1. Forecasting
Chapter 15

2. Forecasting Components Time Series Methods Forecast Accuracy
Chapter Topics
Forecasting Components
Time Series Methods
Forecast Accuracy
Regression Methods
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3. Forecasting Components
A variety of forecasting methods are available for use depending on the time frame of the forecast and the existence of 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 Patterns
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4. Time Horizon in Forecasting
Short-term forecasts (days or weeks) are required for inventory management, production plans and resource requirements planning.
Medium-term forecasts (weeks and months) are required for estimating product family sales, resource requirements in aggregate production planning.
Long-term forecasts (Months and years) are required for estimating capacity needs, growth trends in strategic planning.

5. Forecasting Components Patterns (1 of 2)
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 lengthy time span.
Seasonal pattern - Oscillating movement in demand that occurs periodically in the short run and is repetitive.
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6. Forecasting Components Patterns (2 of 2)
Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend w/Season
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7. Forecasting Components Forecasting Methods
Times Series - Statistical techniques that use historical data to predict future behavior.
Regression Methods - Regression (or causal ) methods that attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does.
Qualitative Methods - Methods using judgment, expertise and opinion to make forecasts.
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8. Time Series Methods Overview
Statistical techniques that make use of historical data collected over a long period of time.
Methods assume that what has occurred in the past will continue to occur in the future.
Forecasts based on only one factor - time.
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9. Time-Series Forecasting Moving Averages Exponential Smoothing
Time-Series Methods
Time-Series Forecasting
Moving Averages
Exponential Smoothing
Exponential Smoothing with Trend Adjustment
Trend Projections using regression
Trend Projections with seasonal pattern using regression (will not be covered)
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10. Time Series Methods Moving Average (1 of 5)
Moving average uses values from the recent past to develop forecasts.
This dampens or smoothes random increases and decreases.
Useful for forecasting relatively stable items that do not display any trend or seasonal pattern.
Formula for:
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11. Time Series Methods Moving Average (2 of 5)
Example: Instant Paper Clip Supply Company forecast of orders for the month of November.
Month June July August September October
Order
Three-month moving average:
Five-month moving average:
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12. Time Series Methods Moving Average (3 of 5)
Table Three- and Five-Month Moving Averages
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13. Time Series Methods Moving Average (4 of 5)
Figure Three- and Five-Month Moving Averages
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14. Time Series Methods Moving Average (5 of 5)
Longer-period moving averages react more slowly to changes in demand than do shorter-period moving averages.
The appropriate number of periods to use often requires trial-and-error experimentation.
Disadvantage: Moving average does not react well to changes (trends, seasonal effects, etc.)
Advantage: Easy to use and inexpensive.
Good for short-term forecasting.
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15. Weighted Moving Average
Time Series Methods
Weighted Moving Average
In a weighted moving average, user defined weights are assigned to the most recent data.
Determining precise weights and number of periods requires trial-and-error experimentation.
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16. Exponential Smoothing (1 of 11)
Time Series Methods
Exponential Smoothing (1 of 11)
Exponential smoothing weights recent past data more strongly than more distant data.
Two forms: simple exponential smoothing and adjusted exponential smoothing.
Simple exponential smoothing:
Ft + 1 = Dt + (1 - )Ft or
Ft + 1 = Ft + α (Dt – Ft)
where: Ft + 1 = the forecast for the next period
Dt = actual demand in the present period
Ft = forecasted demand for the present period
 = a weighting factor (smoothing constant).
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17. Exponential Smoothing (2 of 11)
Time Series Methods
Exponential Smoothing (2 of 11)
Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast and the actual value of the series at that point.
The most commonly used values of  are between 0.10 and 0.50.
Determination of  is usually judgmental and subjective and often based on trial-and -error experimentation.
Exponential smoothing is a sophisticated weighted average.
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18. Exponential Smoothing (3 of 11)
Time Series Methods
Exponential Smoothing (3 of 11)
Example: PM Computer Services (see Table 15.4).
Exponential smoothing forecasts using smoothing constant of .30.
Forecast for period 2 (February):
F2 =  D1 + (1- )F1 = (.30)(37) + (.70)(37) = 37 units
Forecast for period 3 (March):
F3 =  D2 + (1- )F2 = (.30)(40) + (.70)(37) = 37.9 units
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19. Exponential Smoothing (4 of 11)
Time Series Methods
Exponential Smoothing (4 of 11)
Table Exponential Smoothing Forecasts,  = .30 and  = .50
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20. Exponential Smoothing (5 of 11)
Time Series Methods
Exponential Smoothing (5 of 11)
The forecasts that use the higher smoothing constant (.50) react more strongly to changes in demand than does the forecast with the lower constant (.30).
But note that both forecasts lag behind actual demand.
Both forecasts tend to be consistently lower than actual demand.
Low smoothing constants are appropriate for stable data without trend; higher smoothing constants are appropriate for data with trends.
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21. Exponential Smoothing (6 of 11)
Time Series Methods
Exponential Smoothing (6 of 11)
Figure Exponential Smoothing Forecasts
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22. Adjusted Exponential Smoothing (7 of 11)
Time Series Methods
Adjusted Exponential Smoothing (7 of 11)
Adjusted exponential smoothing: exponential smoothing with a trend adjustment factor added.
Formula AFt + 1 = Ft Tt+1
where:
T = an exponentially smoothed trend factor
Tt + 1 = (Ft Ft) + (1 - )Tt
Tt = the last period trend factor
 = smoothing constant for trend ( a value between zero and one) is a weight given to the most recent trend data. Determined subjectively.
Notice that this formula for the trend factor reflects a weighted measure of the increase (or decrease) between the current forecast, Ft + 1, and the previous forecast, Ft.

