand (this is the more common case)

17. Seasonality
Additive seasonal variation is constant regardless of changes in average demand
Forecast=Trend + Seasonal
Multiplicative seasonal variation maintains a consistent relationship to the average demand (this is the more common case)
Forecast= Trend x Seasonal factors

18. Seasonal Factor/Index
To account for seasonality within the forecast, the seasonal factor/index is calculated.
The amount of correction needed in a time series to adjust for the season of the year
Season
Past Sales
Average Sales for Each Season
Seasonal Factor
Spring
200
1000/4=250
Actual/Average=200/250=0.8
Summer
350
350/250=1.4
Fall
300
300/250=1.2
Winter
150
150/250=0.6
Total
1000

19. Seasonal Factor/Index
If we expect (forecast) next year’s sales to be 1,100 units, the seasonal forecast is calculated using the seasonal factors:
Season
ExpectedSales
Average Sales for Each Season
Seasonal Factor
Forecast
Spring
1100/4=275 X
0.8 =
220
Summer
1.4
385
Fall
1.2
330
Winter
0.6
165
Total
1,100

20. Seasonality–Trend and Seasonal Factor
Estimate of trend, use linear regression software to obtain more precise results
Quarter
Amount
I – 2008
300
II – 2008
200
III – 2008
220
IV – 2008
530
I – 2009
520
II – 2009
420
III – 2009
400 IV
700
Trend = t

21. Seasonality–Trend and Seasonal Factor
Seasonal factors are calculated for each season, then averaged for similar seasons
Seasonal Factor = Actual/Trend

22. Seasonality–Trend and Seasonal Factor
Forecasts for 2010 are calculated by extending the linear regression and then adjusting by the appropriate seasonal factor
FITS–Forecast Including Trend and Seasonal Factors

23. Decomposition Using Least Squares Regression
Decompose the time series into its components
Find seasonal component
Deseasonalize the demand
Find trend component
Forecast future values for each component
Project trend component into future
Multiply trend component by seasonal component

24. Decomposition Using Least Squares Regression
Period
Quarter
Actual Demand
Average of Same Quarter of Each Year
Seasonal Factor 1 I
600
( )/3=2266.7 2 II
1,550 3
III
1,500 4 IV 5
2,400 6
3,100 7
2,600 8
2,900 9
3,800 10
4,500 11
4,000 12
4,900
Total
33,350
Calculate average of same period values

25. Decomposition Using Least Squares Regression
Period
Quarter
Actual Demand
Average of Same Quarter of Each Year
Seasonal Factor 1 I
600
( )/3=2266.7
2266.7/(33350/12)=0.82 2 II
1,550
( )/3=3050 3
III
1,500
( )/3=2700 4 IV
( )/3=3100 5
2,400 6
3,100 7
2,600 8
2,900 9
3,800 10
4,500 11
4,000 12
4,900
Total
33,350
Calculate seasonal factor for each period

26. Decomposition Using Least Squares Regression
Period
Deseasonalized Demand 1
735.7 2
1412.4 3
1544.0 4
1344.8 5
2942.6 6
2824.7 7
2676.2 8
2599.9 9
4659.2 10
4100.4 11
4117.3 12
4392.9
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 12
ANOVA df SS MS F
Significance F
Regression 1
E-05
Residual 10
Total 11
Coefficients
t Stat
P-value
Intercept
Period
Use linear regression to fit trend line to deseasonalized data
Y= x

27. Create Forecast by Projecting Trend and Reseasonalizing
Period
Quarter
Y from Regression
Seasonal Factor
Forecast 13 I
*13=5003.5 X
0.82 = 14 II
*14=5345.7
1.10 15
III
*15=5687.9
0.97 16 IV
*16=6030.1
1.12
Project Linear Trend
Project Seasonality
Y= x

28. 3.3. Short-term Forecasting Technique
Some basic concepts:
dependent/independent demand
aggregate/disaggregate demand
long-term/short-term forecast (regression and correlation vs. smoothing out the random fluctuations)
The underlying assumption of time series models is that the future values of the time series can be predicted based upon previous time series values (i.e., past conditions that produced the historical data won’t change !)
The need for some forecasting techniques (Fig. 3.11)
What’s wrong with drawing a line (i.e., use the regular averaging process)?

29. 3.3. Short-term Forecasting Techniques
Moving Average:
Q: what n to use? large or small (longer or shorter)?
Q: Drawback of (simple) moving average?
Weighted Moving Average:
Example. Use weighted moving average with weights of 0.1, 0.2, and 0.3 to forecast demand for period 33.
Sol:

30. 3.3. Short-term Forecasting Techniques
Exponential Smoothing Forecasting (ESF):
ESFt = ESFt-1 + α(actual demand t – ESFt-1) …….. (3.6)
=α(actual demand t ) + (1- α) ESFt …….. (3.7)
where:
α= the proportion of the forecast error, under or over estimate, that will be incorporated into (next) forecast (i.e., smoothing constant).
ESFt-1 = Exp. smoothing forecast made at the end of period t-1
= Exp. smoothing forecast for period t

31. 3.3. Short-term Forecasting Techniques
Exponential Smoothing Forecasting (ESF):
Q: Why is it called “exponential” smoothing? Proof
Q: What happens when α=0 or α=1?
Q: what αvalue to use? Small or large and the effects.

32. 3.3. Short-term Forecasting Techniques
Bias = Σ(actual demand i – forecast demand i) /n
Bias (mean error) measures consistently high or low forecast
MAD = Σ|actual demand i – forecast demand i| /n
MSE=
MAD (mean absolute deviation) measures the magnitude of forecast error
What is a good (ideal) forecast?
Which (Bias or MAD) is more critical?
When the forecast errors are normally distributed, the standard deviation of forecast errors = 1.25 MAD

33. 3.3. Some Insights
Focus forecasting: uses the one forecasting model that would have performed the best in the recent past to make the next forecast.
Simple models usually outperform more complex methods, especially for short-term forecasting.
There is no one model that would consistently outperform all the others.
It might be a good idea to average the forecasts from several models used in each period (combination technique).

34. 3.4. Using the Forecasts Aggregating Forecasts:
Long-term or product-line forecasts are more accurate than short-term or detailed forecasts.
Theorem: Suppose that X and Y are independent random variables with normal distribution N(μ1 , σ12 ) and N(μ2 , σ22 ), respectively. Let Z=X + Y, then Z is a normal distribution N(μ1+ μ2 ,σ12 +σ22 ).
Application: Figure 3.17

35. 3.4. Using the Forecasts Pyramid Forecasting:
To coordinate, integrate, and assure (force) consistency between forecasts prepared in different parts/levels of the organization and company goals or constraints. Figs. 18~20.
Incorporating External Information:
Change the forecast directly, if we know the activities that will influence demand for sure. e.g., promotions, product changes, competitor’s action, etc.
Change the forecast model, if we are not sure of the impact of the activities. e.g., use larger α to be more responsive to demand change.