1. Prepared by Lee Revere and John Large
Chapter 5
Forecasting
Prepared by Lee Revere and John Large
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
5-1

2. Learning Objectives Students will be able to:
Understand and know when to use various families of forecasting models.
Compare moving averages, exponential smoothing, and trend time-series models.
Seasonally adjust data.
Understand Delphi and other qualitative decision-making approaches.
Compute a variety of error measures.
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
5-2

3. Chapter Outline 5.1 Introduction 5.2 Types of Forecasts
5.3 Scatter Diagrams and Time Series
5.4 Measures of Forecast Accuracy
5.5 Time-Series Forecasting Models
5.6 Monitoring and Controlling Forecasts
5.7 Using the Computer to Forecast
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
5-3

4. Introduction Eight steps to forecasting:
Determine the use of the forecast.
Select the items or quantities to be forecasted.
Determine the time horizon of the forecast.
Select the forecasting model or models.
Gather the data needed to make the forecast.
Validate the forecasting model.
Make the forecast.
Implement the results.
These steps provide a systematic way of initiating, designing, and implementing a forecasting system.
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5-4

5. Exponential Smoothing
Types of Forecasts
Forecasting Techniques
No single method is superior
Qualitative Models: attempt to include subjective factors
Time-Series Methods: include historical data over a time interval
Causal Methods: include a variety of factors
Delphi
Methods
Moving
Average
Regression Analysis
Jury of Executive
Opinion
Exponential Smoothing
Multiple Regression
Trend Projections
Sales Force
Composite
Decomposition
Consumer
Market Survey
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5-5

6. Qualitative Methods
Delphi Method interactive group process consisting of obtaining information from a group of respondents through questionnaires and surveys
Jury of Executive Opinion obtains opinions of a small group of high-level managers in combination with statistical models
Sales Force Composite allows each sales person to estimate the sales for his/her region and then compiles the data at a district or national level
Consumer Market Survey solicits input from customers or potential customers regarding their future purchasing plans
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7. Scatter Diagrams
Scatter diagrams are helpful when forecasting time-series data because they depict the relationship between variables.
Radios
Televisions
Compact Discs
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5-7

8. Measures of Forecast Accuracy
Forecast errors allow one to see how
well the forecast model works and
compare that model with other forecast
models.
Forecast error
= actual value – forecast value
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5-8

9. Measures of Forecast Accuracy (continued)
Measures of forecast accuracy include:
Mean Absolute Deviation (MAD)
Mean Squared Error (MSE)
Mean Absolute Percent Error (MAPE)
= å |forecast errors| n 2
= å (errors) n
= å actual n
error
100%
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5-9

10. Hospital Days – Forecast Error Example
Ms. Smith forecasted
total hospital
inpatient days last
year. Now that the
actual data are
known, she is
reevaluating
her forecasting
model. Compute the
MAD, MSE, and
MAPE for her
forecast.
Month
Forecast
Actual
JAN
250
243
FEB
320
315
MAR
275
286
APR
260
256
MAY
241
JUN
298
JUL
300
292
AUG
325
333
SEP
326
OCT
350
378
NOV
365
382
DEC
380
396
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5-10

11. Hospital Days – Forecast Error Example
Actual
|error|
error^2
|error/actual|
JAN
250
243 7 49
0.03
FEB
320
315 5 25
0.02
MAR
275
286 11
121
0.04
APR
260
256 4 16
MAY
241 9 81
JUN
298 23
529
0.08
JUL
300
292 8 64
AUG
325
333
SEP
326 6 36
OCT
350
378 28
784
0.07
NOV
365
382 17
289
DEC
380
396
AVERAGE
11.83
192.83
3.68
MAD =
MSE =
MAPE = .0368*100 =
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5-11

12. Decomposition of a Time-Series
Time series can be decomposed into:
Trend (T): gradual up or down movement over time
Seasonality (S): pattern of fluctuations above or below trend line that occurs every year
Cycles(C): patterns in data that occur every several years
Random variations (R): “blips”in the data caused by chance and unusual situations
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13. Components of Decomposition
Actual Data
Trend
Cyclic
Random
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14. Decomposition of Time-Series: Two Models
Multiplicative model assumes demand
is the product of the four components.
demand = T * S * C * R
Additive model assumes demand is the
summation of the four components.
demand = T + S + C + R
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5-14

