110 Chapter Three
Forecasting
A plot helps you to visualize the process and enables you to
check for possible patterns (i.e., nonrandomness) within the limits that
suggest an improved forecast is possible.5 Like the tracking signal, a control
chart focuses attention on deviations that lie outside pre- determined limits.
With either approach, however, it is desirable to check for possible patternsin
the errors, even if all errors are within the limits. If nonrandomness is
found, corrective action is needed. That will result in less variability in
forecast errors, and, thus, in narrower control limits. (Revised control limits
must be com- puted using the resulting forecast errors.) Figure 3.13
illustrates the impact on control limits due to decreased error variability.
Comment The
control chart approach is generally superior to the tracking signal approach. A
major weakness of the tracking signal approach is its use of cumulative errors:
Individual errors can be
obscured so that
large positive and
negative values cancel
each other. Conversely, with control charts, every error
is judged individually. Thus, it can be misleading to rely on a tracking signal
approach to monitor errors. In fact, the historical roots of the trackingsignal
approach date from before the first use of computers in business. At that time,
it was much more difficult to compute standard deviations than to compute
average deviations; for that reason, the concept of a tracking signal was
developed. Now computers and calculators can easily provide standard
deviations. Nonetheless, the use of tracking signals has persisted, probably
because users are unaware of the superiority of the control chart approach.
3.12 CHOOSING A
FORECASTING TECHNIQUE
Many different kinds of forecasting techniques are
available, and no single technique works best in every situation. When
selecting a technique, the manager or analyst must take a num- ber of factors
into consideration.
The two most important factors are cost and accuracy. How
much money is budgeted for generating the forecast? What are the possible costs
of errors, and what are the benefits that might accrue
from an accurate
forecast? Generally speaking,
the higher the
accuracy, the higher the cost,
so it is important to weigh cost–accuracy trade-offs carefully. The best fore-
cast is not necessarily the most accurate or the least costly; rather, it is
some combination of accuracy and cost deemed best by management.
Other factors to consider in selecting a forecasting
technique include the availability of historical data; the availability of
computer software; and the time needed to gather and ana- lyze data and to
prepare the forecast. The forecast horizon is important because some tech-
niques are more suited to long-range forecasts while others work best for the
short range. For example, moving averages and exponential smoothing are
essentially short-range techniques, since they produce forecasts for the next
period. Trend equations can be used to project over much longer time periods.
When using time-series data, plotting the data can be very helpful in choosing
an appropriate method. Several of the qualitative techniques are well suited to
5The theory and application of control charts and the
various methods for detecting patterns in the data are covered in more detail
in Chapter 10, on quality control.
long-range forecasts because they do not require historical
data. The Delphi method and exec- utive opinion methods are often used for
long-range planning. New products and services lack historical data, so
forecasts for them must be based on subjective estimates. In many cases,
experience with similar items is relevant. Table 3.4 provides a guide for
selecting a forecasting method. Table 3.5 provides additional perspectives
on forecasts in terms of the time horizon.
TABLE 3.4 A guide to selecting an appropriate
forecasting method
GAMBAR TABEL
Source: Adapted from J. Holton Wilson and Deborah
Allison-Koerber, “Combining Subjective and Objective Forecasts Improves
Results,” Journal of Business Forecasting, Fall 1992, p. 4.
Copyright © 1992 Institute of Business Forecasting. Used
with permission.
TABLE 3.5 Forecast
factors, by range of forecast
(GAMBAR TABLE)
In some instances, a manager
might use more than one forecasting technique to obtain independent forecasts.
If the different techniques produced approximately the same predictions, that
would give increased confidence in the results; disagreement among the
forecasts would indicate that additional analysis may be needed.
112 Chapter
Three Forecasting
3.13 USING FORECAST INFORMATION
A manager can take a reactive or
a proactive approach to a forecast. A reactive approach views forecasts as
probable future demand, and a manager reacts to meet that demand (e.g., adjusts
production rates, inventories, the
workforce). Conversely, a
proactive approach seeks
to actively influence demand (e.g., by means of advertising, pricing, or
product/service changes).
Generally speaking,
a proactive approach
requires either an
explanatory model (e.g., regression) or a subjective
assessment of the influence on demand. A manager might make two forecasts: one
to predict what will happen under the status quo and a second one based on a
“what if” approach, if the results of the status quo forecast are unacceptable.
3.14 COMPUTER SOFTWARE IN
FORECASTING
Computers play an important role
in preparing forecasts based on quantitative data. Their use allows managers to
develop and revise forecasts quickly, and without the burden of manual
computations. There is a wide range of software packages available for
forecasting. The Excel templates on the text Web site are an example of a
spreadsheet approach. There are templates for moving averages, exponential
smoothing, linear trend equation, trend-adjusted exponential smoothing,
and simple linear
regression. Some templates
are illustrated in
the Solved Problems section at
the end of the chapter.
3.15 OPERATIONS STRATEGY
Forecasts are the basis for many
decisions and an essential input for matching supply and demand. Clearly, the
more accurate an organization’s forecasts, the better prepared it will be to take
advan- tage of future opportunities and reduce potential risks. A worthwhile
strategy can be to work to improve short-term forecasts. Better short-term
forecasts will not only enhance profits through lower inventory levels, fewer
shortages, and improved customer service, they also will enhance forecasting
credibility throughout the organization: If short-term forecasts are
inaccurate, why should other areas of the organization put faith in long-term
forecasts? Also, the sense of con- fidence accurate short-term forecasts would
generate would allow allocating more resources to strategic and medium- to
longer-term planning and less on short-term, tactical activities.
Maintaining accurate, up-to-date
information on prices, demand, and other variables can have a significant
impact on forecast accuracy. An organization also can do other things to
improve forecasts. These do not involve searching for improved techniques but
relate to the inverse relation of accuracy to the forecast horizon: Forecasts
that cover shorter time frames tend to be more accurate than longer-term
forecasts. Recognizing this, management might choose to devote efforts to
shortening the time horizon that forecasts must cover. Essentially, this means
shortening the lead time needed to respond to a forecast. This might involve
build- ingflexibility into operations to
permit rapid response to changing demands for products and services, or to
changing volumes in quantities demanded; shortening the lead time required to
obtain supplies, equipment, and raw materials or the time needed to train or
retrain employees; or shortening the time needed to develop new products and
services.
