Description
Module 03: Forecasting
In this module, you will identify elements of demand forecasting, analyze steps in the forecasting process, and you will focus on the importance of forecasting as it relates to operations management. Demand forecasting may be completed in a simple manner reviewing historical trends or through elaborate systems. This will include the meaningful units in forecasting, how those meaningful units may be different in organizations providing services rather than making products, and how writing down the forecast allows multiple people in multiple roles in the organization to give input to the forecast. We will also look at the impact that a forecasting technique has on receiving the level of detail needed for a forecast. Each organization chooses its own method or methods based on the level of accuracy that may be required.
Discussion Question
Question Requirements:
Forecasting
You are in charge of creating a forecast for an organization that manufactures laptops. The industry is very competitive and supplies have to be purchased far enough ahead of time so that there is no delay in the manufacturing process should the demand increase.
Which forecasting technique would you choose?
What are the steps in the forecasting process?
Why is it important to create a forecast for the correct period of time?
What happens when a forecast is created for 3 months when an organization needs an accurate forecast for 6 months?
Directions:
Discuss the concepts, principles, and theories from your textbook. Cite your textbooks and cite any other sources.
Write a discussion that includes an introduction paragraph, the body, and a conclusion paragraph to address the assignment’s guide questions.
Module 03: Forecasting
In this module, you will identify elements of demand forecasting, analyze steps in the forecasting
process, and you will focus on the importance of forecasting as it relates to operations
management. Demand forecasting may be completed in a simple manner reviewing historical trends
or through elaborate systems. This will include the meaningful units in forecasting, how those
meaningful units may be different in organizations providing services rather than making products, and
how writing down the forecast allows multiple people in multiple roles in the organization to give input
to the forecast. We will also look at the impact that a forecasting technique has on receiving the level
of detail needed for a forecast. Each organization chooses its own method or methods based on the
level of accuracy that may be required.
Discussion Question
Question Requirements:
Forecasting
You are in charge of creating a forecast for an organization that manufactures laptops. The industry is
very competitive and supplies have to be purchased far enough ahead of time so that there is no
delay in the manufacturing process should the demand increase.
1.
2.
3.
4.
Which forecasting technique would you choose?
What are the steps in the forecasting process?
Why is it important to create a forecast for the correct period of time?
What happens when a forecast is created for 3 months when an organization needs an
accurate forecast for 6 months?
Directions:
• Discuss the concepts, principles, and theories from your textbook. Cite your textbooks and
cite any other sources.
• Write a discussion that includes an introduction paragraph, the body, and a conclusion
paragraph to address the assignment’s guide questions.
• Your initial post should address all components of the question with a 600-word limit.
Learning Outcomes
1. Analyze the importance of forecasting in terms of operations management.
2. Articulate the importance of developing and monitoring forecasts.
Readings
Required:
• Chapter 3 in Operations Management
• Chapter 3 PowerPoint Presentation
• Che-Jung CHANG, Guiping LI, Jianhong GUO, & Kun-Peng YU. (2020). DataDriven Forecasting Model for Small Data Sets. Economic Computation & Economic
Cybernetics Studies & Research, 54(4), 217–
229.
• Piotrowska-Woroniak, J., & Szul, T. (2022). Application of a Model Based on Rough
Set Theory (RST) to Estimate the Energy Efficiency of Public Buildings. Energies
(19961073), 15(23), 8793.
Recommended:
• Shang, Z., Li, M., Chen, Y., Li, C., Yang, Y., & Li, L. (2022). A novel model based
on multiple input factors and variance reciprocal: application on wind speed
forecasting. Soft Computing – A Fusion of Foundations, Methodologies &
Applications, 26(17), 8857–8877.
