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For this assignment, plan to identify the process early in the week in order for you to compile data which can then be presented in the final assignment. Submit the required content to include the data and flowchart in one final document.

Please be sure to consider a process that you would perform daily, and only present the data for the week of class.

Please see attached grading guide for criteria and assigned points.

Select a process you perform daily, but would like to spend less time doing, such as driving to work.

Design a flowchart and provide written analysis by using any appropriate tool.

Comment on the factors that affect the process design.

Identify at least one metric to measure the process.

Describe which forecasting methods would be applicable.

Discuss how one could manage this process by using PERT/CPM techniques.

Submit your flowchart for the process and the data collected at the end of the week by collecting data for the identified metric every day of the workweek.

Use APA format to include a reference page with the course text at a minimum.

Individual Assignment: Flowchart for a Process
Purpose of Assignment
The purpose of this assignment is to apply quality-management tools to help examine a process.
Students will design a flow chart, comment on the factors affecting the process design, and identify a
metric to evaluate the success of the process.
Grading Guide
Not Met
The student selects a process they perform
daily but would like to spend less time doing,
such as driving to work. (5 pts)
The student designs a flowchart and provides
written analysis using an appropriate tool. (10
The student comments on the factors that
affect the process design. (5 pts)
The student identifies at least one metric to
measure the process. (5 pts)
The student describes which forecasting
methods would be applicable. (10 pts)
The student discusses how one could
manage this process by using PERT/CPM
techniques. (10 pts)
The student submits their flowchart for the
process and the data collected at the end of
the week by collecting data for the identified
metric every day of the workweek. (10 pts)
Writing Guidelines
The paper—including tables and graphs,
headings, title page, and reference page—is
consistent with APA formatting guidelines and
Not Met
Writing Guidelines
Not Met
meets course-level requirements. (5 pts)
Intellectual property is recognized with in-text
citations and a reference page. (5 pts)
Paragraph and sentence transitions are
present, logical, and maintain the flow
throughout the paper. (5 pts)
Sentences are complete, clear, and concise.
(5 pts)
Rules of grammar and usage are followed
including spelling and punctuation. (5 pts)
Assignment Total
Additional comments:
Part 2 Managing Customer
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8 Forecasting
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Accurate forecasting is crucial to maintaining the proper amount of product
in the supply chain. Kimberly-Clark recently incorporated demand-signal data
—information on actual consumer sales—into its forecasting system and
greatly increased the accuracy of the forecasts. Here a worker moves
pallets of paper products at a Kimberly-Clark warehouse in Beech Island,
South Carolina.
Annette M. Drowlette/Agusta Chronicle/ZUMAPRESS.com/Newscom
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What do Kleenex tissues, Huggies diapers, and Scott paper
towels all have in common? They are all produced by
Kimberly-Clark, a $21 billion multi-national company based in
Irving, Texas. With 106 production and warehouse facilities
worldwide one can only imagine the complexity of ensuring
that retail customers located in 175 countries receive their
orders on time. Any time the retailer’s inventories are out of
sync with production forecasts, it can have a dramatic effect
on Kimberly-Clark’s bottom line: empty shelves at the retail
level force consumers to seek out competitors’ products
while too much inventory at Kimberly-Clark is very costly. For
example, during the high-volume flu season a one-day
reduction in safety stock inventories translates into a $10
million savings across the supply chain network. It is no
wonder that forecast accuracy is a top priority at KimberlyClark. Forecast errors drive the need for safety stocks
(greater forecast errors equate to greater uncertainty in
demands) and result in inefficient operations and higher
costs. Consequently, Kimberly-Clark undertook a major
project to improve its forecasting performance.
Prior to the onset of the project, forecasts were based on
historical shipment data. The shipments were geared to
satisfy actual customer orders. Intuitively, those data should
be good for making forecasts of future orders. However,
actual shipments may be subject to all sorts of anomalies
such as supply disruptions, factory or transportation capacity
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limits, or severe weather, all of which could delay the
shipments and miss the dates the customer actually wanted
the product. Perhaps the biggest problem with using past
shipment data for making forecasts is that it is backwardlooking; forecasts assume that what happened in the past
will happen in the future. Such an approach will miss spikes
in consumer demand. For example, Hurricane Sandy
pummeled the east coast in 2012 and caused a drop in the
sales of paper products in the northeast region. Estimating
weekly sales on the basis of historical shipment data when
there was no storm will be fraught with errors; even
managerial judgment to temper the forecasts will not provide
much relief. When would consumers in the northeast turn
their attention from buying generators and portable lighting
products to paper towels and diapers again?
The project to improve forecasting performance was a major
part of a larger project to create a demand-driven supply
chain. Kimberly-Clark reduced the number of production
facilities and warehouses, opened new larger facilities, and
repurposed others to handle a smaller set of customers or to
ship only promotional items. All told, this design not only
improved logistical efficiency but also simplified the
forecasting effort. The key, however, to creating a demanddriven supply chain was to incorporate demand-signal data—
information about actual consumer purchases—into its plans
to resupply retailers with product. In close collaboration with
Terra Technology, whose Multi-Enterprise Demand Sensing
(MDS) system was chosen for the forecasting tool, KimberlyClark incorporated the point-of-sale data (POS) from three of
its largest retail customers in North America. The software
uses that data along with inventory in the distribution
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channel, shipments from warehouses, and the retailer’s own
forecasts to create a daily operational forecast. These inputs
are re-evaluated weekly for their influence on the forecast.
For example, POS might be the best predictor of a shipment
forecast on a three-week horizon, but actual orders could be
the best predictor for the current week. A new metric for
evaluating forecast performance was created; it was defined
as the absolute difference between shipments and forecast
and reported as a percentage of shipments. Using that
metric and the new forecasting system, Kimberly-Clark
observed forecast error reductions as high as 35 percent in
the first week of the horizon and 20 percent on a two-week
horizon. These forecast error reductions can translate into
one to three weeks reduction in safety stocks.
Sources: James A. Cooke, “Kimberly-Clark Connects Its supply Chain to the Store Shelf,” DC Velocity, April 10, 2013; Paul Taylor,
“Demand Forecasting Pays Off for Kimberly-Clark,” Financial Times, September 10, 2011; Heather Clancy, “Kimberly-Clark Makes
Sense of Demand,” CGT, http://consumergoods.edgl.com; Kimberly-Clark Annual Report, 2013, http://www.Kimberly-Clark.com.
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Learning Goals
After reading this chapter, you should be able to:
1. Explain how managers can change demand patterns.
2. Describe the two key decisions on making forecasts.
3. Calculate the five basic measures of forecast errors.
4. Compare and contrast the four approaches to
judgmental forecasting.
5. Use regression to make forecasts with one or more
independent variables.
. Make forecasts using the five most common
statistical approaches for time-series analysis.
7. Describe the six steps in a typical forecasting
Balancing supply and demand begins with making accurate
forecasts, and then reconciling them across the supply chain
as shown by Kimberly-Clark. A forecast is a prediction of
future events used for planning purposes. Planning, on the
other hand, is the process of making management decisions
on how to deploy resources to best respond to the demand
forecasts. Forecasting methods may be based on
mathematical models that use available historical data, or on
qualitative methods that draw on managerial experience and
judgments, or on a combination of both.
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A prediction of future events used for
planning purposes.
In this chapter our focus is on demand forecasts. We begin
with different types of demand patterns. We examine
forecasting methods in three basic categories: (1) judgment,
(2) causal, and (3) time-series methods. Forecast errors are
defined, providing important clues for making better
forecasts. We next consider the forecasting techniques
themselves, and then how they can be combined to bring
together insights from several sources. We conclude with
overall processes for making forecasts and designing the
forecasting system.
Forecasts are useful for both managing processes and
managing supply chains. At the supply chain level, a firm
needs forecasts to coordinate with its customers and
suppliers. At the process level, output forecasts are needed to
design the various processes throughout the organization,
including identifying and dealing with in-house bottlenecks.
As you might imagine, the organization-wide forecasting
process cuts across functional areas. Forecasting overall
demand typically originates with marketing, but internal
customers throughout the organization depend on forecasts
to formulate and execute their plans as well. Forecasts are
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critical inputs to business plans, annual plans, and budgets.
Finance needs forecasts to project cash flows and capital
requirements. Human resources uses forecasts to anticipate
hiring and training needs. Marketing is an important source
for sales forecast information because it is closest to
external customers. Operations and supply chain managers
need forecasts to plan output levels, purchases of services
and materials, workforce and output schedules, inventories,
and long-term capacities. Managers at all levels need
estimates of future demands, so that they can plan activities
that are consistent with the firm’s competitive priorities.
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Managing Demand
Before we get into the tools and techniques for forecasting demands, it is
important to understand that the timing and sizing of customer demand
can often be manipulated. Accurately forecasting customer demand is a
difficult task because the demand for services and goods can vary greatly.