Lean systems are demand driven;
goods are produced to fulfill orders rather than to hold in inventory until demand
arises. Consequently, they are far less dependent on short-term fore- casts
than more traditional systems.
In certain situations forecasting
can be very difficult when orders have to be placed far in advance. This is the
case, for example, when demand is sensitive to weather conditions, such as the
arrival of spring, and there is a narrow window for demand. Orders for products
or services that relate to this (e.g., garden materials, advertising space)
often have to be placed many months in advance—far beyond the ability of
forecasters to accurately predict weather conditions and,
hence, the timing
of demand. In
such cases, there
may be pressures
from salespeople who want low quotas and financial people who don’t want
to have to deal with the cost of
excess inventory to
have conservative forecasts.
Conversely, operations people may want more optimistic forecasts to
reduce the risk of being blamed for possible shortages.
Sharing forecasts or demand data throughout
the supply chain can improve forecast qual- ity in the supply chain, resulting
in lower costs and shorter lead times. For example, both Hewlett-Packard and
IBM require resellers to include such information in their contracts.
The following reading provides
additional insights on forecasting and supply chains.
Gazing at the Crystal Ball
Ram Reddy
Disregarding Demand Forecasting
Technologies during Tough Economic Times Can Be a Costly Mistake
It’s no secret that the IT sector
has felt the brunt of the economic down-turn. Caught up in the general
disillusionment with IT has been demand forecasting (DF) technologies. Many
companies blame DF technologies for supply chain problems such as excess
inventory. Pinning the blame on and discontinuing DF technologies is the
equivalent of throwing out the baby with the bathwater. The DF misunderstanding
stems from the fact that, despite
sophisticated mathematical models
and underlying technologies, the
output from these systems is, at best, an educated guess about the future.
A forecast from these systems is
only as good as the assumptions and
data used to
build the forecast.
Even the best
forecast fails whenan
unexpected event—such as
a recession—clobbers the
underlying assumptions.
However, this doesn’t
imply that DF
technologies aren’t delivering
the goods. But, unfortunately, many DF and supply chain technology
implementations have recently fallen victim to this mindset. DF is part science and part art (or
intuition)—having the potential to significantly impact a company’s bottom
line. In this column, you’ll find an overview of how DF is supposed to work and
contrast that with how most companies actually practice it. I’ll conclude with
suggestions on how to avoid common mistakes implementing and using this
particular class of technologies.
The Need for DF Systems
DF is
crucial to minimizing
working capital and
associated expenses and
extracting maximum value from a company’s capital investments in property,
plant, and equipment (PPE). It takes a manufacturing company a lot of lead time
to assemble and stage the raw materials and components to manufacture a given
number of products per day. The manufacturing company, in turn, generates its
sales forecast numbers using data from a variety of sources such as
distribution channels, factory
outlets, value-added resellers,
historical sales data,
and general macroeconomic data. Manufacturing
companies can’t operate without a demand forecast because they won’t know the
quantities of finished goods to produce.
The manufacturing companynyyyy wants to
make sure all
or much of
its finished product moves off
the store shelves or dealer lots as quickly as possible. Unsold products
represent millions of dollars tied up in inventory.
The flip side of this equation is
the millions of dollars invested in PPE to manufacture the finished products.
The company and its supporting supply chain must utilize as close to 100 percent
of its PPE investments. Some manufacturing plants make products in lots of 100
or 1,000. Generally, it’s cost prohibitive to have production runs of one unit.
So how do you extract maximum value from your investments and avoid having
money tied up in unsold inventory?
DF and supply chain management
(SCM) technologies try to solve this
problem by generating
a production plan
to meet forecasted demand and
extract maximum value
from PPE, while
reducing the amount of capital
tied up in inventory. Usually, the demand forecast is pretty close to the
actual outcomes, but there are times when demand forecasts don’t
match the outcomes.
In addition to
unforeseen economic events, a
new product introduction may be a stellar success or an abysmal failure. In the
case of a phenomenal success, the manufacturing plant may not be able to meet
demand for its product.
Consider the
case of the
Chrysler PT Cruiser.
It succeeded way beyond the demand forecast’s
projections. Should it have started with manufacturing capacity to fulfill the
runaway demand? Absolutely not. Given the additional millions of dollars of
investment in PPE necessary to add that capacity, it would’ve backfired if the
PT Cruiser had been a flop. The value provided by DF and supporting SCM
technologies in this instance was the ability to add capacity to meet the
amended forecast based on actual events. Demand forecasts can and do frequently
miss their targets. The point to underscore here is that the underlying DF and
supporting SCM technologies are critical to a company’s ability to react and
respond in a coordinated manner when market conditions change.
The manufacturing company and its
supply chain are able to beefit from sharing information about the changed
market conditions and responding
to them in a coordinated
manner. Despite best
practices embedded in DF and SCM technologies to support this manner of
collaboration, it plays out differently in the real world.
(continued)
114 Chapter Three Forecasting
(concluded)
How It Works in Real Life — Worst
Practices
A company prepares its forecast
by taking into account data about past sales, feedback from distribution
channels, qualitative assessments from field sales managers, and macroeconomic
data. DF and SCM technologies take these inputs and add existing capacities
within the company and across the supply chain to generate a production plan
for optimum financial performance.
There’s been
incredible pressure on
executives of publicly
traded companies to keep up stock prices. This pressure, among other
reasons, may cause manufacturing company executives to make bold projections to
external financial analysts (or Wall Street) about future sales without using
the demand forecast generated from the bottom up. When the company realizes
this disparity between the initial projection and the forecast, the forecast is
changed to reflect the projections made by the company’s officers, negating its
accuracy.
The company
arbitrarily sets sales
targets for various
regions to meet Wall Street
numbers that are totally out of sync with input provided by the regional sales
managers for the DF process. Even though the regional sales
managers’ input may
have a qualitative
element (art), they tend to be
more accurate, given their proximity to the customers in the region.
Unfortunately, the arbitrary sales targets make their way back to the supply
chain, and the result is often excessive inventory build-up starting at the
distribution channels to the upstream suppliers.