Forecasting
3-1
You should be able to:
LO 3.1
List features common to all forecasts
LO 3.2 Explain why forecasts are generally wrong
LO 3.3 List the elements of a good forecast
LO 3.4 Outline the steps in the forecasting process
LO 3.5 Summarize forecast errors and use summaries to make decisions
LO 3.6 Describe four qualitative forecasting techniques
LO 3.7 Use a naïve method to make a forecast
LO 3.8 Prepare a moving average forecast
LO 3.9 Prepare a weighted-average forecast
LO 3.10 Prepare an exponential smoothing forecast
LO 3.11 Prepare a linear trend forecast
LO 3.12 Prepare a trend-adjusted exponential smoothing forecast
LO 3.13 Compute and use seasonal relatives
LO 3.14 Compute and use regression and correlation coefficients
LO 3.15 Construct control charts and use them to monitor forecast errors
LO 3.16 Describe the key factors and trade-offs to consider when choosing a
forecasting technique
3-2
Forecast – a statement about the future value of a
variable of interest
We make forecasts about such things as weather,
demand, and resource availability
Forecasts are important to making informed decisions
LO 3.1
3-3
Expected level of demand
The level of demand may be a function of some
structural variation such as trend or seasonal variation
Accuracy
Related to the potential size of forecast error
LO 3.1
3-4
• Accounting. New product/process cost estimates, profit projections,
cash management.
• Finance. Equipment/equipment replacement needs,
timing and amount of funding/borrowing needs.
• Human resources. Hiring activities, including recruitment,
interviewing, and training; layoff planning, including
outplacement counseling.
• Marketing. Pricing and promotion, e-business strategies, global
competition strategies.
• MIS. New/revised information systems, internet services.
• Operations. Schedules, capacity planning, work assignments and
workloads, inventory planning, make-or-buy decisions, outsourcing,
project management.
• Product/service design. Revision of current features, design of new
products or services.
LO 3.1
3-5
Plan the system
Generally involves long-range plans related to:
Types of products and services to offer
Facility and equipment levels
Facility location
Plan the use of the system
Generally involves short- and medium-range plans related to:
Inventory management
Workforce levels
Purchasing
Production
Budgeting
Scheduling
LO 3.1
3-6
1.
2.
3.
4.
LO 3.1
Techniques assume some underlying causal system that
existed in the past will persist into the future
Forecasts are not perfect
Forecasts for groups of items are more accurate than
those for individual items
Forecast accuracy decreases as the forecasting horizon
increases
3-7
Forecasts are not perfect:
Because random variation is always present, there will
always be some residual error, even if all other factors
have been accounted for.
LO 3.2
3-8
The forecast
Should be timely
Should be accurate
Should be reliable
Should be expressed in meaningful units
Should be in writing
Technique should be simple to understand and use
Should be cost-effective
LO 3.3
3-9
1.
2.
3.
4.
5.
6.
LO 3.4
Determine the purpose of the forecast
Establish a time horizon
Obtain, clean, and analyze appropriate data
Select a forecasting technique
Make the forecast
Monitor the forecast errors
3-10
Qualitative forecasting
Qualitative techniques permit the inclusion of soft information
such as:
Human factors
Personal opinions
Hunches
These factors are difficult, or impossible, to quantify
Quantitative forecasting
These techniques rely on hard data
Quantitative techniques involve either the projection of historical
data or the development of associative methods that attempt to use
causal variables to make a forecast
LO 3.6
3-11
Forecasts that use subjective inputs such as opinions from consumer
surveys, sales staff, managers, executives, and experts
Executive opinions
A small group of upper-level managers may meet and collectively develop a
forecast
Salesforce opinions
Members of the sales or customer service staff can be good sources of
information due to their direct contact with customers and may be aware of
plans customers may be considering for the future
Consumer surveys
Since consumers ultimately determine demand, it makes sense to solicit input
from them
Consumer surveys typically represent a sample of consumer opinions
Other approaches
Managers may solicit 0pinions from other managers or staff people or outside
experts to help with developing a forecast.
