Lecture Notes for Week 7
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Transcript Lecture Notes for Week 7
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:
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
i1 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:
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