For example, demand for lawn fertilizer predictably increases in the spring
and summer months; however, the particular weekends when demand is
heaviest may depend on uncontrollable factors such as the weather. These
demand swings are costly to satisfy for any process, even if they are
predictable. However, managers can often do two things to alleviate the
pains of demand swings. First, understand the demand pattern they are
facing; second, employ one or more options to alleviate any avoidable
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Using Operations to Create Value
Managing Processes
Process Strategy and Analysis
Quality and Performance
Capacity Planning
Constraint Management
Lean Systems
Project Management
Managing Customer Demand
Inventory Management
Operations Planning and Scheduling
Resource Planning
Managing Supply Chains
Supply Chain Design
Supply Chain Logistic Networks
Supply Chain Integration
Supply Chain Sustainability
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Demand Patterns
Forecasting demand requires uncovering the underlying patterns from
available information. The repeated observations of demand for a service
or product in their order of occurrence form a pattern known as a time
series . There are five basic patterns of most demand time series:
time series
The repeated observations of demand for a service
or product in their order of occurrence.
1. Horizontal. The fluctuation of data around a constant mean.
2. Trend. The systematic increase or decrease in the mean of the
series over time.
3. Seasonal. A repeatable pattern of increases or decreases in
demand, depending on the time of day, week, month, or season.
4. Cyclical. The less predictable gradual increases or decreases in
demand over longer periods of time (years or decades).
5. Random. The unforecastable variation in demand.
Cyclical patterns arise from two influences. The first is the business cycle,
which includes factors that cause the economy to go from recession to
expansion over a number of years. The other influence is the service or
product life cycle, which reflects the stages of demand from development
through decline. Business cycle demand is difficult to predict because it is
affected by national or international events.
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The four patterns of demand—horizontal, trend, seasonal, and cyclical—
combine in varying degrees to define the underlying time pattern of
demand for a service or product. The fifth pattern,
Figure 8.1 Patterns of Demand
random variation, results from chance causes and thus, cannot be
predicted. Random variation is an aspect of demand that makes every
forecast ultimately inaccurate. Figure 8.1 shows the first four patterns of
a demand time series, all of which contain random variations.
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1270131 – Pearson Education Limited ©
Demand Management Options
Matching supply with demand becomes a challenge when forecasts call
for uneven demand patterns—and uneven demand is more the rule than the
exception. Demand swings can be from one month to the next, one week to
the next, or even one hour to the next. Peaks and valleys in demand are
costly or can cause poor customer service. Air New Zealand can lose sales
because capacity is exceeded for one of its flights, while another of its
flights to the same destination at about the same time has many empty
seats. If nothing is done to even out demand, sales are lost or greater
capacity cushions might be needed. All come at an extra cost. Here we
deal with demand management , the process of changing demand
patterns using one or more demand options.
demand management
The process of changing demand patterns using
one or more demand options.
Various options are available in managing demand, including
complementary products, promotional pricing, prescheduled appointments,
reservations, revenue management, backlogs, backorders, and stockouts.
The manager may select one or more of them, as we illustrate below.
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Complementary Products
One demand option for a company to even out the load on resources is to
produce complementary products , or services that have similar resource
requirements but different demand cycles. For example, manufacturers of
matzoh balls for the Jewish Passover holiday are in a seasonal business.
The B. Manischewitz Company, a kosher foods manufacturer in Jersey City,
New Jersey, previously experienced 40 percent of its annual sales for the 8day Passover holiday alone. It expanded toward markets with year-round
appeal such as low-carb, low-fat foods, including canned soups and
crackers, borscht, cake mixes, dressing and spreads, juices, and
complementary products
Services or products that have similar resource
requirements but different demand cycles.
For service providers, a city parks and recreation department can
counterbalance seasonal staffing requirements for summer activities by
offering ice skating, tobogganing, or indoor activities during the winter
months. The key is to find services and products that can be produced with
the existing resources and can level off the need for resources over the
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Promotional Pricing
Promotional campaigns are designed to increase sales with creative
pricing. Examples include automobile rebate programs, price reductions
for winter clothing in the late summer months, reduced prices for hotel
rooms during off-peak periods, and “two-for-the-price-of-one” automobile
tire sales. Lower prices can increase demand for the product or service
from new and existing customers during traditional slack periods or
encourage customers to move up future buying.
Prescheduled Appointments
Service providers often can schedule customers for definite periods of
order fulfillment. With this approach, demand is leveled to not exceed
supply capacity. An appointment system assigns specific times for service
to customers. The advantages of this method are timely customer service
and the high utilization of service personnel.
Doctors, dentists, lawyers, and automobile repair shops are examples of
service providers that use appointment systems. Doctors can use the
system to schedule parts of their day to visit hospital patients, and lawyers
can set aside time to prepare cases. Care must be taken to tailor the length
of appointments to individual customer needs rather than merely
scheduling customers at equal time intervals.
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Reservation systems, although quite similar to appointment systems, are
used when the customer actually occupies or uses facilities associated
with the service. For example, customers reserve hotel rooms,
automobiles, airline seats, and concert seats. The major advantage of
reservation systems is the lead time they give service managers and the
ability to level demand. Managers can deal with no-shows with a blend of
overbooking, deposits, and cancellation penalties. Sometimes overbooking
means that a customer with reservations cannot be served as promised. In
such cases, bonuses can be offered for compensation. For example, an
airline passenger might not only get on the next available flight, but also
may be given a free ticket for a second flight sometime in the future.
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Revenue Management
A specialized combination of the pricing and reservation options for
service providers is revenue management. Revenue management
(sometimes called yield management) is the process of varying price at the
right time for different customer segments to maximize revenues
generated from existing supply capacity. It works best if customers can be
segmented, prices can be varied by segment, fixed costs are high, variable
costs are low, service duration is predictable, and capacity is lost if not
used (sometimes called perishable capacity). Airlines, hotels, cruise lines,
restaurants (early-bird specials), and rental cars are good examples.
Computerized reservation systems can make hour-by-hour updates, using
decision rules for opening or closing price classes depending on the
difference between supply and continually updated demand forecasts. In
the airlines industry, prices are lowered if a particular airline flight is not
selling as fast as expected, until more seats are booked. Alternately, if
larger than expected demand is developing, prices for the remaining seats
may be increased. Last-minute business travelers pay the higher prices,
whereas leisure travelers making reservations well in advance and staying
over the weekend get the bargain prices. Southwest Airlines now segments
its customers by creating a “Business Select” ticket class that rewards
more perks to frequent fliers willing to pay higher prices.
revenue management
Varying price at the right time for different
customer segments to maximize revenues yielded
by existing supply capacity.
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Much like the appointments or reservations of service providers, a
backlog is an accumulation of customer orders that a manufacturer has
promised for delivery at some future date. Manufacturers in the supply
chain that maintain a backlog of orders as a normal business practice can
allow the backlog to grow during periods of high demand and then reduce
it during periods of low demand. Airplane manufacturers do not promise
instantaneous delivery, as do wholesalers or retailers farther forward in the
supply chain. Instead, they impose a lead time between when the order is
placed and when it is delivered. For example, an automotive parts
manufacturer may agree to deliver to the repair department of a car
dealership a batch of 100 door latches for a particular car model next
Tuesday. The parts manufacturer uses that due date to plan its production
of door latches within its capacity limits. Firms that are most likely to use
backlogs—and increase the size of them during periods of heavy demand—
make customized products and tend to have a make-to-order strategy.
Backlogs reduce the uncertainty of future production requirements and also
can be used to level demand. However, they become a competitive
disadvantage if they get too big.
An accumulation of customer orders that a
manufacturer has promised for delivery at some
future date.
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Backorders and Stockouts
A last resort in demand management is to set lower standards for
customer service, either in the form of backorders or stockouts. Not to be
confused with a backlog, a backorder is a customer order that cannot be
filled when promised or demanded but is filled later. Demand may be too
unpredictable or the item may be too costly to hold it in inventory. Although
the customer is not pleased with the delay, the customer order is not lost
and it is filled at a later date. In contrast, a stockout is an order that
cannot be satisfied, resulting in a loss of the sale. A backorder adds to the
next period’s demand requirement, whereas a stockout does not.
Backorders and stockouts can lead dissatisfied customers to do their
future business with another firm. Generally, backorders and stockouts are
to be avoided.
A customer order that cannot be filled when
promised or demanded but is filled later.
An order that cannot be satisfied, resulting in a loss
of the sale.
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Combinations of demand options can also be used. For example, a
manufacturer of lighting equipment had several products characterized as
“slow movers with spikes,” where only 2 or 3 units were sold for several
weeks, and then suddenly there was a huge order for 10,000 units the next
week. The reason is that their product was purchased by commercial
property managers who might be upgrading the lighting in a large office
building. The result was a forecasting nightmare and having to resort to
high cost supply options to meet the demand spikes. The breakthrough in
solving this problem was to combine the pricing and backlog options.
Contractors are now offered a 3 percent discount (the pricing option) on
any order in excess of 10,000 units that are placed five or more weeks
before they are needed (the backlog option). The advanced warning allows
the manufacturer to smooth out its production processes, saving millions
of dollars annually.
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Key Decisions on Making
Before using forecasting techniques, a manager must make two decisions:
(1) what to forecast, and (2) what type of forecasting technique to select
for different items.
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Deciding What to Forecast
Although some sort of demand estimate is needed for the individual
services or goods produced by a company, forecasting total demand for
groups or clusters and then deriving individual service or product forecasts
may be easiest. Also, selecting the correct unit of measurement (e.g., units,
customers, or machine-hours) for forecasting may be as important as
choosing the best method.
Level of Aggregation
Few companies err by more than 5 percent when forecasting the annual
total demand for all their services or products. However, errors in forecasts
for individual items and shorter time periods may be much higher.
