1. Chapter 13
Forecasting

2. Topics Components of Forecasting Time Series Methods
Accuracy of Forecast
Regression Methods

3. Components of Forecasting
Many forecasting methods are available for use
Depends on the time frame and the patterns
Time Frames:
Short-range (one to two months)
Medium-range (two months to one or two years)
Long-range (more than one or two years)
Patterns:
Trend
Random variations
Cycles
Seasonal pattern

4. Forecasting Components: Patterns
Trend: A long-term movement of the item being forecast
Random variations: movements that are not predictable and follow no pattern
Cycle: A movement, up or down, that repeats itself over a time span
Seasonal pattern: Oscillating movement in demand that occurs periodically and is repetitive

5. Forecasting Components: Forecasting Methods
Times Series (Statistical techniques)
Uses historical data to predict future pattern
Assume that what has occurred in the past will continue to occur in the future
Based on only one factor - time.
Regression Methods
Attempts to develop a mathematical relationship between the item being forecast and the involved factors
Qualitative Methods
Uses judgment, expertise and opinion to make forecasts

6. Forecasting Components: Qualitative Methods
Called jury of executive opinion
Most common type of forecasting method for long-term
Performed by individuals within an organization, whose judgments and opinion are considered valid
Includes functions such as marketing, engineering, purchasing, etc.
Supported by techniques such as the Delphi Method, market research, surveys, etc.

7. Time Series: Techniques
Moving Average
Weighted Moving Average
Exponential Smoothing
Adjusted Exponential Smoothing
Linear Trend

8. Moving Average Uses values from the recent past to develop forecasts
Smoothes out random increases and decreases
Useful for stable items (not possess any trend or seasonal pattern
Formula for:

9. Revisit of 3-Month and 5-Month
Longer-period moving averages react more slowly to changes in demand
Number of periods to use often requires trial-and-error experimentation
Moving average does not react well to changes (trends, seasonal effects, etc.)
Good for short-term forecasting.

10. Weighted Moving Average
Weights are assigned to the most recent data.
Determining precise weights and number of periods requires trial-and-error experimentation
Formula:

11. Exponential Smoothing: Simple Exponential Smoothing
Weights recent past data more strongly
Formula:
Ft + 1 = Dt + (1 - )Ft
where: Ft + 1 = the forecast for the next period
Dt = actual demand in the present period
Ft = the previously determined forecast for the present period
 = a weighting factor (smoothing constant)
Commonly used values of  are between .10 and .50
Determination of  is usually judgmental and subjective

12. Comparing Different Smoothing Constants
Forecast that uses the higher smoothing constant (.50) reacts more strongly to changes in demand
Both forecasts lag behind actual demand
Both forecasts tend to be lower than actual demand
Recommend low smoothing constants for stable data without trend; higher constants for data with trends

13. Exponential Smoothing: Adjusted
Exponential smoothing with a trend adjustment factor added
Formula: A Ft + 1 = Ft Tt+1
where: T = an exponentially smoothed trend factor
Tt (Ft Ft) + (1 - )Tt
Tt = the last period trend factor
 = smoothing constant for trend (between zero and one)
Weights are given to the most recent trend data and determined subjectively
Forecast is higher than the simple exponentially smooth
Useful for increasing trend of the data

14. Linear Trend Line
When demand displays an obvious trend over time, a linear trend line, can be used to forecast
Does not adjust to a change in the trend
Formula: Y= a+ b x

15. Seasonal Adjustments
Seasonal pattern is a repetitive up-and-down movement in demand
Can occur on a monthly, weekly, or daily basis.
Forecast can be developed by multiplying the normal forecast by a seasonal factor
Seasonal factor can be determined by dividing the actual demand for each seasonal period by total annual demand:
lies between zero and one
Si =Di/D

16. Forecast Accuracy Overview
Forecasts will always deviate from actual values
Difference between forecasts and actual values referred to as forecast error
Like forecast error to be as small as possible
If error is large, either technique being used is the wrong one, or parameters need adjusting
Measures of forecast errors:
Mean Absolute deviation (MAD)
Mean absolute percentage deviation (MAPD)
Cumulative error (E bar)
Average error, or bias (E)

17. Forecast Accuracy: Mean Absolute Deviation
MAD is the average absolute difference between the forecast and actual demand.
Most popular and simplest-to-use measures of forecast error.
Formula:
The lower the value of MAD, the more accurate the forecast
MAD is difficult to assess by itself
Must have magnitude of the data

18. Mean Absolute Deviation
A variation on MAD
Measures absolute error as a percentage of demand rather than per period
Formula:

19. Cumulative Error Sum of the forecast errors (E =et).
A large positive value indicates forecast is biased low
A large negative value indicates forecast is biased high
Cumulative error for trend line is always almost zero
Not a good measure for this method

20. Regression Methods Overview
Time series techniques relate a single variable being forecast to time.
Regression is a forecasting technique that measures the relationship of one variable to one or more other variables.
Simplest form of regression is linear regression.

21. Regression Methods Linear Regression
Linear regression relates demand (dependent variable ) to an independent variable.

22. Regression Methods: Correlation
Measure of the strength of the relationship between independent and dependent variables
Formula:
Value lies between +1 and -1.
Value of zero indicates little or no relationship between variables.
Values near 1.00 and indicate strong linear relationship.

23. Regression Methods: Coefficient of Determination
Percentage of the variation in the dependent variable that results from the independent variable.
Computed by squaring the correlation coefficient, r.
If r = .948, r2 = .899
Indicates that 89.9% of the amount of variation in the dependent variable can be attributed to the independent variable, with the remaining 10.1% due to other, unexplained, factors.

24. Multiple Regression
Multiple regression relates demand to two or more independent variables.
General form:
y = 0 +  1x1 +  2x  kxk
where  0 = the intercept
  k = parameters representing contributions of the independent variables
x xk = independent variables