Seeing the inventory pile up, the
manufacturing company may decide to shut down a production line. This action
affects upstream suppliers who had procured raw materials and components to
meet the execu-tive-mandated production numbers, which may cause them to treat
any future forecasted numbers
with suspicion. Most
cost efficiencies that could be obtained through planned procurement
of raw materials and components go out the window. It’s very likely that the
companies try to blame DF and SCM technologies for failing to provide a
responsive andefficient supply chain, even though the fault may lie in the
company’s misuse of the technologies and not the technologies themselves.
Guarding against the Extremes
Earlier in this column, I said
that DF is part art or intuition and part science. The art/intuition part comes
in when subject-matter experts (SMEs) make educated estimates about future
sales. These SMEs could range from distribution outlet owners to sales and
marketing gurus and economists. Their intuition is typically combined with data
(such as historical sales figures) to generate the forecast for the next
quarter or year. During a recession, the SMEs tend to get overly pessimistic.
The demand forecasts generated from this mindset lead to inventory shortages
when the economy recovers. Similarly, during an economic expansion, the SMEs
tend to have an overly rosy picture of the future. This optimism leads to
inventory gluts when the economy starts to slow down. In both instances,
blaming and invalidating DF and SCM technologies is counterproductive in the
long run.
It’s very rare that a demand
forecast and the actual outcome match 100 percent. If it’s close enough to
avoid lost sales or create an excess inventory situation, it’s deemed a
success. DF and supporting SCM technologies are supposed to form a closed loop
with actual sales at the cash register
providing a feedback
mechanism. This feedback is
especially essential during economic upturns or downturns. It provides
the necessary information to a company and its supply chain to react in a
coordinated and efficient manner.
Don’t let the current
disillusionment with DF and SCM technologies impede the decision-making process
within your company. The intelligent enterprise needs these technologies to
effectively utilize its capital resources and efficiently produce to meet its
sales forecasts.
Ram Reddy is the author of Supply
Chains to Virtual Integration (McGraw-Hill, 2001). He is the president of
Tactica Consulting Group, a technology and business strategy consulting
company.
Questions
1. What is DF and why is it important?
2. Why might a company executive make bold
predictions about future demand to Wall Street analysts?
3. How might an executive’s comments to Wall
Street analysts affect demand forecasts, and what are the consequences of doing
so?
Source: Ram Reddy, “Gazing at the
Crystal Ball,” Intelligent Enterprise, June 13,
2002. Copyright © 2002 Pention
Media, Inc. Used with permission
SUMMARY
Forecasts are vital inputs for
the design and the operation of the productive systems because they help managers
to anticipate the future.
Forecasting techniques can be
classified as qualitative or quantitative. Qualitative techniques rely on
judgment, experience, and expertise to formulate forecasts; quantitative
techniques rely on the use of historical data or associations among variables
to develop forecasts. Some of the techniques are simple, and others are
complex. Some work better than others, but no technique works all the time.
Moreover, all forecasts include a certain degree of inaccuracy, and allowance
should be made for this. The techniques generally assume that the same
underlying causal system that existed in the past will continue to exist in the
future.
The qualitative techniques
described in this chapter include consumer surveys, salesforce estimates,
executive opinions, and manager and staff opinions. Two major quantitative
approaches are described: analysis of time-series data and associative
techniques. The time-series techniques rely strictly on the examination of
historical data; predictions are made by projecting past movements of a
variable into the future without considering specific factors that might
influence the variable. Associative techniques attempt to explicitly identify
influencing factors and to incorporate that information into equations that can
be used for predictive purposes.
All forecasts tend to be
inaccurate; therefore, it is important to provide a measure of accuracy. It is
possible to compute several measures of forecast accuracy that help managers to
evaluate the performance of a given technique and to choose among alternative
forecasting techniques. Control of forecasts involves deciding whether a
forecast is performing adequately, typically using a control chart.
When selecting
a forecasting technique,
a manager must
choose a technique
that will serve
the intended purpose at an acceptable level of cost and accuracy.
The various forecasting
techniques are summarized in Table 3.6 . Table 3.7 lists the formulas
used in the forecasting techniques and in the methods of measuring their
accuracy. Note that the Excel templates on the text Web site that accompanies
this book are especially useful for tedious calculations.
1. Demand forecasts are essential inputs for
many business decisions; they help managers decide how much supply or capacity
will be needed to match expected demand, both within the organization and in
the supply chain.
2. Because of random variations in demand, it
is likely that the forecast will not be perfect, so managers need to be
prepared to deal with forecast errors.
3. Other, nonrandom factors might also be
present, so it is necessary to monitor forecast errors to check for nonrandom
patterns in forecast errors.
4. It is important to choose a forecasting technique
that is cost-effective and one that minimizes forecast error.
TABLE 3.6 Forecasting
approaches
(di lewat)
TABLE 3.7 Summary of formulas
|
Technique
|
Formula
|
Definitions
|
|
MAD
|
n
MAD = ∑|e|
 n |
MAD = Mean absolute deviation
e = Error, A
F
n = Number of errors
|
|
MSE
|
n
MSE = ∑|e2
n - 2 |
MSE = Mean squared error
n = Number of errors
|
|
MAPE
|
|
MAPE = Mean absolute percent error
n = Number of errors
|
|
Moving
average forecast
|
n
∑
Ft =
i-1=At-i
 n |
A = Demand in period t
i
n = Number of periods
|
|
Weighted
average
|
|
Wt = Weight for the period t
At
= Actual value in period t
|
|
Exponential
smoothing forecast
|
|
α= Smoothing factor
|
|
Linear
trend forecast
|
|
a = y
intercept
b = Slope
|
|
Trend-adjusted
forecast
|
|
t = Current period
TAFt+1= Trend-adjusted
forecast for next period
S =Previous forecast plus smoothed error
T =Trend component
|
|
Linear
regression forecast
|
|
yc
= Computed value of dependent variable
x = Predictor (independent) variable
b = Slope of the line
a = Value of y when x = 0
|
|
Standard
error of estimate
|
|
Se = Standard error of estimate
y = y
value of each data point
n =Number
of data points
|
|
Tracking
signal
|
|
|
|
Control
limits
|
|
ѴMSE = standard deviation
z =
Number of standard deviations;
2 and 3 are typical values
|
Chapter Three
Forecasting 117
|
associative model, 82
|
judgmental
forecasts, 82
|
regression,
101
|
|
bias, 108
|
least
squares line, 101
|
seasonal
relative, 97
|
|
centered
moving average, 98
|
linear trend equation, 92
|
seasonal
variations, 95
|
|
control
chart, 106
|
mean
absolute deviation
|
seasonality,
84
|
|
correlation,
104
|
(MAD), 81
|
standard
error of estimate, 103
|
|
cycle, 84
|
mean
absolute percent error
|
time
series, 84
|
|
Delphi
method, 83
|
(MAPE), 81
|
time-series
forecasts, 82
|
|
error, 80
|
mean
squared error (MSE), 81
|
tracking
signal, 108
|
|
exponential
smoothing, 89
|
moving
average, 86
|
trend, 84
|
|
focus
forecasting, 91
|
naive
forecast, 84
|
trend-adjusted
exponential
|
|
forecast,
75
|
predictor
variables, 101
|
smoothing,
95
|
|
irregular
variation, 84
|
random
variations, 84
|
weighted
average, 88
|
SOLVED PROBLEMS
Forecasts based on averages. Given the following data : Problem 1
|
Period
|
Number of Complaints
|
|
1
|
60
|
|
2
|
65
|
|
3
|
55
|
|
4
|
58
|
|
5
|
64
|
Prepare a forecast for period 6 using each of these
approaches:
a. The appropriate
naive approach.