Recognizing this reality, many companies use a two-tier forecasting
system. They first cluster (or “roll up”) several similar services or products
in a process called aggregation , making forecasts for families of
services or goods that have similar demand requirements and common
processing, labor, and materials requirements. Next, they derive forecasts
for individual items, which are sometimes called stock-keeping units. A
stock-keeping unit (SKU) is an individual item or product that has an
identifying code and is held in inventory somewhere along the supply chain,
such as in a distribution center.
The act of clustering several similar services or
products so that forecasts and plans can be made
for whole families.
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Units of Measurement
Rather than using dollars as the initial unit of measurement, forecasts often
begin with service or product units, such as individual products, express
packages to deliver, or customers needing maintenance service or repairs
for their cars. Forecasted units can then be translated to dollars by
multiplying them by the unit price. If accurately forecasting demand for a
service or product is not possible in terms of number of units, forecast the
standard labor or machine-hours required of each of the critical resources.
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Choosing the Type of Forecasting
Forecasting systems offer a variety of techniques, and no one of them is
best for all items and situations. The forecaster’s objective is to develop a
useful forecast from the information at hand with the technique that is
appropriate for the different patterns of demand. Two general types of
forecasting techniques are used: judgment methods and quantitative
methods. Judgment methods translate the opinions of managers, expert
opinions, consumer surveys, and salesforce estimates into quantitative
estimates. Quantitative methods include causal methods, time-series
analysis, and trend projection with regression. Causal methods use
historical data on independent variables, such as promotional campaigns,
economic conditions, and competitors’ actions, to predict demand. Timeseries analysis is a statistical approach that relies heavily on historical
demand data to project the future size of demand and recognizes trends
and seasonal patterns. Trend projection with regression is a hybrid
between a time-series technique and the causal method.
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1270131 – Pearson Education Limited ©
A Moto X phone manufactured by Motorola Mobility. Motorola considerably
improved its demand forecasting process by closely collaborating with its
major retailers, obtaining point-of-sale data from them.
Mark Lennihan/Associated Press
judgment methods
A forecasting method that translates the opinions
of managers, expert opinions, consumer surveys,
and salesforce estimates into quantitative
causal methods
A quantitative forecasting method that uses
historical data on independent variables, such as
promotional campaigns, economic conditions, and
competitors’ actions, to predict demand.
time-series analysis
A statistical approach that relies heavily on
historical demand data to project the future size of
demand and recognizes trends and seasonal
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trend projection with regression
A forecasting model that is a hybrid between a
time-series technique and the causal method.
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Forecast Error
For any forecasting technique, it is important to measure the accuracy of
its forecasts. Forecasts almost always contain errors. Random error results
from unpredictable factors that cause the forecast to deviate from the
actual demand. Forecasting analysts try to minimize forecast errors by
selecting appropriate forecasting models, but eliminating all forms of
errors is impossible.
Forecast error for a given period t is simply the difference found by
subtracting the forecast from actual demand, or
forecast error
The difference found by subtracting the forecast
from actual demand for a given period.
This equation (notice the alphabetical order with
coming before
) is
the starting point for creating several measures of forecast error that cover
longer periods of time.
There are five basic measures of forecast error: CFE, MSE,
, MAD, and
MAPE. Figure 8.2 shows the output from the Error Analysis routine in
Forecasting’s dropdown menu of POM for Windows. Part (a) gives a big
picture view of how well the forecast has been tracking the actual demand.
Part (b) shows the detailed calculations needed to obtain the summary
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error terms. Finally, Part (c) gives the summary error measures summarized
across all 10 time periods, as derived from Part (b).
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Cumulative Sum of Forecast Errors
The cumulative sum of forecast errors (CFE)
forecast error:
measures the total
cumulative sum of forecast errors (CFE)
A measurement of the total forecast error that
assesses the bias in a forecast.
CFE is a cumulative sum. Figure 8.2(b) shows that it is the sum of the
errors for all 10 periods. For any given period, it would be the sum of errors
up through that period. For example, it would be
period 2. CFE is also called the bias error and results from consistent
mistakes—the forecast is always too high or too low. This type of error
typically causes the greatest disruption to planning efforts. For example, if
a forecast is consistently lower than actual demand, the value of CFE will
gradually get larger and larger. This increasingly large error indicates some
systematic deficiency in the forecasting approach. The average forecast
error, sometimes called the mean bias, is simply
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Figure 8.2(a) Graph of Actual and Forecast Demand Using Error Analysis
of Forecasting in POM for Windows
Figure 8.2(b) Detailed Calculations of Forecast Errors
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Dispersion of Forecast Errors
The mean squared error (MSE) , standard deviation of the errors
, and mean absolute deviation (MAD) measure the dispersion of
forecast errors attributed to trend, seasonal, cyclical, or random effects:
mean squared error (MSE)
A measurement of the dispersion of forecast
standard deviation of the errors ( )
A measurement of the dispersion of forecast
mean absolute deviation (MAD)
A measurement of the dispersion of forecast
Figure 8.2(b) shows the squared error in period 1 is 4, and MSE is 87.9
for the whole sample. The standard deviation of the errors, shown as
29.648 in Figure 8.2(b) , is calculated using a separate function available
in Excel. The absolute value of the error in period 2 is 6, and MAD is 8.1
across the whole sample.
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The mathematical symbol is used to indicate the absolute value—that is,
it tells you to disregard positive or negative signs. If MSE, , or MAD is
small, the forecast is typically close to actual demand; by contrast, a large
value indicates the possibility of large forecast errors. The measures do
differ in the way they emphasize errors. Large errors get far more weight in
MSE and because the errors are squared. MAD is a widely used measure
of forecast error and is easily understood; it is merely the mean of the
absolute forecast errors over a series of time periods, without regard to
whether the error was an overestimate or an underestimate.
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Mean Absolute Percent Error
The mean absolute percent error (MAPE) relates the forecast error to
the level of demand and is useful for putting forecast performance in the
proper perspective:
mean absolute percent error (MAPE)
A measurement that relates the forecast error to the
level of demand and is useful for putting forecast
performance in the proper perspective.
For example, an absolute forecast error of 100 results in a larger
percentage error when the demand is 200 units than when the demand is
10,000 units. MAPE is the best error measure to use when making
comparisons between time series for different SKUs. Looking again at
Figure 8.2(b) , the percent error in period 2 is 16.22 percent, and MAPE,
the average over all 10 periods, is 17.062 percent.
Finally, Figure 8.2(c) summarizes the key error terms across all 10 time
periods. They are actually found in selected portions of Figure 8.2(b) .
For example, CFE is
which is in the error column of Figure 8.2(b)
in the TOTALS row. MAD is 8.1, found in the
column and AVERAGE
row. Finally, MAPE is 17.062%, which is in the
column and
Figure 8.2(c) Error Measures
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Example 8.1 Calculating Forecast Error Measures
The following table shows the actual sales of upholstered chairs for a
furniture manufacturer and the forecasts made for each of the last 8
months. Calculate CFE, MSE, , MAD, and MAPE for this product.
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Using the formulas for the measures, we get
Cumulative forecast error (bias):
Average forecast error (mean bias):
Mean squared error:
Standard deviation of the errors:
Mean absolute deviation:
Mean absolute percent error:
A CFE of
indicates that the forecast has a slight bias to
overestimate demand. The MSE, , and MAD statistics provide
measures of forecast error variability. A MAD of 24.4 means that the
average forecast error was 24.4 units in absolute value. The value of ,
27.4, indicates that the sample distribution of forecast errors has a
standard deviation of 27.4 units. A MAPE of 10.2 percent implies that,
on average, the forecast error was within about 10 percent of actual
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demand. These measures become more reliable as the number of
periods of data increases.
Decision Point
Although reasonably satisfied with these forecast performance results,
the analyst decided to test out a few more forecasting methods before
reaching a final forecasting method to use for the future.
Computer Support
Computer support, such as from OM Explorer or POM for Windows, makes
error calculations easy when evaluating how well forecasting models fit
with past data. Errors are measured across past data, often called the
history file in practice. They show the various error measures across the
entire history file for each forecasting method evaluated. They also make
forecasts into the future, based on the method selected.
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Judgment Methods
Forecasts from quantitative methods are possible only when there is
adequate historical data, (i.e., the history file). However, the history file may
be nonexistent when a new product is introduced or when technology is
expected to change. The history file might exist but be less useful when
certain events (such as rollouts or special packages) are reflected in the
past data, or when certain events are expected to occur in the future. In
some cases, judgment methods are the only practical way to make a
forecast. In other cases, judgment methods can also be used to modify
forecasts that are generated by quantitative methods. They may recognize
that one or two quantitative models have been performing particularly well
in recent periods. Adjustments certainly would be called for if the
forecaster has important contextual knowledge. Contextual knowledge is
knowledge that practitioners gain through experience, such as cause-andeffect relationships, environmental cues, and organizational information
that may have an effect on the variable being forecast. Adjustments also
could account for unusual circumstances, such as a new sales promotion
or unexpected international events. They could also have been used to
remove the effect of special one-time events in the history file before
quantitative methods are applied. Four of the more successful judgment
methods are as follows: (1) salesforce estimates, (2) executive opinion,
(3) market research, and (4) the Delphi method.
