Operations Management
Seventh Edition
R. Dan Reid & Nada R. Sanders
Chapter 8
Forecasting
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Learning Objectives
1.
2.
3.
4.
5.
6.
7.
Identify principles of forecasting.
Explain the steps involved in the forecasting process.
Identify types of forecasting methods and their characteristics.
Describe time series models.
Describe causal modeling using linear regression.
Compute forecast accuracy.
Explain the factors that should be considered when selecting a
forecasting model.
8. Explain the nine-step process of CPFR.
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2
Learning Objective 1
Identify principles of forecasting.
LO 1
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3
Forecasting Defined
•
•
•
•
LO 1
Predicting future events.
One of the most important business functions, as decisions are
based on a forecast of the future.
Goal: Generate good forecasts on the average over time and keep
errors low.
Forecasting is an ongoing process.
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4
Principles of Forecasting
Forecasting models differ in complexity, in how much data they use,
and in how they generate forecasts.
Common features are that forecasts are:
1. rarely perfect
2. more accurate for grouped data than for individual items
3. more accurate for shorter than longer time periods
LO 1
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5
Learning Objective 2
Explain the steps involved in the forecasting process.
LO 2
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6
Steps in the Forecasting Process
• Decide what needs to be forecast:
o
level of detail, units of analysis, and time horizon required
• Evaluate and analyze appropriate data:
o
identify needed data and whether it’s available
• Select and test the forecasting model:
o
cost, ease of use, and accuracy
• Generate the forecast.
• Monitor forecast accuracy over time.
LO 2
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7
Learning Objective 3
Identify types of forecasting methods and their characteristics.
LO 3
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8
Types of Forecasting Methods
Forecasting methods classified into two groups.
TABLE 8.1 Types of Forecasting Methods
Qualitative Methods
1. Characteristics Based on human judgment, opinions;
subjective and nonmathematical.
Quantitative Methods
Based on mathematics; quantitative
in nature.
2. Strengths
Can incorporate latest changes in the Consistent and objective; able to
environment and “inside information.” consider much information and data
at one time.
3. Weaknesses
Can bias the forecast and reduce
forecast accuracy.
LO 3
Often quantifiable data are not
available. Only as good as the data on
which they are based.
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9
Types of Forecasting Models
• Qualitative methods — judgmental methods:
o
o
forecasts generated subjectively by the forecaster
educated guesses
• Quantitative methods — based on mathematical modeling:
o
LO 3
forecasts generated through mathematical modeling
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10
Qualitative Forecasting Methods
TABLE 8.2 Qualitative Forecasting Methods
Type
Characteristics
Executive
opinion
A group of managers meet
Good for strategic or newand come up with a forecast. product forecasting.
One person’s opinion can
dominate the forecast.
Market
research
Uses surveys and interviews
to identify customer
preferences.
Good determinant of
customer preferences.
It can be difficult to
develop a good
questionnaire.
Delphi
method
MKT
Seeks to develop a
consensus among a group of
experts.
Excellent for forecasting
long-term product demand,
technological changes, and
scientific advances.
Time-consuming to
develop.
LO 3
Strengths
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Weaknesses
11
Quantitative Forecasting Methods
•
o
o
LO 3
•
Time Series Models
Assume information
needed to generate a
forecast is contained in a
time series of data
Assume the future will
follow same patterns as the
past
Causal Models or Associative
Models
o
o
o
Explore cause-and-effect
relationships
Use leading indicators to
predict the future
Housing starts and appliance
sales
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12
Learning Objective 4
Describe time series models.
LO 4
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13
Time Series Models
•
Forecaster looks for data patterns as:
o
•
Historic pattern to be forecasted:
o
o
o
o
•
LO 4
Data = historic pattern + random variation
Level (long-term average)—data fluctuates around a constant mean.
Trend—data exhibits an increasing or decreasing pattern.
Seasonality—any pattern that regularly repeats itself and is of a
constant length.
Cycle—patterns created by economic fluctuations.
Random variation cannot be predicted.