b. A three-period
moving average.
c. A weighted
average using weights of .50 (most recent), .30, and .20.
d. Exponential
smoothing with a smoothing constant of .40.
a. Plot the data to
see if there is a pattern. Here we have only variations around an average
(i.e., no trend or cycles). Therefore, the most recent value of the series
becomes the next forecast: 64.
b. Use the latest
values.
c.
d. Start with period
2. Use the data in period 1 as the forecast for period 2, and then use
exponential smoothing for successive forecasts.
|
Period
|
Number of Complaints
|
Forecast
|
Calculations
|
|
1
|
 60 |
|
[The previous value of the series is used
|
|
2
|
65
|
60
|
as the starting forecast.]
|
|
3
|
55
|
62
|
60 + .40 (65 – 60) = 62
|
|
4
|
58
|
59,2
|
62 + .40 (55 – 62) = 59.2
|
|
5
|
64
|
58,72
|
59.2 + .40 (58 – 59.2) = 58.72
|
|
6
|
|
60,83
|
58.72 + .0 (64 – 58.72) = 60.83
|
118
Chapter Three Forecasting
You also can obtain the forecasts and a plot using an Excel
template, as shown:
(Gambar di lewat)
Using seasonal relatives.Apple’s Citrus Fruit Farm ships
boxed fruit anywhere in the world. Using the
following information, a
manager wants to
forecast shipments for
the first four
months of next year.
|
Month
|
Seasonal Relative
|
Month
|
Seasonal Relative
|
|
Jan.
|
1.2
|
Jul.
|
0.8
|
|
Feb.
|
1.2
|
Aug.
|
0.6
|
|
Mar.
|
1.3
|
Sep.
|
0.7
|
|
Apr.
|
1.1
|
Oct.
|
1.0
|
|
May.
|
0.8
|
Nov.
|
1.1
|
|
Jun.
|
0.7
|
Des.
|
1.4
|
The monthly forecast equation being used is:
Ft =
402 + 3t
Where
t0 = January
of last year
Ft =
Forecast of shipments for month t
a. Determine trend
amounts for the first four months of next year: January, t = 24;
February, t = 25; etc. Thus,
Fjan =
402 + 3(24) = 474
FFeb =
402 + 3(25) = 477
FMar =
402 + 3(26) = 480
FApr =
402 + 3(27) = 483
b. Multiply each
monthly trend by the corresponding seasonal relative for that month.
|
Month
|
Seasonal Relative
|
Forecast
|
|
Jan.
|
1.2
|
474(1.2) = 568.8
|
|
Feb.
|
1.3
|
477(1.3) = 620.1
|
|
Mar.
|
1.3
|
480(1.3) = 624.0
|
|
Apr.
|
1.1
|
483(1.1) = 531.3
|
Chapter Three Forecasting 119
Linear trend line. Plot the data on a graph, and verify
visually that a linear trend line is appropriate. Develop a linear trend
equation for the following data. Then use the equation to predict the next two
values of the series.
|
Period
|
Demand
|
|
1
|
44
|
|
2
|
52
|
|
3
|
50
|
|
4
|
54
|
|
5
|
55
|
|
6
|
55
|
|
7
|
60
|
|
8
|
56
|
|
9
|
62
|
Gambar dilewat
A plot of the data indicates that a linear trend line is
appropriate:
|
Period
|
|
Demand
|
|
|
t
|
t2
|
y
|
ty
|
|
1
|
1
|
44
|
44
|
|
2
|
4
|
52
|
104
|
|
3
|
9
|
50
|
150
|
|
4
|
16
|
54
|
216
|
|
5
|
25
|
55
|
275
|
|
6
|
36
|
55
|
330
|
|
7
|
49
|
60
|
420
|
|
8
|
64
|
56
|
448
|
|
9
|
81
|
62
|
558
|
|
45
|
285
|
488
|
2,545
|
∑ t = 45 and ∑ t2 = 285
n∑ry - ∑t∑y 9(2,545) – 45(488)
n∑ry - ∑t∑y 9(2,545) – 45(488)
b= = = 1,75
n∑t2 – (∑t)2 9(285)
– 45(45)
∑y - b∑t 488 –
1.75(45)
a= = = 45.47
n 9
Thus, the trend equation is Ft 45.47
1.75t. The next two forecasts are:
F10 = 45.47 +
1.75(10) = 62.97
F11 = 45.47 +
1.75(11) = 64.72
120 Chapter
Three Forecasting
You also can use an Excel template to obtain the coefficients and a
plot. Simply replace the existing data in the template with your data.