Salesforce estimates are forecasts compiled from estimates made
periodically by members of a company’s salesforce. The salesforce is the
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group most likely to know which services or products customers will be
buying in the near future and in what quantities. Forecasts of individual
salesforce members can be combined easily to get regional or national
sales estimates. However, individual biases of the salespeople may taint
the forecast. For example, some people are naturally optimistic, whereas
others are more cautious. Adjustments in forecasts may need to be made
to account for these individual biases.
salesforce estimates
The forecasts that are compiled from estimates of
future demands made periodically by members of
a company’s salesforce.
Executive opinion is a forecasting method in which the opinions,
experience, and technical knowledge of one or more managers or
customers are summarized to arrive at a single forecast. All of the factors
going into judgmental forecasts would fall into the category of executive
opinion. Executive opinion can also be used for technological
forecasting . The quick pace of technological change makes keeping
abreast of the latest advances difficult.
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executive opinion
A forecasting method in which the opinions,
experience, and technical knowledge of one or
more managers are summarized to arrive at a
single forecast.
technological forecasting
An application of executive opinion to keep abreast
of the latest advances in technology.
Market research is a systematic approach to determine external
consumer interest in a service or product by creating and testing
hypotheses through data-gathering surveys. Conducting a market research
study includes designing a questionnaire, deciding how to administer it,
selecting a representative sample, and analyzing the information using
judgment and statistical tools to interpret the responses. Although market
research yields important information, it typically includes numerous
qualifications and hedges in the findings.
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market research
A systematic approach to determine external
consumer interest in a service or product by
creating and testing hypotheses through datagathering surveys.
The Delphi method is a process of gaining consensus from a group of
experts while maintaining their anonymity. This form of forecasting is
useful when no historical data are available from which to develop
statistical models and when managers inside the firm have no experience
on which to base informed projections. A coordinator sends questions to
each member of the group of outside experts, who may not even know who
else is participating. The coordinator prepares a statistical summary of the
responses along with a summary of arguments for particular responses.
The report is sent to the same group for another round, and the participants
may choose to modify their previous responses. These rounds continue
until consensus is obtained.
Delphi method
A process of gaining consensus from a group of
experts while maintaining their anonymity.
In the remainder of this chapter, we turn to the commonly used quantitative
forecasting approaches.
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Causal Methods: Linear
Causal methods are used when historical data are available and the
relationship between the factor to be forecasted and other external or
internal factors (e.g., government actions or advertising promotions) can
be identified. These relationships are expressed in mathematical terms and
can be complex. Causal methods are good for predicting turning points in
demand and for preparing long-range forecasts. We focus on linear
regression, one of the best known and most commonly used causal
In linear regression , one variable, called a dependent variable, is related
to one or more independent variables by a linear equation. The dependent
variable (such as demand for door hinges) is the one the manager wants
to forecast. The independent variables (such as advertising
expenditures and new housing starts) are assumed to affect the dependent
variable and thereby “cause” the results observed in the past. Figure 8.3
shows how a linear regression line relates to the data. In technical terms,
the regression line minimizes the squared deviations from the actual data.
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linear regression
A causal method in which one variable (the
dependent variable) is related to one or more
independent variables by a linear equation.
dependent variable
The variable that one wants to forecast.
independent variables
Variables that are assumed to affect the dependent
variable and thereby “cause” the results observed in
the past.
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Figure 8.3 Linear Regression Line Relative to Actual Demand
In the simplest linear regression models, the dependent variable is a
function of only one independent variable and, therefore, the theoretical
relationship is a straight line:
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The objective of linear regression analysis is to find values of a and b that
minimize the sum of the squared deviations of the actual data points from
the graphed line. Computer programs are used for this purpose. For any set
of matched observations for Y and X, the program computes the values of
a and b and provides measures of forecast accuracy. Three measures
commonly reported are (1) the sample correlation coefficient, (2) the
sample coefficient of determination, and (3) the standard error of the
The sample correlation coefficient, r, measures the direction and strength of
the relationship between the independent variable and the dependent
variable. The value of r can range from
A correlation
coefficient of
implies that period-by-period changes in direction
(increases or decreases) of the independent variable are always
accompanied by changes in the same direction by the dependent variable.
An r of
means that decreases in the independent variable are
always accompanied by increases in the dependent variable, and vice
versa. A zero value of r means no linear relationship exists between the
variables. The closer the value of r is to
, the better the regression
line fits the points.
The sample coefficient of determination measures the amount of variation
in the dependent variable about its mean that is explained by the regression
line. The coefficient of determination is the square of the correlation
coefficient, or
. The value of
equations with a value of
ranges from 0.00 to 1.00. Regression
close to 1.00 mean a close fit.
The standard error of the estimate,
, measures how closely the data on
the dependent variable cluster around the regression line. Although it is
similar to the sample standard deviation, it measures the error from the
dependent variable, Y, to the regression line, rather than to the mean. Thus,
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it is the standard deviation of the difference between the actual demand
and the estimate provided by the regression equation.
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Example 8.2 Using Linear Regression to Forecast
Product Demand
The supply chain manager seeks a better way to forecast the demand
for door hinges and believes that the demand is related to advertising
expenditures. The following are sales and advertising data for the past
5 months:
Active Model 8.1 in MyOMLab provides insight on
varying the intercept and slope of the model.
Sales (Thousands of Units)
Advertising (Thousands of $)
The company will spend $1,750 next month on advertising for the
product. Use linear regression to develop an equation and a forecast for
this product.
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We used POM for Windows to determine the best values of a, b, the
correlation coefficient, the coefficient of determination, and the standard
error of the estimate.
The regression equation is
and the regression line is shown in Figure 8.4 . The sample
correlation coefficient, r, is 0.98, which is unusually close to 1.00 and
suggests an unusually strong positive relationship exists between sales
and advertising expenditures. The sample coefficient of determination,
, implies that 96 percent of the variation in sales is explained by
advertising expenditures.
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Figure 8.4 Linear Regression Line for the Sales and Advertising Data
Using POM for Windows
Decision Point
The supply chain manager decided to use the regression model as input
to planning production levels for month 6. As the advertising
expenditure will be $1,750, the forecast for month 6 is
, or 183,016 units.
Often several independent variables may affect the dependent variable.
For example, advertising expenditures, new corporation start-ups, and
residential building contracts all may be important for estimating the
demand for door hinges. In such cases, multiple regression analysis is
helpful in determining a forecasting equation for the dependent variable
as a function of several independent variables. Such models can be
analyzed with POM for Windows or OM Explorer and can be quite useful
for predicting turning points and solving many planning problems.
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Time-Series Methods
Rather than using independent variables for the forecast as regression
models do, time-series methods use historical information regarding only
the dependent variable. These methods are based on the assumption that
the dependent variable’s past pattern will continue in the future. Time-series
analysis identifies the underlying patterns of demand that combine to
produce an observed historical pattern of the dependent variable and then
develops a model to replicate it. In this section, we focus on five statistical
time-series methods that address the horizontal, trend, and seasonal
patterns of demand: simple moving averages, weighted moving averages,
exponential smoothing, trend projection with regression, and multiplicative
seasonal method. Before we discuss statistical methods, let us take a look
at the simplest time-series method for addressing all patterns of demand—
the naïve forecast.
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Naïve Forecast
A method often used in practice is the naïve forecast , whereby the
forecast for the next period
equals the demand for the current
. So if the actual demand for Wednesday is 35 customers, the
forecasted demand for Thursday is 35 customers. Despite its name, the
naïve forecast can perform well.
naïve forecast
A time-series method whereby the forecast for the
next period equals the demand for the current
period, or
The naïve forecast method may be adapted to take into account a demand
trend. The increase (or decrease) in demand observed between the last two
periods is used to adjust the current demand to arrive at a forecast.
Suppose that last week the demand was 120 units and the week before it
was 108 units. Demand increased 12 units in 1 week, so the forecast for
next week would be
. The naïve forecast method
also may be used to account for seasonal patterns. If the demand last July
was 50,000 units, and assuming no underlying trend from one year to the
next, the forecast for this July would be 50,000 units. The method works
best when the horizontal, trend, or seasonal patterns are stable and random
variation is small.
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Horizontal Patterns: Estimating the
We begin our discussion of statistical methods of time-series forecasting
with demand that has no apparent trend, seasonal, or cyclical patterns. The
horizontal pattern in a time series is based on the mean of the demands, so
we focus on forecasting methods that estimate the average of a time
series of data. The forecast of demand for any period in the future is the
average of the time series computed in the current period. For example, if
the average of past demand calculated on Tuesday is 65 customers, the
forecasts for Wednesday, Thursday, and Friday are 65 customers each day.
Consider Figure 8.5 , which shows patient arrivals at a medical clinic
over the past 28 weeks. Assuming that the time series has only a horizontal
and random pattern, one approach is simply to calculate the average of the
data. However, this approach has no adaptive quality if there is a trend,
seasonal, or cyclical pattern. The statistical techniques that do have an
adaptive quality in estimating the average in a time series are (1) simple
moving averages, (2) weighted moving averages, and (3) exponential
smoothing. Another option is the simple average, but it has no adaptive
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Figure 8.5 Weekly Patient Arrivals at a Medical Clinic
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Simple Moving Averages
The simple moving average method simply involves calculating the
average demand for the n most recent time periods and using it as the
forecast for future time periods. For the next period, after the demand is
known, the oldest demand from the previous average is replaced with the
most recent demand and the average is recalculated. In this way, the n
most recent demands are used, and the average “moves” from period to
simple moving average method
A time-series method used to estimate the average
of a demand time series by averaging the demand
for the n most recent time periods.