The Delphi method is an iterative process intended to achieve a consensus
LO 3.6
3-12
Forecasts that project patterns identified in recent
time-series observations
Time-series – a time-ordered sequence of observations
taken at regular time intervals
Assume that future values of the time-series can be
estimated from past values of the time-series
LO 3.6
3-13
Trend
Seasonality
Cycles
Irregular variations
Random variation
LO 3.6
3-14
Trend
A long-term upward or downward movement in data
Population shifts
Changing income
Seasonality
Short-term, fairly regular variations related to the calendar or time
of day
Restaurants, service call centers, and theaters all experience
seasonal demand
LO 3.6
3-15
Cycle
Wavelike variations lasting more than one year
These are often related to a variety of economic, political, or even
agricultural conditions
Irregular variation
Due to unusual circumstances that do not reflect typical behavior
Labor strike
Weather event
Random Variation
Residual variation that remains after all other behaviors have been
accounted for
LO 3.6
3-16
Naïve forecast
Uses a single previous value of a time series as the basis
for a forecast
The forecast for a time period is equal to the previous
time period’s value
Can be used with
A stable time series
Seasonal variations
Trend
LO 3.7
3-17
These techniques work best when a series tends to vary
about an average
Averaging techniques smooth variations in the data
They can handle step changes or gradual changes in the
level of a series
Techniques
1.
2.
3.
LO 3.7
Moving average
Weighted moving average
Exponential smoothing
3-18
Technique that averages a number of the most recent
actual values in generating a forecast
n
Ft = MA n =
A
t −i
i =1
n
At − n + … + At − 2 + At −1
=
n
where
Ft = Forecast for time period t
MA n = n period moving average
At −i = Actual value in period t − i
n = Number of periods in the moving average
LO 3.8
3-19
As new data become available, the forecast is updated
by adding the newest value and dropping the oldest
and then re-computing the average
The number of data points included in the average
determines the model’s sensitivity
Fewer data points used—more responsive
More data points used—less responsive
LO 3.7
3-20
The most recent values in a time series are given more
weight in computing a forecast
The choice of weights, w, is somewhat arbitrary and
involves some trial and error
Ft = wt ( At ) + wt −1 ( At −1 ) + … + wt − n ( At − n )
where
wt = weight for period t , wt −1 = weight for period t − 1, etc.
At = the actual value for period t , At −1 = the actual value for period t − 1, etc.
LO 3.9
3-21
A weighted averaging method that is based on the
previous forecast plus a percentage of the forecast
error
Ft = Ft −1 + ( At −1 − Ft −1 )
where
Ft = Forecast for period t
Ft −1 = Forecast for the previous period
= Smoothing constant
At −1 = Actual demand or sales from the previous period
LO 3.10
3-22
A simple data plot can reveal the existence and nature
of a trend
Linear trend equation
Ft = a + bt
where
Ft = Forecast for period t
a = Value of Ft at t = 0
b = Slope of the line
t = Specified number of time periods from
LO 3.11
t =0
3-23
Slope and intercept can be estimated from historical
data
b=
n ty − t y
( )
n t − t
2
2
y − b t
a=
or y − bt
n
where
n = Number of periods
y = Value of the time series
LO
3.11
3-24
The trend adjusted forecast consists of two
components
Smoothed error
Trend factor
TAFt +1 = St + Tt
where
St = Previous forecast plus smoothed error
Tt = Current trend estimate
LO 3.12
3-25
Alpha and beta are smoothing constants
Trend-adjusted exponential smoothing has the ability
to respond to changes in trend
TAFt +1 = St + Tt
St = TAFt + (At − TAFt )
Tt = Tt−1 + (TAFt − TAFt−1 − Tt−1 )
LO 3.12
3-26
Seasonality – regularly repeating movements in
series values that can be tied to recurring events
Expressed in terms of the amount that actual values
deviate from the average value of a series
Models of seasonality
Additive
Seasonality is expressed as a quantity that gets added to or
subtracted from the time-series average in order to
incorporate seasonality
Multiplicative
Seasonality is expressed as a percentage of the average (or
trend) amount which is then used to multiply the value of a
series in order to incorporate seasonality
LO 3.12
3-27
Seasonal relatives
The seasonal percentage used in the multiplicative seasonally
adjusted forecasting model
Using seasonal relatives
To deseasonalize data
Done in order to get a clearer picture of the nonseasonal (e.g.,
trend) components of the data series
Divide each data point by its seasonal relative
To incorporate seasonality in a forecast
1.