(Gambar lewat )
Seasonal relatives. Obtain estimates of quarter relatives for these
data using the centered moving average method :
|
|
|
|
|
|
|
YEAR
|
|
|
|
|
|
|
|
|
|
|
|
1
|
|
|
|
2
|
|
|
3
|
|
|
4
|
|
Quarter
|
1
|
2
|
3
|
4
|
1
|
2
|
3
|
4
|
1
|
2
|
3
|
4
|
1
|
|
Demand
|
14
|
18
|
35
|
45
|
28
|
36
|
60
|
71
|
45
|
54
|
84
|
88
|
58
|
Solution
Note that each season has an even number of data points. When an
even-numbered moving average is used (in this case, a four-period moving
average), the “centered value” will not correspond to an actual data point; the
center of 4 is between the second and third data points. To correct for this, a
second set of moving averages must be computed using the MA4 values. The MA2 values are centered between
the MA4 and “line up” with actual data points. For example, the first MA4 value
is 28.25. It is centered between 18 and 35 (i.e., between quarter 2 and quarter
3). When the average of the first two MA
values is taken (i.e., MA ) and
centered, it lines up with the 35 and, hence, with quarter 3.
So, whenever an
even-numbered moving average
is used as
a centered moving
average (e.g., MA4 , MA12
), a second moving average, a two-period moving average, is used to achieve
correspondence with periods. This procedure is not needed when the number of
periods in the centered moving average is odd.
|
Year
|
Quarter
|
Demand
|
MA4
|
MA2
|
Demand/MA2
|
|
1
|
1
|
14
|
|
|
|
|
|
2
|
18
|
28.25
|
|
|
|
|
3
|
35
|
31.75
|
30.00
|
1.17
|
|
|
4
|
46
|
36.25
|
34.00
|
1.35
|
|
2
|
1
|
28
|
42.50
|
39.38
|
0.71
|
|
|
2
|
36
|
48.75
|
45.63
|
0.79
|
|
|
3
|
60
|
53.00
|
50.88
|
1.18
|
|
|
4
|
71
|
57.50
|
55.25
|
1.29
|
|
3
|
1
|
45
|
63.50
|
60.50
|
0.74
|
|
|
2
|
54
|
67.75
|
65.63
|
0.84
|
|
|
3
|
84
|
71.00
|
69.38
|
1.21
|
|
|
4
|
88
|
|
|
|
|
4
|
1
|
58
|
|
|
|
|
|
Quarter
|
|
|
|
1
|
2
|
3
|
4
|
|
0.71
|
0.79
|
1.17
|
1.35
|
|
0.74
|
0.82
|
1.18
|
1.29
|
|
1.45
|
1.61
|
1.21
|
2.64
|
|
|
|
3.56
|
|
|
0.725
|
0.805
|
1.187
|
1.320
|
The sum of these relatives is 4.037. Multiplying each by 4.00/4.037
will standardize the relatives, making their total equal 4.00. The resulting
relatives are quarter 1, .718; quarter 2, .798; quarter 3, 1.176; quarter 4,
1.308.
Regression line. A large midwestern retailer has developed a graph that
summarizes the effect ofadvertising
expenditures on sales
volume. Using the
graph, determine an
equation of the
form y = a + bx
that describes this relationship.
(gambar lewat)
Solution
The linear equation has the form y = a + bx,
where a is the value of y when x = 0 (i.e., where theline intersects the y
axis) and b is the slope of the line (the amount by which y changes for a
one-unit change in x ).
Accordingly, a = 1 and b
= (3 - 1)/(10 - 0) = .2, so y = a + bx becomes
y = 1 + .2x. [Note: (3 - 1) is the change in y, and (10 - 0)
is the change in x. ]
Regression analysis. The owner of a small hardware store has noted a
sales pattern for window locksthat seems to parallel the number of break-ins
reported each week in the newspaper. The data are:
|
Sales:
|
46
|
18
|
20
|
22
|
27
|
34
|
14
|
37
|
30
|
|
Break-ins:
|
9
|
3
|
3
|
5
|
4
|
7
|
2
|
6
|
4
|
a. Plot the data to determine
which type of equation, linear or nonlinear, is appropriate.
b. Obtain a regression equation
for the data.
c. Estimate average sales when
the number of break-ins is five.
(Gambar lewat)
122 Chapter
Three Forecasting
b. You can obtain the regression
coefficients using the appropriate Excel template. Simply replace the existing
data for x and y with your data. Note: Be careful to enter the values for the
variable you want to predict as y values. In this problem, the objective is to
predict sales, so the sales values are entered in the y column. The equation is
yc = 7.129 +
4.275x.
(gambar lewat)
Problem 7
c. For x = 5, yc =
7.129 + 4.275(5) = 28.50.
Accuracy of forecasts. The manager of a large manufacturer of
industrial pumps must choose between two alternative forecasting techniques.
Both techniques have been used to prepare forecasts for a sixmonth period.
Using MAD as a criterion, which technique has the better performance record?
|
|
|
FORECAST
|
|
|
Month
|
Demand
|
Technique 1
|
Technique 2
|
|
1
|
492
|
488
|
495
|
|
2
|
470
|
484
|
482
|
|
3
|
485
|
480
|
478
|
|
4
|
493
|
490
|
488
|
|
5
|
498
|
497
|
492
|
|
6
|
492
|
493
|
493
|
Check that each forecast has an average error of approximately zero.
(See computations that follow.)
|
Month
|
Demand
|
Technique 1
|
e
|
| e |
|
Technique 2
|
e
|
| e |
|
|
1
|
492
|
488
|
4
|
4
|
495
|
-3
|
3
|
|
2
|
470
|
484
|
-14
|
14
|
482
|
-12
|
12
|
|
3
|
485
|
480
|
5
|
5
|
478
|
7
|
7
|
|
4
|
493
|
490
|
3
|
3
|
488
|
5
|
5
|
|
5
|
498
|
497
|
1
|
1
|
492
|
6
|
6
|
|
6
|
492
|
493
|
-1
|
1
|
493
|
-1
|
1
|
|
|
|
|
-2
|
28
|
|
+2
|
34
|
∑|e| 28
MAD1 = = ― = 4.67
n
6
∑|e| 36
MAD1 = = ― = 5.67
n
6
Technique 1 is superior in this comparison because its MAD is smaller,
although six observations would generally be too few on which to base a
realistic comparison.
