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Chapter 13
Forecasting
Topics
 Components of Forecasting
 Time Series Methods
 Accuracy of Forecast
 Regression Methods
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:
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Trend
Random variations
Cycles
Seasonal pattern
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
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
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.
Time Series: Techniques
•
•
•
•
•
Moving Average
Weighted Moving Average
Exponential Smoothing
Adjusted Exponential Smoothing
Linear Trend
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:
 Di
MAn  n
n  number of periods in the moving average
D  data in period i
i
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.
Weighted Moving Average
• Weights are assigned to the most recent data.
• Determining precise weights and number of periods
requires trial-and-error experimentation
• Formula:
n
WMAn   W D
i1 i i
W  the weight for period i, between 0% and 100%
i
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
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
Exponential Smoothing: Adjusted
 Exponential smoothing with a trend adjustment factor
added
 Formula: A Ft + 1 = Ft + 1 + Tt+1
where: T = an exponentially smoothed trend factor
Tt + 1 + (Ft + 1 - 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
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
b   xy  n x y
 x2  n x
a  y b x
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
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:
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Mean Absolute deviation (MAD)
Mean absolute percentage deviation (MAPD)
Cumulative error (E bar)
Average error, or bias (E)
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.
 Dt Ft
MAD 
 Formula:
n
 The lower the value of MAD, the more accurate the forecast
 MAD is difficult to assess by itself
 Must have magnitude of the data
Mean Absolute Deviation
 A variation on MAD
 Measures absolute error as a percentage of demand rather
than per period
 Formula:
 Dt  Ft
MAPD 
 Dt
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
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.
Regression Methods
Linear Regression
 Linear regression relates demand (dependent variable ) to
an independent variable.
y  a  bx
a  y bx
b   xy  n x y
2
2
x

n
x

where :
x  nx  mean of the x data
y  ny  mean of the y data
Regression Methods: Correlation
 Measure of the strength of the relationship between
independent and dependent variables
 Formula:
n xy   x y
r



 
2



2
2
2
n

 x    x  n y   y  





 

 Value lies between +1 and -1.
 Value of zero indicates little or no relationship between
variables.
 Values near 1.00 and -1.00 indicate strong linear
relationship.
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.
Multiple Regression
 Multiple regression relates demand to two or more
independent variables.
General form:
y = 0 +  1x1 +  2x2 + . . . +  kxk
where  0 = the intercept
 1 . . .  k = parameters representing
contributions of the independent
variables
x1 . . . xk = independent variables