2.
LO 3.13
Obtain trend estimates for desired periods using a trend
equation
Add seasonality by multiplying these trend estimates by the
corresponding seasonal relative
3-28
Associative techniques are based on the
development of an equation that summarizes the
effects of predictor variables
Predictor variables – variables that can be used to
predict values of the variable of interest
Home values may be related to such factors as home and
property size, location, number of bedrooms, and number of
bathrooms
LO 3.14
3-29
Regression – a technique for fitting a line to a set of
data points
Simple linear regression – the simplest form of
regression that involves a linear relationship between
two variables
The object of simple linear regression is to obtain an equation
of a straight line that minimizes the sum of squared vertical
deviations from the line (i.e., the least squares criterion)
LO 3.14
3-30
yc = a + bx
where
yc = Predicted (dependent ) variable
x = Predictor (independe nt) variable
b = Slope of the line
a = Value of yc when x = 0 (i.e., the height of the line at the y intercept)
and
b=
n( xy) − ( x )( y )
(
)
n x 2 − ( x )
2
y − b x
a=
or y − b x
n
where
n = Number of paired observatio ns
LO 3.14
3-31
Correlation, r
A measure of the strength and direction of relationship between
two variables
Ranges between -1.00 and +1.00
r=
(
n( xy) − ( x )( y )
)
n x 2 − ( x )
2
(
)
n y 2 − ( y )
2
r2, square of the correlation coefficient
A measure of the percentage of variability in the values of y that is
“explained” by the independent variable
Ranges between 0 and 1.00
LO 3.14
3-32
Variations around the line are random
2. Deviations around the average value (the line)
should be normally distributed
3. Predictions are made only within the range of
observed values
1.
LO 3.14
3-33
Always plot the line to verify that a linear relationship
is appropriate
The data may be time-dependent
If they are
use analysis of time series
use time as an independent variable in a multiple regression
analysis
A small correlation may indicate that other variables
are important
LO 3.14
3-34
Allowances should be made for forecast errors
It is important to provide an indication of the extent to
which the forecast might deviate from the value of the
variable that actually occurs
Forecast errors should be monitored
Error = Actual – Forecast
If errors fall beyond acceptable bounds, corrective
action may be necessary
LO 3.5
3-35
Actual − Forecast
MAD =
t
MAD weights all errors
evenly
t
n
(Actual − Forecast )
MSE =
t
2
t
n −1
Actual t − Forecast t
100
Actual t
MAPE =
n
LO 3.5
MSE weights errors according
to their squared values
MAPE weights errors
according to relative error
3-36
Period
Actual
(A)
Forecast
(F)
(A-F)
Error
|Error|
Error2
[|Error|/Actual]x100
1
107
110
-3
3
9
2.80%
2
125
121
4
4
16
3.20%
3
115
112
3
3
9
2.61%
4
118
120
-2
2
4
1.69%
5
108
109
1
1
1
0.93%
Sum
13
39
11.23%
n=5
n-1 = 4
n=5
MAD
MSE
MAPE
= 2.6
= 9.75
= 2.25%
LO 3.5
3-37
Tracking forecast errors and analyzing them can provide useful
insight into whether forecasts are performing satisfactorily
Sources of forecast errors:
The model may be inadequate due to
a.
b.
c.