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14
Time Series Patterns, Figure 8.1
LO 4
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15
Forecasting Models: Naïve, Simple Mean, Simple
Mean Moving Average
•
Naïve: Ft +1 = At
o
•
Simple Mean: Ft +1 = 
o
•
At
n
The average of all available data—good for level patterns
Simple Moving Average: Ft +1 = 
o
o
o
LO 4
The forecast is equal to the actual value observed during the last period—
good for level patterns
At
n
The average value over a set time period (e.g., the last four weeks)
Each new forecast drops the oldest data point and adds a new observation
More responsive to a trend but still lags behind actual data—good for
level patterns; trend + level = bad forecast
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16
Forecasting Model: Weighted Moving Average
•
Weighted Moving Average: Ft +1 = Ct At
o
o
o
o
LO 4
Method in which “n” of the most recent observations are averaged
and past observations may be weighted differently.
All weights must add to 100% or 1.00; e.g., Ct .5, Ct–1 .3, Ct–2 .2
(weights add to 1.00).
Allows emphasizing one period over others; above indicates more
weight on recent data (Ct = 0.5).
Differs from the simple moving average that weighs all periods
equally—more responsive to trends.
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17
Forecasting Model: Exponential Smoothing
•
Exponential Smoothing: Ft +1 = αAt + 1  α  Ft
o
o
Most frequently used time series method because of ease of use and
minimal amount of data needed.
Need just three pieces of data to start:
•
•
•
o
o
LO 4
Last period’s forecast (Ft)
Last period’s actual value (At)
Select value of smoothing coefficient, α, between 0 and 1.00
If no last period forecast is available, average the last few periods or
use naïve method.
Higher α values (e.g., 0.7 or 0.8) place a lot of weight on current
period’s actual demand and can be influenced by random variation.
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18
Time Series Problem
•
•
•
•
•
LO 4
Determine forecast for periods 7 and 8.
2-period moving average.
4-period moving average.
2-period weighted moving average with
t – 1 weighted 0.6 and t – 2 weighted
0.4.
Exponential smoothing with α = 0.2 and
the period 6 forecast being 375.
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Period
Actual
1
300
2
315
3
290
4
345
5
320
6
360
7
375
8
19
Time Series Problem Solution
Period
Actual
1
300
2
315
3
290
4
345
5
320
6
360
7
375
8
LO 4
2-Period
4-Period
2-Period
Weighted
340.0
328.8
344.0
372.0
367.5
350.0
369.0
372.6
Exponential Smoothing
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20
Forecasting Trend
•
•
Basic forecasting models for trends compensate for the lagging
that would otherwise occur.
One model, trend-adjusted exponential smoothing, uses a threestep process.
o
Step 1 — Smoothing the level of the series
St = αAt +  1  α   St 1 + Tt 1 
o
Step 2 — Smoothing the trend
Tt = β(St  St 1 ) + (1  β)Tt 1
o
LO 4
Step 2 — Smoothing the trend
FITt +1 = St + Tt
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21
Forecasting Trend Problem
A company uses exponential smoothing with trend to forecast usage of its lawn
care products. At the end of July the company wishes to forecast sales for August.
July demand was 62. The trend through June has been 15 additional gallons of
product sold per month. Average sales have been 57 gallons per month. The
company uses α = 0.2 and β = 0.10. Forecast for August.
•
Smooth the level of the series:
SJuly = αAt + (1  α)(St 1 + Tt 1 ) =  0.2  62  +  0.8  57 + 15  = 70
•
Smooth the trend:
TJuly = β  St  St 1  +  1  β  Tt 1 =  0.1  70  57  +  0.9 15  = 14.8
•
Forecast including trend:
FITAugust = St + Tt = 70 + 14.8 = 84.8 gallons
LO 4
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22
Linear Trend Line
• A time series technique that computes a forecast with trend
by drawing a straight line through a set of data using this
formula:
Y = a + bX
where
Y = forecast for period X
X = the number of time periods from X = 0
a = value of Y at X = 0 (Y intercept)
b = slope of the line
LO 4
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23
Forecasting Seasonality
• Remember it is a regularly repeating pattern.