23. Adjusted Exponential Smoothing
The formula for the adjusted exponential smoothing forecast requires an initial value for Tt to start the computational process.
This initial trend factor is most often an estimate determined subjectively or based on past data by the forecaster.
In this case, we will start with the trend, Tt, equal to zero. By the time the forecast value of interest, F13, is computed, we should have a relatively good value for the trend factor.
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24. Exponential Smoothing (8 of 11)
Time Series Methods
Exponential Smoothing (8 of 11)
Example: PM Computer Services exponentially smoothed
forecasts with  = .50 and  = .30 (see Table 15.5 next slide).
Adjusted forecast for period 3:
T3 = (F3 - F2) + (1 - )T2
= (.30)( ) + (.70)(0) = 0.45
AF3 = F3 + T3 = = 38.95

25. Exponential Smoothing (9 of 11)
Time Series Methods
Exponential Smoothing (9 of 11)
Table Adjusted exponentially smoothed forecast values

26. Exponential Smoothing (10 of 11)
Time Series Methods
Exponential Smoothing (10 of 11)
The adjusted forecast is consistently higher than the simple exponentially smoothed forecast.
It is more reflective of the generally increasing trend of the data.

27. Exponential Smoothing (11 of 11)
Time Series Methods
Exponential Smoothing (11 of 11)
Figure Adjusted exponentially smoothed forecast

28. Time Series Methods Linear Trend Line (1 of 5)
When demand displays an obvious trend over time, a least squares regression method, can be used to forecast the demand. The slope of the line (b) shows the amount by which y increases when x increases by 1 unit. Formula:
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29. Time Series Methods Linear Trend Line (2 of 5)
Example: PM Computer Services (see Table 15.6)
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30. Least Squares Calculations
Time Series Methods
Linear Trend Line (3 of 5)
Table 15.6
Least Squares Calculations
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31. Time Series Methods Linear Trend (5 of 5)
Figure Linear Trend Line
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32. Forecast Accuracy Overview
Forecasts will always deviate from actual values.
Difference between forecasts and actual values referred to as forecast error.
We would 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=∑et
Average error, or bias (E)/n
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33. Mean Absolute Deviation (1 of 7)
Forecast Accuracy
Mean Absolute Deviation (1 of 7)
MAD is the average absolute difference between the forecast and actual demand.
Most popular and simplest-to-use measures of forecast error.
Formula:
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34. Mean Absolute Deviation (2 of 7)
Forecast Accuracy
Mean Absolute Deviation (2 of 7)
Example: PM Computer Services (see Table 15.8).
Compare accuracies of different forecasts using MAD:
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35. Mean Absolute Deviation (3 of 7)
Forecast Accuracy
Mean Absolute Deviation (3 of 7)
Table Computational Values for MAD and error
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36. Mean Absolute Deviation (5 of 7)
Forecast Accuracy
Mean Absolute Deviation (5 of 7)
Can be used to compare accuracy of different forecasting techniques working on the same set of demand data (PM Computer Services):
Exponential smoothing ( = .30): MAD = 53.41/11=4.85
Exponential smoothing ( = .50): MAD = 4.04
Linear trend line: MAD = 2.29
Linear trend line has lowest MAD; increasing  from .30 to .50 improved smoothed forecast.
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37. Mean Absolute Percent Deviation (6 of 7)
Forecast Accuracy
Mean Absolute Percent Deviation (6 of 7)
A variation on MAD is the mean absolute percent deviation (MAPD).
Measures absolute error as a percentage of demand rather than per period.
Eliminates problem of interpreting the measure of accuracy relative to the magnitude of the demand and forecast values.
Formula:
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38. Mean Absolute Deviation (7 of 7)
Forecast Accuracy
Mean Absolute Deviation (7 of 7)
MAPD for other two forecasts:
Exponential smoothing ( = .50): MAPD = 8.5%
Linear trend: MAPD = 4.9%
Again, Linear trend line has lowest MAPD; and increasing  from .30 to .50 improves smoothed forecast.
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39. Forecast Accuracy Cumulative Error (1 of 2)
Cumulative error is the sum of the forecast errors (E =et).
A relatively large positive value indicates forecast is biased low, a large negative value indicates forecast is biased high.
If majority of errors are positive, then forecasted values will be consistently low; and vice versa.
The cumulative error for a trend line is always almost zero, and is therefore not a good measure for this method.
Cumulative error for PM Computer Services for  = .30 can be read directly from Table 15.8: E =  et = indicating that forecasts are frequently below the actual demand.
Cumulative error for PM Computer Services for  = .50 is
E = 33.21
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40. Forecast Accuracy Average Error Bias
Average error (bias) is the per period average of cumulative error.
A large positive value of average error indicates a forecast is biased low; a large negative error indicates it is biased high.
Average error for exponential smoothing forecast for  = .30 :
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41. Table 15.9 Comparison of Forecasts for PM Computer Services
Forecast Accuracy
Example Forecasts by Different Measures
Table Comparison of Forecasts for PM Computer Services
Results consistent for all forecasts:
Larger value of alpha is preferable.
Adjusted forecast is more accurate than exponential smoothing.
Linear trend is more accurate than all the others.
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42. 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.
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43. Regression Methods Linear Regression
Linear regression relates demand (dependent variable ) to an independent variable.
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44. Regression Methods Correlation (1 of 2)
Correlation is a 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 a strong linear relationship.