Specifically, the forecast for period
can be calculated at the end of
period t (after the actual demand for period t is known) as
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Example 8.3 Using the Moving Average Method to
Estimate Average Demand
a. Compute a three-week moving average forecast for the arrival of
medical clinic patients in week 4. The numbers of arrivals for the
past 3 weeks were as follows:
Patient Arrivals
b. If the actual number of patient arrivals in week 4 is 415, what is
the forecast error for week 4?
c. What is the forecast for week 5?
Active Model 8.2 in MyOMLab provides insight on
the impact of varying n using the example in Figure
8.5 .
Tutor 8.1 in MyOMLab provides another example to
practice making forecasts with the moving average
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a. The moving average forecast at the end of week 3 is
b. The forecast error for week 4 is
c. The forecast for week 5 requires the actual arrivals from weeks 2
through 4, the 3 most recent weeks of data.
Decision Point
Thus, the forecast at the end of week 3 would have been 397 patients
for week 4, which fell short of actual demand by 18 patients. The
forecast for week 5, made at the end of week 4, would be 402 patients.
If a forecast is needed now for week 6 and beyond, it would also be for
402 patients.
The moving average method may involve the use of as many periods of
past demand as desired. Large values of n should be used for demand
series that are stable, and small values of n should be used for those that
are susceptible to changes in the underlying average. If n is set to its
lowest level (i.e., 1), it becomes the naïve method.
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Weighted Moving Averages
In the simple moving average method, each demand has the same weight
in the average—namely,
. In the weighted moving average method ,
each historical demand in the average can have its own weight. The sum of
the weights equals 1.0. For example, in a three-period weighted moving
average model, the most recent period might be assigned a weight of 0.50,
the second most recent might be weighted 0.30, and the third most recent
might be weighted 0.20. The average is obtained by multiplying the weight
of each period by the value for that period and adding the products
weighted moving average method
A time-series method in which each historical
demand in the average can have its own weight; the
sum of the weights equals 1.0.
For a numerical example of using the weighted moving average method to
estimate average demand, see Solved Problem 2 and Tutor 8.2 of OM
Explorer in MyOMLab.
The advantage of a weighted moving average method is that it allows you
to emphasize recent demand over earlier demand. (It can even handle
seasonal effects by putting higher weights on prior years in the same
season.) The forecast will be more responsive to changes in the underlying
average of the demand series than the simple moving average forecast.
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Exponential Smoothing
The exponential smoothing method is a sophisticated weighted moving
average method that calculates the average of a time series by implicitly
giving recent demands more weight than earlier demands, all the way back
to the first period in the history file. It is the most frequently used formal
forecasting method because of its simplicity and the small amount of data
needed to support it. Unlike the weighted moving average method, which
requires n periods of past demand and n weights, exponential smoothing
requires only three items of data: (1) the last period’s forecast; (2) the
actual demand for this period; and (3) a smoothing parameter, alpha
which has a value between 0 and 1.0. The equation for the exponentially
smoothed forecast for period
is calculated
exponential smoothing method
A weighted moving average method that calculates
the average of a time series by implicitly giving
recent demands more weight than earlier demands.
The emphasis given to the most recent demand levels can be adjusted by
changing the smoothing parameter. Larger values emphasize recent
levels of demand and result in forecasts more responsive to changes in the
underlying average. Smaller values treat past demand more uniformly
and result in more stable forecasts. Smaller values are analogous to
increasing the value of n in the moving average method and giving greater
weight to past demand. In practice, various values of are tried and the
one producing the best forecasts is chosen.
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Exponential smoothing requires an initial forecast to get started. There are
several ways to get this initial forecast. OM Explorer and POM for Windows
use as a default setting the actual demand in the first period, which
becomes the forecast for the second period. Forecasts and forecast errors
then are calculated beginning with period 2. If some historical data are
available, the initial forecast can be found by calculating the average of
several recent periods of demand. The effect of the initial estimate of the
average on successive estimates of the average diminishes over time.
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Example 8.4 Using Exponential Smoothing to Estimate
Average Demand
a. Reconsider the patient arrival data in Example 8.3 . It is now
the end of week 3, so the actual number of arrivals is known to
be 411 patients. Using
, calculate the exponential
smoothing forecast for week 4.
b. What was the forecast error for week 4 if the actual demand
turned out to be 415?
c. What is the forecast for week 5?
Active Model 8.2 in MyOMLab provides insight on
the impact of varying using the example in
Figure 8.5 .
Tutor 8.3 in MyOMLab provides a new practice
example of how to make forecasts with the
exponential smoothing method.
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a. The exponential smoothing method requires an initial forecast.
Suppose that we take the demand data for the first 2 weeks and
average them, obtaining
as an initial
forecast. (POM for Windows and OM Explorer simply use the
actual demand for the first week as a default setting for the initial
forecast for period 1, and do not begin tracking forecast errors
until the second period). To obtain the forecast for week 4, using
exponential smoothing with
, and
, we calculate the forecast for week 4 as
Thus, the forecast for week 4 would be 392 patients.
b. The forecast error for week 4 is
c. The new forecast for week 5 would be
or 394 patients. Note that we used
, not the integer-value
forecast for week 4, in the computation for
. In general, we
round off (when it is appropriate) only the final result to maintain
as much accuracy as possible in the calculations.
Decision Point
Using this exponential smoothing model, the analyst’s forecasts would
have been 392 patients for week 4 and then 394 patients for week 5
and beyond. As soon as the actual demand for week 5 is known, then
the forecast for week 6 will be updated.
Because exponential smoothing is simple and requires minimal data, it is
inexpensive and attractive to firms that make thousands of forecasts for
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each time period. However, its simplicity also is a disadvantage when the
underlying average is changing, as in the case of a demand series with a
trend. Like any method geared solely to the assumption of a stable
average, exponential smoothing results will lag behind changes in the
underlying average of demand. Higher values may help reduce forecast
errors when there is a change in the average; however, the lags will still
occur if the average is changing systematically. Typically, if large values
) are required for an exponential smoothing application,
chances are good that another model is needed because of a significant
trend or seasonal influence in the demand series.
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Trend Patterns: Using Regression
Let us now consider a demand time series that has a trend. A trend in a
time series is a systematic increase or decrease in the average of the
series over time. Where a significant trend is present, forecasts from naïve,
moving average, and exponential smoothing approaches are adaptive, but
still lag behind actual demand and tend to be below or above the actual
Trend projection with regression is a forecasting model that accounts for
the trend with simple regression analysis. To develop a regression model
for forecasting the trend, let the dependent variable, Y, be a period’s
demand and the independent variable, t, be the time period. For the first
period, let
; for the second period, let
; and so on. The
regression equation is
One advantage of the trend projection with regression model is that it can
forecast demand well into the future. The previous models project demand
just one period ahead, and assume that demand beyond that will remain at
that same level. Of course, all of the models (including the trend projection
with regression model) can be updated each period to stay current. One
apparent disadvantage of the trend with regression model is that it is not
adaptive. The solution to this problem comes when you answer the
following question. If you had the past sales of Ford automobiles since
1920, would you include each year in your regression analysis, giving equal
weight to each year’s sales, or include just the sales for more recent years?
You most likely would decide to include just the more recent years, making
your regression model more adaptive. The trend projection with regression
model can thus be made more or less adaptive by the selection of
historical data periods to include in the same way that moving average
(changing n) or exponential smoothing (changing ) models do.
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The trend projection with regression model can be solved with either the
Trend Projection with Regression Solver or the Time Series Forecasting
Solver in OM Explorer. Both solvers provide the regression coefficients,
coefficient of determination
, error measures, and forecasts into the
future. POM for Windows has an alternative model (we do not cover in the
textbook, although a description is provided in MyOMLab) that includes the
trend, called the Trend-Adjusted Smoothing model.
The Trend Projection with Regression Solver focuses exclusively on trend
analysis. Its graph gives a big-picture view of how well the model fits the
actual demand. Its sliders allow you to control when the regression begins,
how many periods are included in the regression analysis, and how many
periods you want forecasted into the future. The Time Series Forecasting
Solver, on the other hand, covers all time series models, including the trend
projection with regression. It also computes a combination forecast, which
we cover in a subsequent section on using multiple techniques.
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Example 8.5 Using Trend Projection with Regression to
Forecast a Demand Series with a Trend
Medanalysis, Inc., provides medical laboratory services to patients of
Health Providers, a group of 10 family-practice doctors associated with
a new health maintenance program. Managers are interested in
forecasting the number of blood analysis requests per week. Recent
publicity about the damaging effects of cholesterol on the heart has
caused a national increase in requests for standard blood tests. The
arrivals over the last 16 weeks are given in Table 8.1 . What is the
forecasted demand for the next three periods?
Table 8.1 Arrivals at Medanalysis for Last 16 Weeks
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Figure 8.6(a) shows the results using the Trend Projection with
Regression Solver when all 16 weeks are included in the regression
analysis, with Figure 8.6(b) showing the worksheet that goes with it.