omission of an important variable
a change or shift in the variable the model cannot handle
the appearance of a new variable
Irregular variations may have occurred
Random variation
Control charts are useful for identifying the presence of non-
random error in forecasts
Tracking signals can be used to detect forecast bias
LO 3.15
3-38
1. Compute the MSE.
2. Estimate of standard deviation of the distribution of errors
s = MSE
3. UCL: 0 + z MSE
4. LCL: 0 – z MSE
where z = Number of standard deviations from the mean
LO 3.15
3-39
Factors to consider
Cost
Accuracy
Availability of historical data
Availability of forecasting software
Time needed to gather and analyze data and prepare a
forecast
Forecast horizon
LO 3.16
3-40
The better forecasts are, the more able organizations will
be to take advantage of future opportunities and reduce
potential risks
A worthwhile strategy is to work to improve short-term forecasts
Accurate up-to-date information can have a significant effect on
forecast accuracy:
Prices
Demand
Other important variables
Reduce the time horizon forecasts have to cover
Sharing forecasts or demand data through the supply chain can
improve forecast quality
LO 3.16
3-41
Purchase answer to see full
attachment
In this module, you will identify elements of demand forecasting, analyze steps in the forecasting
process, and you will focus on the importance of forecasting as it relates to operations
management. Demand forecasting may be completed in a simple manner reviewing historical trends
or through elaborate systems. This will include the meaningful units in forecasting, how those
meaningful units may be different in organizations providing services rather than making products, and
how writing down the forecast allows multiple people in multiple roles in the organization to give input
to the forecast. We will also look at the impact that a forecasting technique has on receiving the level
of detail needed for a forecast. Each organization chooses its own method or methods based on the
level of accuracy that may be required.
Discussion Question
Question Requirements:
Forecasting
You are in charge of creating a forecast for an organization that manufactures laptops. The industry is
very competitive and supplies have to be purchased far enough ahead of time so that there is no
delay in the manufacturing process should the demand increase.
1.
2.
3.
4.
Which forecasting technique would you choose?
What are the steps in the forecasting process?
Why is it important to create a forecast for the correct period of time?
What happens when a forecast is created for 3 months when an organization needs an
accurate forecast for 6 months?
Directions:
• Discuss the concepts, principles, and theories from your textbook. Cite your textbooks and
cite any other sources.
• Write a discussion that includes an introduction paragraph, the body, and a conclusion
paragraph to address the assignment’s guide questions.
• Your initial post should address all components of the question with a 600-word limit.
Learning Outcomes
1. Analyze the importance of forecasting in terms of operations management.
2. Articulate the importance of developing and monitoring forecasts.
Readings
Required:
• Chapter 3 in Operations Management
• Chapter 3 PowerPoint Presentation
• Che-Jung CHANG, Guiping LI, Jianhong GUO, & Kun-Peng YU. (2020). DataDriven Forecasting Model for Small Data Sets. Economic Computation & Economic
Cybernetics Studies & Research, 54(4), 217–
229.
• Piotrowska-Woroniak, J., & Szul, T. (2022). Application of a Model Based on Rough
Set Theory (RST) to Estimate the Energy Efficiency of Public Buildings. Energies
(19961073), 15(23), 8793.
Recommended:
• Shang, Z., Li, M., Chen, Y., Li, C., Yang, Y., & Li, L. (2022). A novel model based
on multiple input factors and variance reciprocal: application on wind speed
forecasting. Soft Computing – A Fusion of Foundations, Methodologies &
Applications, 26(17), 8857–8877.
Forecasting
3-1
You should be able to:
LO 3.1
List features common to all forecasts
LO 3.2 Explain why forecasts are generally wrong
LO 3.3 List the elements of a good forecast
LO 3.4 Outline the steps in the forecasting process
LO 3.5 Summarize forecast errors and use summaries to make decisions
LO 3.6 Describe four qualitative forecasting techniques
LO 3.7 Use a naïve method to make a forecast
LO 3.8 Prepare a moving average forecast
LO 3.9 Prepare a weighted-average forecast
LO 3.10 Prepare an exponential smoothing forecast
LO 3.11 Prepare a linear trend forecast
LO 3.12 Prepare a trend-adjusted exponential smoothing forecast
LO 3.13 Compute and use seasonal relatives
LO 3.14 Compute and use regression and correlation coefficients
LO 3.15 Construct control charts and use them to monitor forecast errors
LO 3.16 Describe the key factors and trade-offs to consider when choosing a
forecasting technique
3-2
Forecast – a statement about the future value of a
variable of interest
We make forecasts about such things as weather,
demand, and resource availability
Forecasts are important to making informed decisions
LO 3.1
3-3
Expected level of demand
The level of demand may be a function of some
structural variation such as trend or seasonal variation
Accuracy
Related to the potential size of forecast error
LO 3.1
3-4
• Accounting. New product/process cost estimates, profit projections,
cash management.