45. Coefficient of Determination
Regression Methods
Coefficient of Determination
The coefficient of determination is the percentage of the variation in the dependent variable that results from the independent variable.
Computed by squaring the correlation coefficient, r.
For the State University example:
r = .948, r2 = .899
This value indicates that 89.9% of the amount of variation in attendance can be attributed to the number of wins by the team, with the remaining 10.1% due to other, unexplained, factors.

46. Multiple Regression (1 of 4)
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

47. EXAMPLE: The State University athletic department
The State University athletic department wants to develop its budget for the coming year, using a forecast for football attendance. Football attendance accounts for the largest portion of its revenues, and the athletic director believes attendance is directly related to the number of wins by the team. The business manager has accumulated total annual attendance figures for the past 8 years:
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48. Linear Regression Example (1 of 3)
Regression Methods
Linear Regression Example (1 of 3)
State University Athletic Department.
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49. Linear Regression Example (2 of 3)
Regression Methods
Linear Regression Example (2 of 3)
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50. Linear Regression Example (3 of 3)
Regression Methods
Linear Regression Example (3 of 3)
Figure 15.6
Linear Regression Line
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51. Example Problem Solution Computer Software Firm (1 of 4)
Problem Statement:
For the data below, develop an exponential smoothing forecast
using  = .40, and an adjusted exponential smoothing forecast
using  = .40 and  = .20.
Compare the accuracy of the forecasts using MAD and cumulative error.

52. Example Problem Solution Computer Software Firm (2 of 4)
Step 1: Compute the Exponential Smoothing Forecast.
Using Ft+1 =  Dt + (1 - )Ft
or Ft + 1 = Ft + α(Dt – Ft )
Step 2: Compute the Adjusted Exponential Smoothing
Forecast
AFt+1 = Ft +1 + Tt+1
Tt+1 = (Ft +1 - Ft) + (1 - )Tt

53. Example Problem Solution
Computer Software Firm (3 of 4)

54. Example Problem Solution Computer Software Firm (4 of 4)
Step 3: Compute the MAD Values
Step 4: Compute the Cumulative Error.
E(Ft) = 35.97
E(AFt) = 30.60

55. Example Problem Solution Building Products Store (1 of 5)
For the following data:
Develop a linear regression model
Determine the strength of the linear relationship using correlation.
Determine a forecast for lumber given 10 building permits in the next quarter.

56. Example Problem Solution Building Products Store (2 of 5)
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57. Example Problem Solution Building Products Store (3 of 5)
Step 1: Compute the Components of the Linear Regression Equation.
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58. Example Problem Solution Building Products Store (4 of 5)
Step 2: Develop the Linear regression equation.
y = a + bx, y = x
Step 3: Compute the Correlation Coefficient.

59. Y = a + bx = 1.36 + 1.25(10) = 13.86 or 1,386 board ft
Example Problem Solution
Building Products Store (5 of 5)
Step 4: Calculate the forecast for x = 10 permits.
Y = a + bx = (10) = or 1,386 board ft