• Examples:
o
University enrollment varies between quarters or semesters;
higher in the fall than in the summer
• Seasonal index:
o
LO 4
Percentage amount by which data for each season are above or
below the mean
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24
Forecasting Seasonality, Steps 1-3
1. Calculate the average demand per season.
o
E.g., average quarterly demand
2. Calculate a seasonal index for each season of each year.
o
Divide the actual demand of each season by the average
demand per season for that year
3. Average the indexes by season.
o
LO 4
E.g., take the average of all spring indexes, then of all summer
indexes, and so on.
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25
Forecasting Seasonality, Steps 4-5
4. Forecast demand for the next year and divide by the number
of seasons.
o
Use regular forecasting method and divide by four for average
quarterly demand
5. Multiply next year’s average seasonal demand by each
average seasonal index.
o
LO 4
Result is a forecast of demand for each season of next year
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26
Seasonality Problem
A university must develop forecasts for the next year’s quarterly
enrollments. It has collected quarterly enrollments for the past two years. It
has also forecast total enrollment for next year to be 90,000 students.
What is the forecast for each quarter of next year?
Quarter
Fall
24,000
Winter
23,000
22,000
Spring
19,000
19,000
Summer 14,000
17,000
Total
LO 4
Year 1 Seasonal Index Year 2 Seasonal Index Avg. Index Year 3
1.2
26,000
1.238
1.22
27,450
80,000
84,000
90,000
Average 20,000
21,000
22,500
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27
Solution to Seasonality Problem for the University,
Steps 1-3
Solution
Step 1 Calculate the Average Demand for Each Quarter or “Season.” We do this by dividing the total
annual demand for each year by 4:
Year 1: 80/4 = 20
Year 2: 84/4 = 21
Step 2 Compute a Seasonal Index for Every Season of Every Year for Which You Have Data. To do
this we divide the actual demand for each season by the average demand per season.
Quarter
Enrollment (in thousands): Year 1
Enrollment (in thousands): Year 2
Fall
24/20 = 1.20
26/21 = 1.238
Winter
23/20 = 1.15
22/21 = 1.048
Spring
19/20 = 0.95
19/21 = 0.905
Summer
14/20 = 0.70
17/21 = 0.810
Step 3 Calculate the Average Seasonal Index for Each Season. You can see that the seasonal indexes
vary from year to year for the same season. The simplest way to handle this is to compute an average
index, as follows:
LO 4
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28
Solution to Seasonality Problem for the University,
Steps 4-5
Quarter
Average Seasonal Index
Fall
(1.2 + 1.238)/2 = 1.219
Winter
(1.15 + 1.048)/2 = 1.099
Spring
(0.95 + 0.905)/2 = 0.928
Summer
(0.70 + 0.810)/2 = 0.755
LO 4
Step 4 Calculate the Average Demand per Season for Next
Year. We are told that the university forecast annual enrollment
for the next year to be 90,000 students. The average demand
per season, or quarter, is
90,000/4 = 22,500
Step 5 Multiply Next Year’s Average Seasonal Demand by Each
Seasonal Index. This last step will give us the forecast for each
quarter of next year:
Quarter
Forecast (Students)
Fall
22,500(1.219) = 27, 428
Winter
22,500(1.099) = 24, 728
Spring
22,500(0.928) = 20, 880
Summer
22,500(0.755) = 16, 988
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29
Learning Objective 5
Describe causal modeling using linear regression.
LO 5
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30
Causal Models
• Often, leading indicators can help to predict changes in future
demand—e.g., housing starts.
• Causal models establish a cause-and-effect relationship
between independent and dependent variables.
• A common tool of causal modeling is linear regression:
Y = a + bX
• Additional related variables may require multiple regression
modeling.
LO 5
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31
Linear Regression
•
•
Identify dependent (Y) and independent
(X) variables
Solve for the slope of the line
b=
•
XY  nXY
X  nX
2
2
Solve for the y intercept
a = Y  bX
•
LO 5
Develop your equation for the trend line
Y = a + bX
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32
Linear Regression Problem
A maker of golf shirts has been tracking the relationship between sales and
advertising dollars. Use linear regression to find out what sales might be if
the company invested $53,000 in advertising next year.