Looking at the Results sheet of Figure 8.6(a) , we see that the Y
intercept of the trend line (a) is 28.50 and the slope of the line (b) is
2.35. Thus, the trend equation is
, where t is the time
period for which you are forecasting. The forecast for period 19 is
The error terms are
(which is to be
expected when the regression begins at the same time that error
analysis begins),
, and
. The coefficient of determination
decent at 0.69. The trend line is rising gently and reaches 73 for period
19. Each period the forecast predicts an increase of 2.35 arrivals per
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Figure 8.6(a) Trend Projection with Regression Results
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Figure 8.6(b) Detailed Calculations of Forecast Errors
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Seasonal Patterns: Using Seasonal
Seasonal patterns are regularly repeating upward or downward movements
in demand measured in periods of less than one year (hours, days, weeks,
months, or quarters). In this context, the time periods are called seasons.
For example, customer arrivals at a fast-food shop on any day may peak
between 11 . . and 1 . . and again from 5 . . to 7 . .
An easy way to account for seasonal effects is to use one of the
techniques already described, but to limit the data in the time series to
those time periods in the same season. For example, for a day-of-the-week
seasonal effect, one time series would be for Mondays, one for Tuesdays,
and so on. Such an approach accounts for seasonal effects, but has the
disadvantage of discarding considerable information on past demand.
Other methods are available that analyze all past data, using one model to
forecast demand for all of the seasons. We describe only the multiplicative
seasonal method , whereby an estimate of average demand is multiplied
by seasonal factors to arrive at a seasonal forecast. The four-step
procedure presented here involves the use of simple averages of past
demand, although more sophisticated methods for calculating averages,
such as a moving average or exponential smoothing approach, could be
used. The following description is based on a seasonal pattern lasting one
year and seasons of one month, although the procedure can be used for
any seasonal pattern and season of any length.
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multiplicative seasonal method
A method whereby seasonal factors are multiplied
by an estimate of average demand to arrive at a
seasonal forecast.
1. For each year, calculate the average demand per season by dividing
annual demand by the number of seasons per year.
2. For each year, divide the actual demand for a season by the average
demand per season. The result is a seasonal factor for each season
in the year, which indicates the level of demand relative to the
average demand. For example, a seasonal factor of 1.14 calculated
for April implies that April’s demand is 14 percent greater than the
average demand per month.
3. Calculate the average seasonal factor for each season, using the
results from step 2. Add the seasonal factors for a season and
divide by the number of years of data.
4. Calculate each season’s forecast for next year. Begin by forecasting
next year’s annual demand using the naïve method, moving
averages, exponential smoothing, or trend projection with
regression. Then, divide annual demand by the number of seasons
per year to get the average demand per season. Finally, make the
seasonal forecast by multiplying the average demand per season by
the appropriate seasonal factor found in step 3.
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Example 8.6 Using the Multiplicative Seasonal Method to
Forecast the Number of Customers
The manager of the Stanley Steemer carpet cleaning company needs a
quarterly forecast of the number of customers expected next year. The
carpet cleaning business is seasonal, with a peak in the third quarter
and a trough in the first quarter. The manager wants to forecast
customer demand for each quarter of year 5, based on an estimate of
total year 5 demand of 2,600 customers.
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The following table calculates the seasonal factor for each week.
It shows the quarterly demand data from the past 4 years, as well as the
calculations performed to get the average seasonal factor for each
Seasonal Factor
Seasonal Factor (2)
For example, the seasonal factor for quarter 1 in year 1 is calculated by
dividing the actual demand (45) by the average demand for the whole
. When this is done for all 4 years, we then can
average the seasonal factors for quarter 1 over all 4 years. The result is
a seasonal factor of 0.2043 for quarter 1.
Once seasonal factors are calculated for all four seasons (see last
column in the table on the previous page), we then turn to making the
forecasts for year 5. The manager suggests a forecast of 2,600
customers for the whole year, which seems reasonable given that the
annual demand has been increasing by an average of 400 customers
each year (from 1,000 in year 1 to 2,200 in year 4, or
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. The computed forecast demand is found by extending that trend, and
projecting an annual demand in year 5 of
customers. (This same result is confirmed using the Trend Projection
with Regression Solver of OM Explorer.) The quarterly forecasts are
straight-forward. First, find the average demand forecast for year 5,
which is
Then multiple this average demand by the
average seasonal index, giving us
Figure 8.7 shows the computer solution using the Seasonal
Forecasting Solver in OM Explorer. Figure 8.7(b) , the results,
confirms all of the calculations made above. Notice in Figure 8.7(a) ,
the inputs sheet that a computer demand forecast is provided as a
default for year 5. However, there is an option for user-supplied demand
forecast that overrides the computer-supplied forecast if the manager
wishes to make a judgmental forecast based on additional information.
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Figure 8.7 Demand Forecasts Using the Seasonal Forecasting Solver
of OM Explorer
Decision Point
Using this seasonal method, the analyst makes a demand forecast as
low as 133 customers in the first quarter and as high as 1,300
customers in the third quarter. The season of the year clearly makes a
An alternative to the multiplicative seasonal method is the additive
seasonal method , whereby seasonal forecasts are generated by adding
or subtracting a seasonal constant (say, 50 units) to the estimate of
average demand per season. This approach is based on the assumption
that the seasonal pattern is constant, regardless of average demand. The
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amplitude of the seasonal adjustment remains the same regardless of the
level of demand.
additive seasonal method
A method in which seasonal forecasts are
generated by adding a constant to the estimate of
average demand per season.
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Criteria for Selecting Time-Series
Of all the time series forecasting methods available, which should be
chosen? Forecast error measures provide important information for
choosing the best forecasting method for a service or product. They also
guide managers in selecting the best values for the parameters needed for
the method: n for the moving average method, the weights for the weighted
moving average method, for the exponential smoothing method, and
when regression data begins for the trend projection with regression
method. The criteria to use in making forecast method and parameter
choices include (1) minimizing bias (CFE); (2) minimizing MAPE, MAD, or
MSE; (3) maximizing
for trend projections using regression; (4) using a
holdout sample analysis; (5) using a tracking signal; (6) meeting
managerial expectations of changes in the components of demand; and (7)
minimizing the forecast errors in recent periods. The first three criteria
relate to statistical measures based on historical performance, the fourth is
a test under realistic conditions, the fifth evaluates forecast performance
and the potential need to change the method, the sixth reflects
expectations of the future that may not be rooted in the past, and the
seventh is a way to use whatever method seems to be working best at the
time a forecast must be made.
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Using Statistical Criteria
Statistical performance measures can be used in the selection of which
forecasting method to use. The following guidelines will help when
searching for the best time-series models:
1. For projections of more stable demand patterns, use lower values
or larger n values to emphasize historical experience.
2. For projections of more dynamic demand patterns using the models
covered in this chapter, try higher values or smaller n values. When
historical demand patterns are changing, recent history should be
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Using a Holdout Sample
Often, the forecaster must make trade-offs between bias (CFE) and the
measures of forecast error dispersion (MAPE, MAD, and MSE). Managers
also must recognize that the best technique in explaining the past data is
not necessarily the best technique to predict the future, and that
“overfitting” past data can be deceptive. A forecasting method may have
small errors relative to the history file, but may generate high errors for
future time periods. For this reason, some analysts prefer to use a holdout
sample as a final test (see Experiential Learning Exercise 8.1 at the
end of this chapter). To do so, they set aside some of the more recent
periods from the time series and use only the earlier time periods to
develop and test different models. Once the final models have been
selected in the first phase, they are tested again with the holdout sample.
Performance measures, such as MAD and CFE, would still be used but they
would be applied to the holdout sample. Whether this idea is used or not,
managers should monitor future forecast errors, and modify their
forecasting approaches as needed. Maintaining data on forecast
performance is the ultimate test of forecasting power—rather than how well
a model fits past data or holdout samples.
holdout sample
Actual demands from the more recent time periods
in the time series that are set aside to test different
models developed from the earlier time periods.
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Using a Tracking Signal
A tracking signal is a measure that indicates whether a method of
forecasting is accurately predicting actual changes in demand. The
tracking signal measures the number of MADs represented by the
cumulative sum of forecast errors, the CFE. The CFE tends to be close to 0
when a correct forecasting system is being used. At any time, however,
random errors can cause the CFE to be a nonzero number. The tracking
signal formula is
tracking signal
A measure that indicates whether a method of
forecasting is accurately predicting actual changes
in demand.
Each period, the CFE and MAD are updated to reflect current error, and the
tracking signal is compared to some predetermined limits. The MAD can
be calculated in one of two ways: (1) as the simple average of all absolute
errors (as demonstrated in Example 8.1 ) or (2) as a weighted average
determined by the exponential smoothing method:
If forecast errors are normally distributed with a mean of 0, the relationship
between and MAD is simple:
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This relationship allows use of the normal probability tables to specify
limits for the tracking signal. If the tracking signal falls outside those
limits, the forecasting model no longer is tracking demand adequately. A
tracking system is useful when forecasting systems are computerized
because it alerts analysts when forecasts are getting far from desirable
limits. Figure 8.8 shows tracking signal results for 23 periods plotted on
a control chart. The control chart is useful for determining whether any
action needs to be taken to improve the forecasting model. In the example,
the first 20 points cluster around 0, as we would expect if the forecasts are
not biased. The CFE will tend toward 0. When the underlying characteristics
of demand change but the forecasting model does not, the tracking signal
eventually goes out of control. The steady increase after the 20th point in
Figure 8.8 indicates that the process is going out of control. The 21st
and 22nd points are acceptable, but the 23rd point is not.