15. Moving Averages Simple moving average = å demand in previous n periods
Moving average methods consist of computing an average of the most recent n data values for the time series and using this average for the forecast of the next period.
Simple moving average =
å demand in previous n periods n
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5-15

16. Wallace Garden Supply’s Three-Month Moving Average
Actual
Shed
Sales
Three-Month
Moving Average
January 10
February 12
March 13
April 16
May 19
June 23
July 26
( )/3 = 11 2/3
( )/3 = 13 2/3
( )/3 = 16
( )/3 = 19 1/3
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5-16

17. Weighted Moving Averages
Weighted moving averages use weights to put more emphasis on recent periods.
Weighted moving average =
(weight for period n) (demand in period n) ∑ weights
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5-17

18. Calculating Weighted Moving Averages
Weights
Applied
Period
Last month 3
Two months ago 2
Three months ago 1
3*Sales last month +
2*Sales two months ago +
1*Sales three
months ago 6
Sum of weights
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5-18

19. Wallace Garden’s Weighted Three-Month Moving Average
Actual
Shed
Sales
Three-Month Weighted
Moving Average 10 12 13 16 19 23
January
February
March
April
May
June
July 26
[3*13+2*12+1*10]/6 = 12 1/6
[3*16+2*13+1*12]/6 =14 1/3
[3*19+2*16+1*13]/6 = 17
[3*23+2*19+1*16]/6 = 20 1/2
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5-19

20. Exponential Smoothing
Exponential smoothing is a type of
moving average technique that involves
little record keeping of past data.
New forecast
= previous forecast + (previous actual –previous forecast)
Mathematically this is expressed as:
Ft = Ft-1 + (Yt-1 - Ft-1)
Ft = new forecast
Ft-1 = previous forecast
 = smoothing constant
Yt-1 = previous period actual
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5-20

21. Port of Baltimore Exponential Smoothing Example
Qtr
Actual Tonnage Unloaded
Rounded Forecast using  =0.10 1
180
175 2
168
176= ( ) 3
159
175 = ( ) 4
173 = ( ) 5
190
173 = ( ) 6
205
175 = ( ) 7
178 = ( ) 8
182
178 = ( ) 9 ?
179= ( )
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
5-21

22. Port of Baltimore Exponential Smoothing Example
Qtr
Actual Tonnage Unloaded
Rounded Forecast using  =0.50 1
180
175 2
168
178 = ( ) 3
159
173 = ( ) 4
166 = ( ) 5
190
170 = ( ) 6
205
180 = ( ) 7
193 = ( ) 8
182
186 = ( ) 9 ?
184 = ( )
To accompany Quantitative Analysis for Management, 9e
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5-22

23. Selecting a Smoothing Constant
To select the best smoothing constant, evaluate the accuracy of each forecasting model.
Actual
Forecast with a = 0.10
Absolute
Deviations
Forecast with a = 0.50
180
175 5
168
176 8
178 10
159 16
173 14 2
166 9
190 17
170 20
205 30 25
193 13
182 4
186
MAD
10.0 12
The lowest MAD results from  = 0.10
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5-23

24. PM Computer: Moving Average Example
PM Computer assembles customized personal computers from generic parts.
The owners purchase generic computer parts in volume at a discount from a variety of sources whenever they see a good deal.
It is important that they develop a good forecast of demand for their computers so they can purchase component parts efficiently.
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5-24

25. PM Computers: Data Compute a 2-month moving average
Period month actual demand
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 June 50
7 July 43
8 Aug 47
9 Sept 56
Compute a 2-month moving average
Compute a 3-month weighted average using weights of 4,2,1 for the past three months of data
Compute an exponential smoothing forecast using  = 0.7
Using MAD, what forecast is most accurate?
To accompany Quantitative Analysis for Management, 9e
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5-25

26. PM Computers: Moving Average Solution
MAD
Exponential smoothing resulted in the lowest MAD.
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5-26

27. Exponential Smoothing with Trend Adjustment
Simple exponential smoothing fails to respond to trends, so a more complex model is necessary with trend adjustment.
Simple exponential smoothing - first-order smoothing
Trend adjusted smoothing - second-order smoothing
Low  gives less weight to more recent trends, while high  gives higher weight to more recent trends.
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5-27

28. Exponential Smoothing with Trend Adjustment
Forecast including trend (FITt+1) = new forecast (Ft) + trend correction(Tt)
Tt = (1 - )Tt-1 + (Ft – Ft-1)
where
Ti = smoothed trend for period 1
Ti-1 = smoothed trend for the preceding period
= trend smoothing constant
Ft = simple exponential smoothed forecast for period t
Ft-1 = forecast for period t-1
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5-28