• Finance. Equipment/equipment replacement needs,
timing and amount of funding/borrowing needs.
• Human resources. Hiring activities, including recruitment,
interviewing, and training; layoff planning, including
outplacement counseling.
• Marketing. Pricing and promotion, e-business strategies, global
competition strategies.
• MIS. New/revised information systems, internet services.
• Operations. Schedules, capacity planning, work assignments and
workloads, inventory planning, make-or-buy decisions, outsourcing,
project management.
• Product/service design. Revision of current features, design of new
products or services.
LO 3.1
3-5
Plan the system
Generally involves long-range plans related to:
Types of products and services to offer
Facility and equipment levels
Facility location
Plan the use of the system
Generally involves short- and medium-range plans related to:
Inventory management
Workforce levels
Purchasing
Production
Budgeting
Scheduling
LO 3.1
3-6
1.
2.
3.
4.
LO 3.1
Techniques assume some underlying causal system that
existed in the past will persist into the future
Forecasts are not perfect
Forecasts for groups of items are more accurate than
those for individual items
Forecast accuracy decreases as the forecasting horizon
increases
3-7
Forecasts are not perfect:
Because random variation is always present, there will
always be some residual error, even if all other factors
have been accounted for.
LO 3.2
3-8
The forecast
Should be timely
Should be accurate
Should be reliable
Should be expressed in meaningful units
Should be in writing
Technique should be simple to understand and use
Should be cost-effective
LO 3.3
3-9
1.
2.
3.
4.
5.
6.
LO 3.4
Determine the purpose of the forecast
Establish a time horizon
Obtain, clean, and analyze appropriate data
Select a forecasting technique
Make the forecast
Monitor the forecast errors
3-10
Qualitative forecasting
Qualitative techniques permit the inclusion of soft information
such as:
Human factors
Personal opinions
Hunches
These factors are difficult, or impossible, to quantify
Quantitative forecasting
These techniques rely on hard data
Quantitative techniques involve either the projection of historical
data or the development of associative methods that attempt to use
causal variables to make a forecast
LO 3.6
3-11
Forecasts that use subjective inputs such as opinions from consumer
surveys, sales staff, managers, executives, and experts
Executive opinions
A small group of upper-level managers may meet and collectively develop a
forecast
Salesforce opinions
Members of the sales or customer service staff can be good sources of
information due to their direct contact with customers and may be aware of
plans customers may be considering for the future
Consumer surveys
Since consumers ultimately determine demand, it makes sense to solicit input
from them
Consumer surveys typically represent a sample of consumer opinions
Other approaches
Managers may solicit 0pinions from other managers or staff people or outside
experts to help with developing a forecast.
The Delphi method is an iterative process intended to achieve a consensus
LO 3.6
3-12
Forecasts that project patterns identified in recent
time-series observations
Time-series – a time-ordered sequence of observations
taken at regular time intervals
Assume that future values of the time-series can be
estimated from past values of the time-series
LO 3.6
3-13
Trend
Seasonality
Cycles
Irregular variations
Random variation
LO 3.6
3-14
Trend
A long-term upward or downward movement in data
Population shifts
Changing income
Seasonality
Short-term, fairly regular variations related to the calendar or time
of day
Restaurants, service call centers, and theaters all experience
seasonal demand
LO 3.6
3-15
Cycle
Wavelike variations lasting more than one year
These are often related to a variety of economic, political, or even
agricultural conditions
Irregular variation
Due to unusual circumstances that do not reflect typical behavior
Labor strike
Weather event
Random Variation
Residual variation that remains after all other behaviors have been
accounted for
LO 3.6
3-16
Naïve forecast
Uses a single previous value of a time series as the basis
for a forecast
The forecast for a time period is equal to the previous
time period’s value
Can be used with
A stable time series
Seasonal variations
Trend
LO 3.7
3-17
These techniques work best when a series tends to vary
about an average
Averaging techniques smooth variations in the data
They can handle step changes or gradual changes in the
level of a series
Techniques
1.