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Figure 8.8 Tracking Signal
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Forecasting as a Process
Often companies must prepare forecasts for hundreds or even thousands
of services or products repeatedly. For example, a large network of health
care facilities must calculate demand forecasts for each of its services for
every department. This undertaking involves voluminous data that must be
manipulated frequently. However, software can ease the burden of making
these forecasts and coordinating the forecasts between customers and
suppliers. Many forecasting software packages are available, including
Manugistics, Forecast Pro, and SAS. The forecasting routines in OM
Explorer and POM for Windows give some hint of their capabilities.
Forecasting is not just a set of techniques, but instead a process that must
be designed and managed. While there is no one process that works for
everyone, here we describe two comprehensive processes that can be quite
effective in managing operations and the supply chain.
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A Typical Forecasting Process
Many inputs to the forecasting process are informational, beginning with
the history file on past demand. The history file is kept up-to-date with the
actual demands. Clarifying notes and adjustments are made to the
database to explain unusual demand behavior, such as the impact of
special promotions and closeouts. Often the database is separated into
two parts: base data and nonbase data. The second category reflects
irregular demands. Final forecasts just made at the end of the prior cycle
are entered in the history file so as to track forecast errors. Other
information sources are from salesforce estimates, outstanding bids on
new orders, booked orders, market research studies, competitor behavior,
economic outlook, new product introductions, pricing, and promotions. If
point-of-sale data are used, as is done by Kimberly-Clark in the opening
vignette, then considerable information sharing will take place with
customers. For new products, a history database is fabricated based on the
firm’s experience with prior products and the judgment of personnel.
Outputs of the process are forecasts for multiple time periods into the
future. Typically, they are on a monthly basis and are projected out from six
months to two years. Most software packages have the ability to “roll up”
or “aggregate” forecasts for individual stock-keeping units (SKUs) into
forecasts for whole product families. Forecasts can also be “blown down”
or “disaggregated” into smaller pieces. In a make-to-stock environment,
forecasts tend to be more detailed and can get down to specific individual
products. In a make-to-order environment, the forecasts tend to be for
groups of products. Similarly, if the lead times to buy raw materials and
manufacture a product or provide a service are long, the forecasts go
farther out into the future.
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The forecast process itself, typically done on a monthly basis, consists of
structured steps. These steps often are facilitated by someone who might
be called a demand manager, forecast analyst, or demand/supply planner.
However, many other people are typically involved before the plan for the
month is authorized.
Step 1. The cycle begins mid-month just after the forecasts have
been finalized and communicated to the stakeholders. Now is the
time to update the history file and review forecast accuracy. At the
end of the month, enter actual demand and review forecast accuracy.
Step 2. Prepare initial forecasts using some forecasting software
package and judgment. Adjust the parameters of the software to
find models that fit the past demand well and yet reflect the demand
manager’s judgment on irregular events and information about future
sales pulled from various sources and business units.
Step 3. Hold consensus meetings with the stakeholders, such as
marketing, sales, supply chain planners, and finance. Make it easy
for business unit and field sales personnel to make inputs. Use the
Internet to get collaborative information from key customers and
suppliers. The goal is to arrive at consensus forecasts from all of
the important players.
Step 4. Revise the forecasts using judgment, considering the inputs
from the consensus meetings and collaborative sources.
Step 5. Present the forecasts to the operating committee for review
and to reach a final set of forecasts. It is important to have a set of
forecasts that everybody agrees upon and will work to support.
Step 6. Finalize the forecasts based on the decisions of the
operating committee and communicate them to the important
stakeholders. Supply chain planners are usually the biggest users.
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As with all work activity, forecasting is a process and should be continually
reviewed for improvements. A better process will foster better
relationships between departments such as marketing, sales, and
operations. It will also produce better forecasts. This principle is the first
one in Table 8.2 to guide process improvements.
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Table 8.2 Some Principles for the Forecasting Process
Better processes yield better forecasts.
Demand forecasting is being done in virtually every company, either formally
or informally. The challenge is to do it well—better than the competition.
Better forecasts result in better customer service and lower costs, as well as
better relationships with suppliers and customers.
The forecast can and must make sense based on the big picture, economic
outlook, market share, and so on.
The best way to improve forecast accuracy is to focus on reducing forecast
Bias is the worst kind of forecast error; strive for zero bias.
Whenever possible, forecast at more aggregate levels. Forecast in detail only
where necessary.
Far more can be gained by people collaborating and communicating well
than by using the most advanced forecasting technique or model.
Source: From Thomas F. Wallace and Robert A. Stahl, Sales Forecasting: A New Approach (Cincinnati, OH: T. E. Wallace &
Company, 2002), p. 112. Copyright © 2002 T.E. Wallace & Company. Used with permission.
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Using Multiple Forecasting Methods
Step 2 of the forecasting process relates to preparing an initial forecast.
However, we need not rely on a single forecasting method. Several different
forecasts can be used to arrive at a forecast. Initial statistical forecasts
using several time-series methods and regression are distributed to
knowledgeable individuals, such as marketing directors and sales teams,
(and sometimes even suppliers and customers) for their adjustments. They
can account for current market and customer conditions that are not
necessarily reflected in past data. Multiple forecasts may come from
different sales teams, and some teams may have a better record on
forecast errors than others.
Research during the last two decades suggests that combining forecasts
from multiple sources often produces more accurate forecasts.
Combination forecasts are forecasts that are produced by averaging
independent forecasts based on different methods, different sources, or
different data. It is intriguing that combination forecasts often perform
better over time than even the best single forecasting procedure. For
example, suppose that the forecast for the next period is 100 units from
technique 1 and 120 units from technique 2 and that technique 1 has
provided more accurate forecasts to date. The combination forecast for
next period, giving equal weight to each technique, is 110 units (or
). When this averaging technique is used
consistently into the future, its combination forecasts often will be much
more accurate than those of any single best forecasting technique (in this
example, technique 1). Combining is most effective when the individual
forecasts bring different kinds of information into the forecasting process.
Forecasters have achieved excellent results by weighting forecasts equally,
and this is a good starting point. However, unequal weights may provide
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better results under some conditions. Managerial Practice 8.1 shows how
Fiskars Corporation successfully used combination forecasts.
combination forecasts
Forecasts that are produced by averaging
independent forecasts based on different methods,
different sources, or different data.
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Managerial Practice 8.1 Combination
Forecasts and the Forecasting Process
Fiskars Corporation, which generated more than $1.1 billion in sales
in 2013, is the second oldest incorporated entity in the world and
produces a variety of high-quality products such as garden shears,
pruners, hand tools, scissors, ratchet tools, screwdrivers, and the
like. Business is highly seasonal and prices quite variable. About 10
percent to 15 percent of the annual revenue comes from one-time
promotions, and 25 percent to 35 percent of its products are new
every year. Quality is very important at Fiskars; its scissors were
selected as the Official Net-Cutting Scissors of the NCAA National
Championship in 2014.
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Fiskars Brands, Inc. totally overhauled its forecasting process for
products such as those shown here. It introduced time-series
methods, with much emphasis placed on combination forecasts.
Sales staff added their judgmental modifications, which were
combined with forecasts from several time-series techniques to
produce more accurate forecasts down to the level of the product.
Given the highly volatile demand environment, Fiskars Brands, Inc., a
subsidiary of Fiskars Corporation located in Madison, Wisconsin,
needed to improve its forecasting process. It serves 2,000
customers ranging from large discounters to local craft stores
providing about 2,300 products. Fiskars Brands introduced a
statistical-based analysis in its forecasting process along with a
Web-based business intelligence tool for reporting. It put much
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more emphasis on combination forecasts. Instead of asking
members of the sales staff to provide their own forecasts, forecasts
were sent to them, and they were asked for their validation and
refinement. Their inputs are most useful relative to additions,
deletions, and promotions. Converting multiple forecasts into one
number (forecasts from time-series techniques, sales input, and
customer input) creates more accurate forecasts by product.
Fiskars’s software has the ability to weigh each input. It gives more
weight to a statistical forecast for in-line items, and inputs from the
sales staff get much more weight for promoted products and new
It also segments products by value and forecastability so as to
concentrate forecasting efforts on products that have the biggest
impact on the business. High-value items that are easier to forecast
(stable demand with low forecast errors to date) tend to do well
with the time-series techniques, and judgmental adjustments are
made with caution. High-value items that are difficult to forecast get
top priority in the forecasting effort, and spark the need for
collaboration with customers and suppliers. Much less attention is
given to improving forecasts for low-value items for which there is
some history and fairly steady demand.
judgmental adjustment
An adjustment made to forecasts from one
or more quantitative models that accounts
for recognizing which models are
performing particularly well in recent past, or
take into account contextual information.
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Finally, Fiskars instituted a Web-based program that gives the entire
company visibility to forecast information in whatever form it needs.
For example, Finance wants monthly, quarterly, and yearly
projections in dollars, whereas Operations wants projections in units
as well as accuracy measures. Everybody can track updated
forecast information by customer, brand, and product.
Source: David Montgomery, “Flashpoints for Changing Your Forecasting Process,” The Journal of Business
Forecasting, (Winter 2006–2007), pp. 35–37; http://www.fiskars.com, April 15, 2014.
OM Explorer and POM for Windows allow you to evaluate several
forecasting models, and then you can create combination forecasts from
them. In fact, the Time-Series Forecasting Solver of OM Explorer
automatically computes a combination forecast as a weighted average,
using the weights that you supply for the various models that it evaluates.