Sales $ (Y) Adv.$ (X)
XY
X2
Y2
1
130
32
4,160
2,304
16,900
2
151
52
7,852
2,704
22,801
3
150
50
7,500
2,500
22,500
4
158
55
8,690
3,025
24,964
5
153.85
53
Total
589
189
28,202
9,253
87,165
Average
147.25
47.25
LO 5
b=
b=
XY  nXY
X  nX
2
2
28202  4  47.25 147.25 
9253  4  47.25 
2
= 1.15
a = Y  bX = 147.25  1.15  47.25 
a = 92.9
Y = a + bX = 92.9 + 1.15 X
Y = 92.9 + 1.15  53  = 153.85
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33
Correlation Coefficient — How Good Is the Fit?
•
Correlation coefficient (r) measures the direction and strength of the
linear relationship between two variables. The closer the r value is to
1.00, the better the regression line fits the data points.
r=
=
n  XY    X  Y 
 n  X

2
   X   
2
 n  Y

2
   Y 
2
4  28,202   189  589 
4(9253)  (189)   4  87,165    589  


2
•
LO 5
2
= 0.992
Coefficient of determination (r2) measures the amount of variation in
the dependent variable about its mean that is explained by the
regression line. Values of r2 close to 1.00 are desirable.
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34
Multiple Regression
• An extension of linear regression but:
o
Multiple regression develops a relationship between a
dependent variable and multiple independent variables. The
general formula is:
Y  B0  B1 X1  B2 X2 
LO 5
 BK X K
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35
Learning Objective 6
Compute forecast accuracy.
LO 6
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36
Measuring Forecast Accuracy
• Forecasts are never perfect.
• Need to measure over time.
• Need to know how much we should rely on our chosen
forecasting method.
• Measuring forecast error:
Et = At  Ft
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37
Forecast Accuracy Measures and Tracking Signal
•
Mean absolute deviation (MAD)
o
•
Mean squared error (MSE)
o
•
Penalizes larger errors
MAD =
Measures whether your model is
working; quality and bias
n
  actual  forecast 
2
MSE =
Tracking signal
o
LO 6
Measures the total error in a
forecast without regard to sign
 actual  forecast
Tracking signal =
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n
  actual  forecast 
MAD
38
Accuracy and Tracking Signal Problem
A company is comparing the accuracy of two forecasting methods. Forecasts using
both methods are shown below along with the actual values for January through
May. The company also uses a tracking signal with ±4 limits to decide when a
forecast should be reviewed. Which forecasting method is best?
LO 6
Month
Actual sales
Method A
Forecast
Method A
Error
Method A
Cum. Error
Method A
Tracking Signal
Method B
Forecast
Method B
Error
Method B
Cum. Error
Method B
Tracking Signal
Jan.
30
28
2
2
2
27
2
2
1
Feb.
26
25
1
3
3
25
1
3
1.5
March
32
32
0
3
3
29
3
6
3
April
29
30
−1
2
2
27
2
8
4
May
31
30
1
3
3
29
2
10
5
MAD
1
2
MSE
1.4
4.4
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39
Learning Objective 7
Explain the factors that should be considered when selecting a
forecasting model.
LO 7
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40
Selecting the Right Forecasting Model
1. Amount and type of available data.
•
Some methods require more data than others
2. Degree of accuracy required.
•
Increasing accuracy means more data
3. Length of forecast horizon.
•
Different models for 3 months versus 10 years
4. Presence of data patterns.
•
LO 7
Lagging will occur when a forecasting model meant for a level
pattern is applied with a trend
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41
Forecasting Software
• Spreadsheets
o
o
Microsoft Excel
limited statistical analysis of forecast data
• Statistical packages
o
o
SPSS, SAS, NCSS, Minitab
forecasting plus statistical and graphic capabilities
• Specialty forecasting packages
o
LO 7
extensive range of forecasting capability
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42
Guidelines for Selecting Software
•
•
•
•
•
•
•
•
•
•
LO 7
Does the package have the features you want?