29. Trend Projection Trend projections are used to forecast
time-series data that exhibit a linear
trend.
Least squares may be used to determine a trend projection for future forecasts.
Least squares determines the trend line forecast by minimizing the mean squared error between the trend line forecasts and the actual observed values.
The independent variable is the time period and the dependent variable is the actual observed value in the time series.
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5-29

30. Trend Projection (continued)
The formula for the trend
projection is:
Y = b + b X
where: Y = predicted value
b1 = slope of the trend line
b0 = intercept
X = time period (1,2,3…n)
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5-30

31. Midwestern Manufacturing Trend Projection Example
Midwestern Manufacturing Company’s demand for electrical generators over the period of 1996 – 2000 is given below.
Year
Time
Sales
1996 1 74
1997 2 79
1998 3 80
1999 4 90
2000 5
105
2001 6
142
2002 7
122
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5-31

32. Midwestern Manufacturing Company Trend Solution
Sales = (time)
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33. Midwestern Manufacturing’s Trend
Trend Line
Forecast points
Actual demand line
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5-33

34. Seasonal Variations
Seasonal indices can be used to make adjustments in the forecast for seasonality.
A seasonal index indicates how a particular season compares with an average season.
The seasonal index can be found by dividing the average value for a particular season by the average of all the data.
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5-34

35. Eichler Supplies: Seasonal Index Example
Month
Sales
Demand
Average
Two-Year
Monthly
Seasonal
Index
Year 1 2 80
100 90 94
0.957 75 85
0.851
0.904
110
1.064
Jan
Feb
Mar
Apr
May
115
131
123
1.309 …
Total Average Demand 1,128
Seasonal Index:
= Average 2 -year demand/Average monthly demand
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
5-35

36. Seasonal Variations with Trend
Centered Moving Average (CMA) is an approach that prevents a variation due to trend from being incorrectly interpreted as a variation due to the season.
Steps of Multiplicative Time-Series Model 1. Compute the CMA for each observation.
Compute seasonal ratio (observation/CMA).
3. Average seasonal ratios to get seasonal indices.
4. If seasonal indices do not add to the number of seasons, multiply each index by (number of seasons)/(sum of the indices).
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5-36

37. Turner Industries Seasonal Variations with Trend
Turner Industries’ sales figures are shown below with the CMA and seasonal ratio.
CMA (qtr 3 / yr 1 ) = .5(108) (116) 4
Seasonal Ratio = Sales Qtr 3 = 150
CMA
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5-37

38. Decomposition Method with Trend and Seasonal Components
Decomposition is the process of
isolating linear trend and seasonal
factors to develop more accurate
forecasts.
There are five steps to decomposition: 1. Compute the seasonal index for each season. 2. Deseasonalize the data by dividing
each number by its seasonal index.
3. Compute a trend line with the deseasonalized data.
4. Use the trend line to forecast.
5. Multiply the forecasts by the seasonal index.
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5-38

39. Turner Industries: Decomposition Method
Turner Industries has noticed a trend in quarterly sales figures. There is also a seasonal component. Below is the seasonal index and deseasonalized sales data. *
108
0.85 =
Seasonal Index for Qtr 1 = = 0.85 2
This value is derived by averaging the season rations for each quarter.
Refer to slide 5-37.
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5-39

40. Turner Industries: Decomposition Method
Using the deseasonalized data, the following trend line was computed:
Sales = X
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41. Turner Industries: Decomposition Method
Using the trend line, the following forecast was computed:
Sales = X
For period 13 (quarter 1/ year 4):
Sales = (13)
= (before seasonality adjustment)
After seasonality adjustment:
Sales = (0.85) =
Seasonal index for quarter 1
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5-41

42. Multiple Regression with Trend and Seasonal Components
Multiple regression can be used to
develop an additive decomposition
model.
One independent variable is time.
Seasons are represented by dummy independent variables.
Y = a + b X + b X + b X + b X
Where X = time period
X = 1 if quarter 2
= 0 otherwise
X = 1 if quarter 3
X = 1 if quarter 4 1 2 3 4
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43. Monitoring and Controlling Forecasts
Tracking signals measure how well predictions fit actual data.
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44. Monitoring and Controlling Forecasts
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