Control chart. Given the demand data that follow, prepare a naive
forecast for periods 2 through 10. Then determine each forecast error, and use
those values to obtain 2s control limits. If demand in the next two periods
turns out to be 125 and 130, can you conclude that the forecasts are in
control?
|
Period:
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
Demand:
|
118
|
117
|
120
|
119
|
126
|
122
|
117
|
123
|
121
|
124
|
For a naive forecast, each period’s demand becomes the forecast for the
next period. Hence, the forecasts and errors are:
|
Period
|
Demand
|
Forecast
|
Error
|
Error2
|
|
1
|
118
|
-
|
-
|
-
|
|
2
|
117
|
118
|
1
|
1
|
|
3
|
120
|
117
|
3
|
9
|
|
4
|
119
|
120
|
1
|
1
|
|
5
|
126
|
119
|
7
|
49
|
|
6
|
122
|
126
|
4
|
16
|
|
7
|
117
|
122
|
5
|
25
|
|
8
|
123
|
117
|
6
|
36
|
|
9
|
121
|
123
|
2
|
4
|
|
10
|
124
|
121
|
3
|
9
|
|
|
|
|
+6
|
150
|
(RUMUS LEWAT)
The control limits are 2(4.33) 8.66.
The forecast for period 11 was 124. Demand turned out to be 125, for an
error of 125 124 1. This is within the limits of 8.66. If the next demand is 130 and the
naive forecast is 125 (based on the period 11 demand of 125), the error is 5. Again, this is within the limits, so you
cannot conclude the forecast is not working properly. With more values—at least
five or six—you could plot the errors to see whether you could detect any
patterns suggesting the presence of nonrandomness.
1. What are the main advantages that
quantitative techniques for forecasting have over qualitative techniques? What
limitations do quantitative techniques have?
2. What are some of the consequences of poor
forecasts? Explain.
3. List the specific weaknesses of each of
these approaches to developing a forecast:
a. Consumer
surveys.
b. Salesforce
composite.
c. Committee of
managers or executives.
4. Why are forecasts generally wrong?
5. What is the purpose of establishing control
limits for forecast errors?
6. What factors would you consider in deciding
whether to use wide or narrow control limits for forecasts?
7. Contrast the use of MAD and MSE in
evaluating forecasts.
8. What advantages as a forecasting tool does
exponential smoothing have over moving averages?
9. How does the number of periods in a moving
average affect the responsiveness of the forecast?
10. What factors enter into the
choice of a value for the smoothing constant in exponential smoothing?
11. How accurate is your local
five-day weather forecast? Support your answer with actual data.
12. Explain how using a
centered moving average with a length equal to the length of a season eliminates
seasonality from a time series.
13. Contrast the terms sales
and demand.
14. Contrast the reactive and
proactive approaches to forecasting. Give several examples of types of
organizations or situations in which each type is used.
15. Explain how flexibility in
production systems relates to the forecast horizon and forecast accuracy.
16. How is forecasting in the
context of a supply chain different from forecasting for just a single
organization? List possible supply chain benefits and discuss potential
difficulties in doing supply chain forecasting.
17. Which type of forecasting
approach, qualitative or quantitative, is better?
18. Suppose a software producer
is about to release a new version of its popular software. What infor- mation
do you think it would take into account in forecasting initial sales?
19. Choose the type of
forecasting technique (survey, Delphi, averaging, seasonal, naive, trend, or
associative) that would be most appropriate for predicting
a. Demand for
Mother’s Day greeting cards.
b. Popularity
of a new television series.
c. Demand for
vacations on the moon.
d. The impact
a price increase of 10 percent would have on sales of orange marmalade.
e. Demand for
toothpaste in a particular supermarket.
TAKING STOCK
1. Explain the trade-off
between responsiveness and stability in a forecasting system that uses
time-series data.
2. Who needs to be involved in
preparing forecasts?
3. How has technology had an
impact on forecasting?
CRITICAL THINKING EXERCISES
1. It has been said that
forecasting using exponential smoothing is like driving a car by looking in the
rear-view mirror. What are the conditions that would have to exist for driving
a car that are analogous to the assumptions made when using exponential
smoothing?
2. What capability would an
organization have to have to not need forecasts?
3. When a new business is
started, or a patent idea needs funding, venture capitalists or investment
bankers will want to see a business plan that includes forecast information
related to a profit and loss statement. What type of forecasting information do
you suppose would be required?
4. Discuss how you would manage
a poor forecast.
5. Omar has heard from some of
his customers that they will probably cut back on order sizes in the next
quarter. The company he works for has been reducing its sales force due to
falling demand and he worries that he could be next if his sales begin to fall
off. Believing that he may be able to convince his customers not to cut back on
orders, he turns in an optimistic forecast of his next quarter sales to his
manager. What are the pros and cons of doing that?
6. Give three examples of
unethical conduct involving forecasting and the ethical principle each
violates.
PROBLEMS
1.
A commercial bakery has recorded sales (in
dozens) for three products, as shown below:
|
Day
|
Blueberry Muffins
|
Cinnamon Buns
|
Cupcakes
|
|
1
|
30
|
18
|
45
|
|
2
|
34
|
17
|
26
|
|
3
|
32
|
19
|
27
|
|
4
|
34
|
19
|
23
|
|
5
|
35
|
22
|
22
|
|
6
|
30
|
23
|
48
|
|
7
|
34
|
23
|
29
|
|
8
|
36
|
25
|
20
|
|
9
|
29
|
24
|
14
|
|
10
|
31
|
26
|
18
|
|
11
|
35
|
27
|
47
|
|
12
|
31
|
28
|
26
|
|
13
|
37
|
29
|
27
|
|
14
|
34
|
31
|
24
|
|
15
|
33
|
33
|
22
|
a. Predict orders for the
following day for each of the products using an appropriate naive method. Hint:
Plot each data set.
b. What should the use of sales
data instead of demand imply?
2. National Scan, Inc., sells
radio frequency inventory tags. Monthly sales for a seven-month period were as
follows:
Month Sales (000 units)
|
Feb.
|
19
|
|
Mar.
|
18
|
|
Apr.
|
15
|
|
May
|
20
|
|
Jun.
|
18
|
|
Jul.
|
22
|
|
Aug.
|
20
|
a. Plot the monthly data on a
sheet of graph paper.
b. Forecast September sales
volume using each of the following:
(1) The naive
approach.
(2) A five
month moving average.
(3) A
weighted average using .60 for August, .30 for July, and .10 for June.
(4) Exponential smoothing with a smoothing
constant equal to .20, assuming a a March forecast of 19(000).
