1. Manufacturing Planning and Control
MPC 6th Edition
Chapter 3

2. Forecasting
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.

3. Agenda Forecast information Uses for forecast information
Forecasting techniques
Forecast evaluation
Linkage of planning and forecasting

4. 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 activities require more detailed forecasts in terms of product families and time periods
Master production scheduling and control demand highly detailed forecasts, which only need to cover a short period of time

5. 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, 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

6. 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

7. Forecasting for Master Production Scheduling and Control
Forecast is presented in terms of individual products (units)
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

8. Regression Analysis
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
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

9. Least Squares Method Y = a + bx
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

10. Least Squares Example 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

11. Least Squares Example Quarter Sales 1 600 2 1,550 3 1,500 4 5 2,400 6
3,100 7
2,600 8
2,900 9
3,800 10
4,500 11
4,000 12
4,900

12. Least Squares Regression Line
Regression errors are the vertical distance from the point to the line

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

14. 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

15. 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)

16. Seasonal Factor
To account for seasonality within the forecast, the seasonal factor 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

17. Seasonal Factor
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

18. Seasonality–Trend and Season
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

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

20. Seasonality–Trend and Season
Forecasts are calculated by extending the linear regression and then adjusting by the appropriate seasonal factor
FITS–Forecast Including Trend and Seasonal Factors

21. 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

22. 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

23. 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=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

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
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

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
3050/(33350/12)=1.10 3
III
1,500
( )/3=2700
2700/(33350/12)=0.97 4 IV
( )/3=3100
3100/(33350/12)=1.12 5
2,400
0.82 6
3,100
1.10 7
2,600
0.97 8
2,900
1.12 9
3,800 10
4,500 11
4,000 12
4,900
Total
33,350
Seasonal factors repeat each year

26. Decomposition Using Least Squares Regression
Period
Quarter
Actual Demand
Seasonal Factor
Deseasonalized Demand
(Actual/Seasonal Factor) 1 I
600
0.82
600/0.82=735.7 2 II
1,550
1.10
1550/1.10=1412.4 3
III
1,500
0.97
1500/0.97=1544.0 4 IV
1.12
1500/1.12=1344.8 5
2,400
2942.6 6
3,100
2824.7 7
2,600
2676.2 8
2,900
2599.9 9
3,800
4659.2 10
4,500
4100.4 11
4,000
4117.3 12
4,900
4392.9
Calculate deseasonalized demand for each period

27. Least Squares Regression for Deseasonalized Data
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

28. 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

29. Short-Term Forecasting Techniques
Statistical Forecasting Models
Moving Average–Unweighted average of a given number of past periods is used to forecast the future
Exponential Smoothing–Weighted average of all past periods is used to forecast the future
Both assume that there is an underlying pattern of demand that is consistent over some period of time

30. Moving Average Forecasting
i – period number
t – current period
n - number of periods in moving average (smaller n makes forecast more responsive to recent values

31. Exponential Smoothing Forecasting
α – smoothing constant (0≤α≤1) (higher α makes forecast more responsive to recent values)
t – current period
ESF t-1 – exponential smoothing forecast from previous period

32. Forecast Evaluation Is the forecast too high or too low?
Mean Error (bias)
What is the magnitude of the forecast error?
Mean Absolute Deviation (MAD)
Standard Deviation of forecast error = 1.25*MAD
Measuring both bias and MAD is critical to understanding the quality of the forecast

33. Forecast Evaluation

34. Aggregating Forecasts
The SOP process reconciles differences in forecasts from various sources
Customer/product knowledge
Sum of individual product detailed forecasts (by product family, for example)
SOP result is an aggregate demand forecast
Long-term and/or aggregate forecasts are more accurate than short-term, detailed forecasts

35. Pyramid Forecasting
One means of aggregating and disaggregating forecasts is pyramid forecasting
Ensures consistency as the forecast sources are integrated
Provides a logical framework for summing lower level forecasts and distributing higher level forecast changes to individual products

36. Pyramid Forecasting

37. External Information
Activities or conditions that may invalidate the assumption that history is a good predictor must be accounted for in the forecasting process
Special promotions, product changes, advertising, competitors’ actions
Changes to forecasting process may be needed
Change exponential smoothing parameter to place more (or less) emphasis on recent history
Forecast more frequently to identify conditions that result in higher forecast errors

38. Principles
Forecast models should be as simple as possible. Simple models often outperform more complicated approaches.
Inputs (data) and outputs (forecasts) must be monitored for quality and appropriateness.
Information on the sources of variation (seasonality, market trends, company policies) should be incorporated into the forecasting system.
Forecasts from different sources must be reconciled and made consistent with company plans and constraints.

39. Quiz – Chapter 3
A forecast used for Master Production Scheduling and Control is likely to cover a period of _____________.
Regression analysis where the relationship between variables is a straight line is called _______ _______.
In a time series analysis, time is the _________ variable.
An exponential smoothing forecast considers all past data (T/F).
In an exponential smoothing forecast, a higher level of alpha (α) will place more emphasis on recent history (T/F).
Mean error of a forecast provides information concerning the forecast’s ________.