2.
3.
LO 3.7
Moving average
Weighted moving average
Exponential smoothing
3-18
Technique that averages a number of the most recent
actual values in generating a forecast
n
Ft = MA n =
A
t −i
i =1
n
At − n + … + At − 2 + At −1
=
n
where
Ft = Forecast for time period t
MA n = n period moving average
At −i = Actual value in period t − i
n = Number of periods in the moving average
LO 3.8
3-19
As new data become available, the forecast is updated
by adding the newest value and dropping the oldest
and then re-computing the average
The number of data points included in the average
determines the model’s sensitivity
Fewer data points used—more responsive
More data points used—less responsive
LO 3.7
3-20
The most recent values in a time series are given more
weight in computing a forecast
The choice of weights, w, is somewhat arbitrary and
involves some trial and error
Ft = wt ( At ) + wt −1 ( At −1 ) + … + wt − n ( At − n )
where
wt = weight for period t , wt −1 = weight for period t − 1, etc.
At = the actual value for period t , At −1 = the actual value for period t − 1, etc.
LO 3.9
3-21
A weighted averaging method that is based on the
previous forecast plus a percentage of the forecast
error
Ft = Ft −1 + ( At −1 − Ft −1 )
where
Ft = Forecast for period t
Ft −1 = Forecast for the previous period
= Smoothing constant
At −1 = Actual demand or sales from the previous period
LO 3.10
3-22
A simple data plot can reveal the existence and nature
of a trend
Linear trend equation
Ft = a + bt
where
Ft = Forecast for period t
a = Value of Ft at t = 0
b = Slope of the line
t = Specified number of time periods from
LO 3.11
t =0
3-23
Slope and intercept can be estimated from historical
data
b=
n ty − t y
( )
n t − t
2
2
y − b t
a=
or y − bt
n
where
n = Number of periods
y = Value of the time series
LO
3.11
3-24
The trend adjusted forecast consists of two
components
Smoothed error
Trend factor
TAFt +1 = St + Tt
where
St = Previous forecast plus smoothed error
Tt = Current trend estimate
LO 3.12
3-25
Alpha and beta are smoothing constants
Trend-adjusted exponential smoothing has the ability
to respond to changes in trend
TAFt +1 = St + Tt
St = TAFt + (At − TAFt )
Tt = Tt−1 + (TAFt − TAFt−1 − Tt−1 )
LO 3.12
3-26
Seasonality – regularly repeating movements in
series values that can be tied to recurring events
Expressed in terms of the amount that actual values
deviate from the average value of a series
Models of seasonality
Additive
Seasonality is expressed as a quantity that gets added to or
subtracted from the time-series average in order to
incorporate seasonality
Multiplicative
Seasonality is expressed as a percentage of the average (or
trend) amount which is then used to multiply the value of a
series in order to incorporate seasonality
LO 3.12
3-27
Seasonal relatives
The seasonal percentage used in the multiplicative seasonally
adjusted forecasting model
Using seasonal relatives
To deseasonalize data
Done in order to get a clearer picture of the nonseasonal (e.g.,
trend) components of the data series
Divide each data point by its seasonal relative
To incorporate seasonality in a forecast
1.
2.