The models include the naïve, moving average, exponential smoothing, and
regression projector methods. Alternately, you can create a simple Excel
spreadsheet that combines forecasts generated by POM for Windows to
create combination forecasts. The Time Series Forecasting Solver also
allows you evaluate your forecasting process with a holdout sample. The
forecaster makes a forecast just one period ahead, and learns of given
actual demand. Next the solver computes forecasts and forecast errors for
the period. The process continues to the next period in the holdout sample
with the forecaster committing to a forecast for the next period. To be
informed, the forecaster should also be aware of how well the other
forecasting methods have been performing, particularly in the recent past.
Another way to take advantage of multiple techniques is focus
forecasting , which selects the best forecast (based on past error
measures) from a group of forecasts generated by individual techniques.
Every period, all techniques are used to make forecasts for each item. The
forecasts are made with a computer because there can be 100,000 SKUs at
a company, each needing to be forecast. Using the history file as the
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starting point for each method, the computer generates forecasts for the
current period. The forecasts are compared to actual demand, and the
method that produces the forecast with the least error is used to make the
forecast for the next period. The method used for each item may change
from period to period.
focus forecasting
A method of forecasting that selects the best
forecast from a group of forecasts generated by
individual techniques.
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Adding Collaboration to the Process
In step three of the forecasting process we try to achieve consensus of the
forecast. One way to achieve that consensus in a formal way is to employ
collaborative planning, forecasting, and replenishment (CPFR) , a
process for supply chain integration that allows a supplier and its
customers to collaborate on making the forecast by using the Internet.
Traditionally, suppliers and buyers in most supply chains prepare
independent demand forecasts. With CPFR, firms initiate customerfocused operations teams that share with retailers their real-time data and
plans, including forecasts, inventories, sales to retailers’ shelves,
promotions, product plans, and exceptions. CPFR involves four interactive
collaborative planning, forecasting, and replenishment
A process for supply chain integration that allows a
supplier and its customers to collaborate on
making the forecast by using the Internet.
Strategy and Planning: establish the ground rules for the collaborative
relationship such as business goals, scope of collaboration, and
assignment of roles and responsibilities.
Demand and Supply Management: develop sales forecasts, procedures
for order planning, and inventory positions.
Execution: manage the generation of orders between supplier and
customers and the production, shipment, and delivery of products for
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customer purchase.
Analysis: monitor the planning process and operations for out of bound
conditions and evaluate to achievement of business goals.
Many firms have used CPFR to coordinate forecasts and plans up and
down the supply chain. CPFR enables firms to collaborate with their
retailers’ distribution centers’ customers and increase their ability to
forecast effectively. The real key to a successful implementation of CPFR
is the forging of a cultural alliance that involves peer-to peer relations and
cross-functional teams.
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Ever wonder how CPFR came into existence? Walmart has long been known
for its careful analysis of cash register receipts and for working with
suppliers to reduce inventories. To combat the ill effects of forecast errors
on inventories, Benchmarking Partners, Inc. was funded in the mid-1990s by
Walmart, IBM, SAP, and Manugistics to develop a software package.
Walmart initiated the new system with Listerine, a primary product of
Warner-Lambert (now produced by Johnson & Johnson). How did it work?
Walmart and Warner-Lambert independently calculated the demand they
expected for Listerine six months into the future, taking into consideration
factors such as past sales trends and sales promotions. If the forecasts
differed by more than a predetermined percentage, they exchanged written
comments and supporting data. They went through as many cycles as
needed to converge to an acceptable forecast. The program was
successful; Walmart saw a reduction in stockouts from 15 percent to 2
percent, increased sales, and reduced inventory costs, while WarnerLambert benefitted from a smoother production plan and lower average
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costs. The system was later generalized and called collaborative planning,
forecasting, and replenishment, or CPFR.
Mark Peterson/CORBIS
Forecasting as a Nested Process
Forecasting is not a stand-alone activity, but instead part of a larger
process that encompasses the remaining chapters. After all, demand is
only half of the equation—the other half is supply. Future plans must be
developed to supply the resources needed to meet the forecasted demand.
Resources include the workforce, materials, inventories, dollars, and
equipment capacity. Making sure that demand and supply plans are in
balance begins in the next chapter, Chapter 10 , “Inventory Management,”
and continues with Chapter 11 , “Operations Planning and Scheduling,”
and Chapter 12 , “Resource Planning.”
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6 Lean Systems
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An Aldi discount grocery store.
Kristoffer Tripplaar/Alamy
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Aldi is a discount supermarket chain with headquarters in
Germany and over 8000 stores worldwide including Australia,
Europe, Great Britain, Ireland, and the United States. With
roots and distribution in several countries throughout Europe,
it is a different kind of retailer that prides itself in displaying
key dietary and nutritional information on the front of their
packaging to enable customers to make informed choices
about their food. Aldi also makes its packaging from recycled
materials to keep the planet green. Its emphasis on core
values of simplicity, consistency, and corporate responsibility
are closely tied to the principles of lean production, which Aldi
uses to keep costs down in all areas, provide customers
more value for their money, and remain more competitive in a
business with razor thin margins.
Aldi’s waste reduction efforts start with training its
employees to do many different tasks, which improves
flexibility and lowers staff costs. In addition, consistent with
total quality management (TQM) principles, all workers have
the responsibility to get it right the first time, whether it is
accurate pricing or ordering the appropriate replenishment
stocks. In return, they are paid some of the better wages in
the United States in the grocery industry. In the stores, all
items have bar codes in a number of places to save time in
finding them, which makes the checkout process more
efficient. Aldi is also known for having smaller stores, which
are made possible by the fact that it sells fewer variations of
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each product and so less space is used for display. It also
means that Aldi can get quantity discounts and economies of
scale in sourcing products. Holding only the stock that is
needed for each product is further facilitated through a justin-time ordering and delivery system. Products are delivered
as needed in display-ready cases; some of them are even
sold directly from a pallet or a platform to minimize handling
and increase the efficiency of getting a large volume into the
store quickly. In contrast to several of its 24-hour
competitors, Aldi stores are only open from 8 . . to 8 . .
on most days, which reduces the use of energy and staff
salary costs. By limiting the use of credit cards, except
Discover in some stores in the United States and Visa and
MasterCard in Ireland, and using only cash or debit cards
saves Aldi the surcharge fees levied by most credit card
companies. Finally, Aldi’s shopping carts utilize a 25¢ (in the
United States) or a €1 (in Europe) coin system to make sure
that customers return them to the parking stations near the
store, which saves labor costs in collecting the carts that
would otherwise be left scattered across the parking lots or
potentially be lost or stolen.
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Using Operations to Create Value
Managing Processes
Process Strategy and Analysis
Quality and Performance
Capacity Planning
Constraint Management
Lean Systems
Project Management
Managing Customer Demand
Inventory Management
Operations Planning and Scheduling
Resource Planning
Managing Supply Chains
Supply Chain Design
Supply Chain Logistic Networks
Supply Chain Integration
Supply Chain Sustainability
Aldi’s lean philosophy extends into the supply chain as well.
Up to 60 percent of its fruits and vegetables are sourced
locally to save on transportation costs and time. As part of
its inventory reduction policies, suppliers are not allowed to
hold more than one month of normal orders and
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requirements of Aldi’s private label products in inventory at
any given point of time, unless Aldi submits a written
authorization for a temporary or permanent change in
suppliers’ inventory levels. Due to its relentless focus on lean
principles, it is no wonder that Aldi is a clear leader in prices
among leading grocery brands according to a study of 6,200
consumers conducted in May 2014 by Market Force
Information, a customer intelligence solutions firm. Aldi’s
products can be as much as 30 percent cheaper than its
competitors in some cases. In addition, Publix and Aldi were
ranked second and third in customer satisfaction in North
America after Trader Joe’s due to their courteous service, fast
checkouts, and the quality of their private label brand
products. All these initiatives have contributed to Aldi’s
explosive growth globally—a new store opens roughly every
week in the United Kingdom alone.
Sources: “Competitive Advantage through Efficiency: An Aldi Case Study,” http://businesscasestudies.co.uk/aldi/competitiveadvantage-through-efficiency/introduction.html#axzz39GsjgbiQ; http://en.wikipedia.org/wiki/Aldi; https://corporate.aldi.us; http:/
/www.producenews.com/news-dep-menu/test-featured/13168-consumer-study-reveals-top-grocery-stores (August 2, 2014).
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Learning Goals
After reading this chapter, you should be able to:
1. Describe how lean systems can facilitate the
continuous improvement of processes.
2. Identify the strategic supply chain and process
characteristics of lean systems.
3. Explain the differences between one-worker, multiplemachine (OWMM) and group technology (GT)
approaches to lean system layouts.
4. Understand value stream mapping and its role in
waste reduction.
5. Understand kanban systems for creating a production
schedule in a lean system.
. Explain the implementation issues associated with
the application of lean systems.
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Aldi is a learning organization and an excellent example of an approach for
designing supply chains known as lean systems, which allow firms like Aldi
to continuously improve its operations and spread the lessons learned
across the entire corporation. Lean systems are operations systems that
maximize the value added by each of a company’s activities by removing
waste and delays from them. They encompass the company’s operations
strategy, process design, quality management, constraint management,
layout design, supply chain design, and technology and inventory
management and can be used by both service …
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