What platform is the package available for?
How easy is the package to learn and use?
Is it possible to implement new methods?
Do you require interactive or repetitive forecasting?
Do you have very large data sets?
Is there local support and training available?
Does the package give the right answers?
What is the cost of the package?
Is it compatible with your existing software?
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43
Learning Objective 8
Explain the nine-step process of CPFR.
LO 8
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44
Collaborative Planning, Forecasting, and
Replenishment (CPFR)
•
•
•
•
•
•
•
•
•
LO 8
Establish collaborative relationships between buyers and sellers.
Create a joint business plan.
Create a sales forecast.
Identify exceptions for sales forecast.
Resolve/collaborate on exception items.
Create order forecast.
Identify exceptions for order forecast.
Resolve/collaborate on exception items.
Generate order.
CPFR is an iterative process.
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45
Forecasting within OM: How It All Fits
Together
•
•
Forecasts impact not only other business functions but all other
operations decisions. Operations managers make many forecasts,
such as the expected demand for a company’s products.
These forecasts are then used to determine:
o
o
o
o
o
o
LO 8
Product designs that are expected to sell (Chapter 2)
The quantity of product to produce (Chapters 5 and 6)
The amount of needed supplies and materials (Chapter 12)
Future space requirements (Chapter 10)
Capacity and location needs (Chapter 9)
The amount of labor needed (Chapter 11)
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46
Forecasting within OM: Strategic Operations
and Tactical Planning
•
Forecasts are also used to:
o
Drive strategic operations decisions, such as choice of competitive
priorities, changes in processes, and large technology purchases
(Chapter 3)
o Serve as the basis for tactical planning; developing worker schedules
(Chapter 11)
Virtually all operations management decisions are based on a
forecast of the future.
LO 8
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47
Forecasting across the Organization
• Forecasting is critical to management of all organizational
functional areas:
o
o
o
o
LO 8
Marketing—relies on forecasting to predict demand and future
sales
Finance—forecasts stock prices, financial performance, capital
investment needs
Information systems—provide ability to share databases and
information
Human resources—relies on forecasting to predict future hiring
requirements, job market conditions, and costs
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48
Chapter 8 Highlights (LO 1–3)
•
•
•
Three basic principles of forecasting are: forecasts are rarely
perfect, are more accurate for groups than individual items, and
are more accurate in the shorter term than longer time horizons.
The forecasting process involves five steps: decide what to
forecast, evaluate and analyze appropriate data, select and test
model, generate forecast, and monitor accuracy.
Forecasting methods can be classified into two groups: qualitative
methods are based on subjective opinion of forecaster and
quantitative methods are based on mathematical modeling.
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49
Chapter 8 Highlights (LO 4)
•
Time series models are based on the assumption that all
information needed is contained in the time series of data.
o
There are four basic patterns of data: level or horizontal, trend, seasonality,
and cycles. In addition, data usually contain random variation. Some
forecast models used to forecast the level of a time series are: naïve,
simple mean, simple moving average, weighted moving average, and
exponential smoothing. Separate models are used to forecast trends and
seasonality.
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50
Chapter 8 Highlights (LO 5)
•
Causal models assume that the variable being forecast is related
to other variables in the environment.
o
A simple causal model is linear regression, in which a straight-line
relationship is modeled between the variable we are forecasting and
another variable in the environment. The correlation measures the
strength of the linear relationship between these two variables.
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51
Chapter 8 Highlights (LO 6–8)
•
•
•
Three useful measures of forecast error are mean absolute
deviation (MAD), mean square error (MSE), and tracking signal.
There are four factors in selecting a model: amount and type of
data available, degree of accuracy required, length of forecast
horizon, and patterns present in the data.
Collaborative Planning, Forecasting, and Replenishment (CPFR) is a
collaborative process between trading partners that establishes
formal guidelines for joint forecasting, replenishment, and
planning.
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52
Copyright
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