LO 3.13
Obtain trend estimates for desired periods using a trend
equation
Add seasonality by multiplying these trend estimates by the
corresponding seasonal relative
3-28
Associative techniques are based on the
development of an equation that summarizes the
effects of predictor variables
Predictor variables – variables that can be used to
predict values of the variable of interest
Home values may be related to such factors as home and
property size, location, number of bedrooms, and number of
bathrooms
LO 3.14
3-29
Regression – a technique for fitting a line to a set of
data points
Simple linear regression – the simplest form of
regression that involves a linear relationship between
two variables
The object of simple linear regression is to obtain an equation
of a straight line that minimizes the sum of squared vertical
deviations from the line (i.e., the least squares criterion)
LO 3.14
3-30
yc = a + bx
where
yc = Predicted (dependent ) variable
x = Predictor (independe nt) variable
b = Slope of the line
a = Value of yc when x = 0 (i.e., the height of the line at the y intercept)
and
b=
n( xy) − ( x )( y )
(
)
n x 2 − ( x )
2
y − b x
a=
or y − b x
n
where
n = Number of paired observatio ns
LO 3.14
3-31
Correlation, r
A measure of the strength and direction of relationship between
two variables
Ranges between -1.00 and +1.00
r=
(
n( xy) − ( x )( y )
)
n x 2 − ( x )
2
(
)
n y 2 − ( y )
2
r2, square of the correlation coefficient
A measure of the percentage of variability in the values of y that is
“explained” by the independent variable
Ranges between 0 and 1.00
LO 3.14
3-32
Variations around the line are random
2. Deviations around the average value (the line)
should be normally distributed
3. Predictions are made only within the range of
observed values
1.
LO 3.14
3-33
Always plot the line to verify that a linear relationship
is appropriate
The data may be time-dependent
If they are
use analysis of time series
use time as an independent variable in a multiple regression
analysis
A small correlation may indicate that other variables
are important
LO 3.14
3-34
Allowances should be made for forecast errors
It is important to provide an indication of the extent to
which the forecast might deviate from the value of the
variable that actually occurs
Forecast errors should be monitored
Error = Actual – Forecast
If errors fall beyond acceptable bounds, corrective
action may be necessary
LO 3.5
3-35
Actual − Forecast
MAD =
t
MAD weights all errors
evenly
t
n
(Actual − Forecast )
MSE =
t
2
t
n −1
Actual t − Forecast t
100
Actual t
MAPE =
n
LO 3.5
MSE weights errors according
to their squared values
MAPE weights errors
according to relative error
3-36
Period
Actual
(A)
Forecast
(F)
(A-F)
Error
|Error|
Error2
[|Error|/Actual]x100
1
107
110
-3
3
9
2.80%
2
125
121
4
4
16
3.20%
3
115
112
3
3
9
2.61%
4
118
120
-2
2
4
1.69%
5
108
109
1
1
1
0.93%
Sum
13
39
11.23%
n=5
n-1 = 4
n=5
MAD
MSE
MAPE
= 2.6
= 9.75
= 2.25%
LO 3.5
3-37
Tracking forecast errors and analyzing them can provide useful
insight into whether forecasts are performing satisfactorily
Sources of forecast errors:
The model may be inadequate due to
a.
b.
c.
omission of an important variable
a change or shift in the variable the model cannot handle
the appearance of a new variable
Irregular variations may have occurred
Random variation
Control charts are useful for identifying the presence of non-
random error in forecasts
Tracking signals can be used to detect forecast bias
LO 3.15
3-38
1. Compute the MSE.
2. Estimate of standard deviation of the distribution of errors
s = MSE
3. UCL: 0 + z MSE
4. LCL: 0 – z MSE
where z = Number of standard deviations from the mean
LO 3.15
3-39
Factors to consider
Cost
Accuracy
Availability of historical data
Availability of forecasting software
Time needed to gather and analyze data and prepare a
forecast
Forecast horizon
LO 3.16
3-40
The better forecasts are, the more able organizations will
be to take advantage of future opportunities and reduce
potential risks
A worthwhile strategy is to work to improve short-term forecasts
Accurate up-to-date information can have a significant effect on
forecast accuracy:
Prices
Demand
Other important variables
Reduce the time horizon forecasts have to cover
Sharing forecasts or demand data through the supply chain can
improve forecast quality
LO 3.16
3-41
Purchase answer to see full
attachment