(5) A linear
trend equation.
c. Which method seems least
appropriate? Why? (Hint: Refer to your plot from part a. )
d. What does use of the term
sales rather than demand presume?
3. A dry cleaner uses
exponential smoothing to forecast equipment usage at its main plant. August
usage was forecasted to be 88 percent of capacity; actual usage was 89.6
percent of capacity. A smoothing constant of .1 is used.
a. Prepare a
forecast for September.
b. Assuming
actual September usage of 92 percent, prepare a forecast for October usage.
4. An electrical contractor’s
records during the last five weeks indicate the number of job requests:
|
Week:
|
1
|
2
|
3
|
4
|
5
|
|
Requests:
|
20
|
22
|
18
|
21
|
22
|
Predict the number of requests for week 6 using each of these methods:
a. Naive.
b. A four-period moving
average.
c. Exponential smoothing with α
= .30. Use 20 for week 2 forecast.
5. A cosmetics manufacturer’s
marketing department has developed a linear trend equation that can be used to
predict annual sales of its popular Hand & Foot Cream.
F t = 80 + 15t
where
F t = Annual
sales (000 bottles)
t is in years
a. Are annual sales increasing
or decreasing? By how much?
b. Predict annual sales for
year 6 using the equation.
6. From the following graph,
determine the equation of the linear trend line for time-share sales for Glib
Marketing, Inc.
(Gambar lewat)
7. Freight car loadings over a
12-year period at a busy port are as follows:
|
Week
|
Number
|
Week
|
Number
|
Week
|
Number
|
|
1
|
220
|
7
|
350
|
13
|
460
|
|
2
|
245
|
8
|
360
|
14
|
475
|
|
3
|
280
|
9
|
400
|
15
|
500
|
|
4
|
275
|
10
|
380
|
16
|
510
|
|
5
|
300
|
11
|
420
|
17
|
525
|
|
6
|
310
|
12
|
450
|
18
|
541
|
a. Determine a linear trend line
for expected freight car loadings.
b. Use the trend equation to
predict expected loadings for weeks 20 and 21.
c. The manager intends to
install new equipment when the volume exceeds 800 loadings per week. Assuming
the current trend continues, the loading volume will reach that level in
approximately what week?
8. Air travel on Mountain Airlines
for the past 18 weeks was:
|
Week
|
Passengers
|
Week
|
Passengers
|
|
1
|
405
|
10
|
440
|
|
2
|
410
|
11
|
446
|
|
3
|
420
|
12
|
451
|
|
4
|
415
|
13
|
455
|
|
5
|
412
|
14
|
464
|
|
6
|
420
|
15
|
466
|
|
7
|
424
|
16
|
474
|
|
8
|
433
|
17
|
476
|
|
9
|
438
|
18
|
482
|
a. Explain why an averaging
technique would not be appropriate for forecasting.
b. Use an appropriate technique
to develop a forecast for the expected number of passengers for the next three
weeks.
9. a. Obtain the linear trend
equation for the following data on new checking accounts at Fair Savings Bank
and use it to predict expected new checking accounts for periods 16 through 19.
|
Period
|
New Accounts
|
Period
|
New Accounts
|
Period
|
New Accounts
|
|
1
|
200
|
6
|
232
|
11
|
281
|
|
2
|
214
|
7
|
248
|
12
|
275
|
|
3
|
211
|
8
|
250
|
13
|
280
|
|
4
|
228
|
9
|
253
|
14
|
288
|
|
5
|
235
|
10
|
267
|
15
|
310
|
b. Use trend-adjusted smoothing
with α = .3 and β = .2 to smooth the new account data in part a. What
is the forecast for period 16?
10. After plotting demand for
four periods, an emergency room manager has concluded that a trendadjusted
exponential smoothing model is appropriate to predict future demand. The
initial estimate of trend is based on the net change of 30 for the three
periods from 1 to 4, for an average of
10 units. Use .5 and .4, and TAF of 250 for period 5. Obtain forecasts for periods 6 through 10.
|
Period
|
Actual
|
Period
|
Actual
|
|
1
|
210
|
6
|
265
|
|
2
|
224
|
7
|
272
|
|
3
|
229
|
8
|
285
|
|
4
|
240
|
9
|
294
|
|
5
|
255
|
10
|
|
11. A manager of a store that
sells and installs spas wants to prepare a forecast for January, February, and
March of next year. Her forecasts are a combination of trend and seasonality.
She uses the following equation to estimate the trend component of monthly
demand: Ft = 70 + 5t, where t = 0 in June of last year.
Seasonal relatives are 1.10 for January, 1.02 for February, and .95 for March.
What demands should she predict?
12. The following equation
summarizes the trend portion of quarterly sales of condominiums over a long
cycle. Sales also exhibit seasonal variations. Using the information given,
prepare a forecast of sales for each quarter of next year (not this year), and
the first quarter of the year following that.
Ft = 40 - 6.5t + 2t2
where
Ft = Unit sales
t = 0 at the first quarter of last year
|
Quarter
|
Relative
|
|
1
|
1.1
|
|
2
|
1.0
|
|
3
|
.6
|
|
4
|
1.3
|
13. Compute seasonal relatives
for this data using the SA method:
|
Quarter
|
Year 1
|
Year 2
|
Year 3
|
Year 4
|
|
1
|
2
|
3
|
7
|
4
|
|
2
|
6
|
10
|
18
|
14
|
|
3
|
2
|
6
|
8
|
8
|
|
4
|
5
|
9
|
15
|
11
|
14. A tourist center is open
on weekends (Friday, Saturday, and Sunday). The owner-manager hopes to improve
scheduling of part-time employees by determining seasonal relatives for each of
these days. Data on recent traffic at the center have been tabulated and are
shown in the following table:
|
|
|
|
WEEK
|
|
|
|
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Friday
|
149
|
154
|
152
|
150
|
159
|
163
|
|
Saturday
|
250
|
255
|
260
|
268
|
273
|
276
|
|
Sunday
|
166
|
162
|
171
|
173
|
176
|
183
|
a. Develop
seasonal relatives for the shop using the centered moving average method.
b. Develop
seasonal relatives for the shop using the SA method (see Example 8B).
c. Explain why
the results of the two methods correlate the way they do.
15. The manager of a
fashionable restaurant open Wednesday through Saturday says that the restau-
rant does about 35 percent of its business on Friday night, 30 percent on
Saturday night, and 20 percent on Thursday night. What seasonal relatives would
describe this situation?
16. Obtain estimates of daily
relatives for the number of customers at a restaurant for the evening meal,
given the following data.
a. Use the
centered moving average method. (Hint: Use a seven-day moving average.)
b. Use the SA
method.
128
Chapter Three Forecasting
|
Day
|
Number
Served
|
Day
|
Number
Served
|
|
1
|
80
|
15
|
84
|
|
2
|
75
|
16
|
78
|
|
3
|
78
|
17
|
83
|
|
4
|
95
|
18
|
96
|
|
5
|
130
|
19
|
135
|
|
6
|
136
|
20
|
140
|
|
7
|
40
|
21
|
44
|
|
8
|
82
|
22
|
87
|
|
9
|
77
|
23
|
82
|
|
10
|
80
|
244
|
88
|
|
11
|
94
|
25
|
99
|
|
12
|
131
|
26
|
144
|
|
13
|
137
|
27
|
144
|
|
14
|
42
|
28
|
48
|
17. A pharmacist has been
monitoring sales of a certain over-the-counter pain reliever. Daily sales
during the last 15 days were
|
Day:
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
Number sold:
|
36
|
38
|
42
|
44
|
48
|
49
|
50
|
49
|
52
|
|
Day:
|
10
|
11
|
12
|
13
|
14
|
15
|
|
|
|
|
Number sold:
|
48
|
52
|
55
|
54
|
56
|
57
|
|
|
|
a. Which method would you
suggest using to predict future sales—a linear trend equation or trend-adjusted
exponential smoothing? Why?
b. If you learn that on some
days the store ran out of the specific pain reliever, would that knowledge
cause you any concern? Explain.
c. Assume that the data refer
to demand rather than sales. Using trend-adjusted smoothing with an initial
forecast of 50 for day 8, an initial trend estimate of 2, and α = β =.3,
develop forecasts for days 9 through 16. What is the MSE for the eight
forecasts for which there are actual data?
18. New car sales for a dealer
in Cook County, Illinois, for the past year are shown in the following table,
along with monthly indexes (seasonal relatives), which are supplied to the
dealer by the regional distributor.
|
Month
|
units Sold
|
Index
|
Month
|
units Sold
|
Index
|
|
Jan.
|
640
|
0.80
|
Jul
|
765
|
0.90
|
|
Feb.
|
648
|
0.80
|
Aug.
|
805
|
1.15
|
|
Mar.
|
630
|
0.70
|
Sept.
|
840
|
1.20
|
|
Apr.
|
761
|
0.94
|
Oct.
|
828
|
1.20
|
|
May.
|
735
|
0.89
|
Nov.
|
840
|
1.25
|
|
Jun.
|
850
|
1.00
|
Dec.
|
800
|
1.25
|
a. Plot the data. Does there
seem to be a trend?
b. Deseasonalize car sales.
c. Plot the deseasonalized data
on the same graph as the original data. Comment on the two graphs.
d. Assuming no proactive
approach on the part of management, discuss (no calculations necessary) how you
would forecast sales for the first three months of the next year.
e. What action might management
consider based on your findings in part b?
19. The following table shows
a tool and die company’s quarterly sales for the current year. What sales would
you predict for the first quarter of next year? Quarter relatives are SR1 =
1.10, SR2 = .99, SR3 = .90, and SR4 = 1.01.
|
Quarter
|
1
|
2
|
3
|
4
|
|
Sales
|
88
|
99
|
108
|
141.4
|
Table 3.4
|
Forecasting Method
|
Amount of Historical Data
|
Data Pattern
|
Forecast Horizon
|
Preparation Time
|
Personnel Background
|
|
Moving average
|
2 to 30 observations
|
Variation around an average
|
Short
|
Short
|
Little sophistication
|
|
Simple exponential smoothing
|
5 to 10 observations
|
Variation around an average
|
Short
|
Short
|
Little sophistication
|
|
Trend-adjusted exponential smoothing
|
10 to 15 observations
|
Trend
|
Short to medium
|
Short
|
moderate sophistication
|
|
Trend models
|
10 to 20; for
seasonality at
east 5 per season
|
Trend
|
Short to medium
|
Short
|
moderate sophistication
|
|
Seasonal
|
Enough to see
2 peaks and
troughs
|
Handles cyclical
and seasonal
patterns
|
Short to medium
|
Short to moderate
|
Little sophistication
|
|
Causal regression models
|
10 observations per
Independent
variable
|
Can handle
complex patterns
|
Short, medium, or long
|
Long development
time, short time
for implementation
|
Considerable sophistication
|
Table 3.5
|
Factor
|
Short Range
|
Intermediate Range
|
Long Range
|
|
1. Frequency
|
Often
|
Occasional
|
|
|
2. Level of aggregation
|
Item
|
Product family
|
Total output
Type of
product/service
|
|
3. Type of model
|
Smoothing
Projection
Regression
|
Projection Seasonal Regression
|
Managerial judgment
|
|
4. Degree of management
involvement
|
Low
|
Moderate
|
High
|
|
5. Cost per forecast
|
Low
|
Moderate
|
High
|
TABLE 3.6 Forecasting
approaches
|
|
Approaches
|
Brief Description
|
|
Judgment/opinion:
|
Consumer surveys
|
Questioning consumers on future plans
|
|
|
Direct-contact composites
|
Joint estimates obtained from salespeople or customer service people
|
|
|
Executive opinion
|
Finance, marketing, and manufacturing managers join to prepare
forecast
|
|
|
Delphi technique
|
Series of questionnaires answered anonymously by knowledgeable
people; successive questionnaires are based on information obtained from
previous surveys
|
|
|
Outside opinion
|
Consultants or other outside experts prepare the forecast
|
|
Statistical:
|
Time series:
|
|
|
|
·
Naive
|
Next value in a series will equal the previous value in a comparable
period
|
|
|
·
Moving averages
|
Forecast is based on an average of recent values
|
|
|
·
Exponential smoothing
|
Sophisticated form of weighted moving average
|
|
|
Associative models:
|
|
|
|
Simple regression
|
Values of one variable are used to predict values of a dependent
variable
|
|
|
Multiple regression
|
Two or more variables are used to predict values of a dependent
variable
|
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