Chapter
8 Forecasting
TEACHING TIP
Balancing supply and demand begins with making accurate forecast. This chapter focuses on
demand forecasts. Forecasting methods may be based on mathematical models that use available
historical data, on qualitative methods, or they may be based on a combination of both.
Forecasting
TEACHING TIP
Mention the opening vignette about Kimberly-Clark and its quest to reduce forecast errors by
crafting a demand-driven supply chain. This involves point–of-sales data and close collaboration
with major retail customers.
1. A forecast is a prediction of future events used for planning purposes.
2. The baseline forecast depends solely on past and present information. Emphasize that
forecasts are critical inputs to business plans, annual plans, and budgets.
a. Finance needs forecasts to project cash low and capital requirements.
b. Human resources needs forecasts to anticipate hiring and training needs.
c. Marketing is an important source for sales forecast information because they are close to
the customer.
d. 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.
3. Managers throughout the organization make forecasts on many different variables other than
future demand, such as competitor strategies, regulatory changes, technological changes,
processing times, supplier lead times, and quality losses.
4. Forecasts are important to managing both processes and managing supply chains.
1. Managing Demand
1. There are five basic patterns of most demand time series.
a. Horizontal—the fluctuation of data around a constant mean.
b. Trend—the systematic increase or decrease in the mean of the series over time.
c. Seasonal—a repeatable pattern of increases or decreases in demand, depending on time
of day, week, month, or season.
d. Cyclical—the less predictable gradual increases or decreases in demand over longer
periods of time (years or decades).
TEACHING TIP
Cyclical patterns are influenced by business cycles and the service or product life cycle.
e. Random—the unforecastable variation in demand.
2. Demand management options: the process of changing demand patterns using one or more
demand options
a. Produce complementary products, or services, that have similar resource requirements
but different demand cycles
b. Promotional Pricing designed to increase sales with creative pricing (e.g., off-peak
pricing, rebates)
c. Prescheduled appointments in which service providers schedule customers for definite
periods of order fulfillment in order to level demand to not exceed supply capacity
d. Reservations, although quite similar to appointment systems, are used when the customer
actually occupies or uses facilities associated with the service
e. 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.
f. Backlogs are the accumulation of customer orders that a manufacturer has promised for
delivery at some future date.
g. Backorder is a customer order that cannot be filled when promised or demanded but is
filled later.
h. Stockout is an order that cannot be satisfied, resulting in a loss of the sale.
2. Key Decisions on Making Forecast
1. Deciding what to forecast
a. Level of aggregation
b. Units of measurement
2. Choosing the type of forecasting technique
a. Judgment methods
b. Causal methods
c. Time Series analysis
d. Trend projection with regression
3. Forecast Error
1. Forecast error is simply the difference found by subtracting the forecast from actual demand
for a given period, or
Et = Dt − Ft
where
Et =
forecast error for period t
Dt =
actual demand for period t
Ft =
forecast for period t
TEACHING TIP
To remember the order of terms in the subtraction, note that Dt comes before Ft , and so
is in alphabetical order.
2. Forecast errors can be classified as either bias errors or random errors.
a. Bias errors are the result of consistent mistakes.
b. Random error results from unpredictable factors that cause the forecast to deviate
from the actual demand.
3. Cumulative Sum of forecast errors
a. Cumulative sum of forecast errors measures the total forecast error.
• Cumulative forecast error (bias):
=
=
n
tt
ECFE
1
• Average forecast error (mean bias):
n
CFE
E=
b. Dispersion of forecast errors: Mean squared error (MSE), standard deviation (s),
mean absolute deviation (MAD) measure the dispersion of forecast errors.
• Mean squared error:
n
E
MSE
n
tt
=
=1
2
• Standard deviation:
( )
1
1
2
−
−
=
=
n
EE
n
tt
• Mean absolute deviation:
n
E
MAD
n
tt
=
=1
•
c. 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:
( )
n
DE
MAPE
n
ttt
=
=1
100/
4. Use Example 8.1: Calculating Forecast Error Measures
A forecasting procedure has been used for the last 8 months, with the following results.
Evaluate how well the procedure is doing, by finishing the following table (Students
complete highlighted sections) and then computing the different forecast error measures.
Month
Demand
(Dt)
Forecast
(Ft)
Error
(Et)
Error
Squared
(Et2)
Absolute
Error
(Et
)
Absolute Percent
Error
(Et
/ Dt)100
1
200
225
-25
625
25
12.5%
2
240
220
20
400
20
8.3
3
300
285
15
225
15
5.0
4
270
290
-20
400
20
7.4
5
230
250
−20
400
20
8.7
6
260
240
20
400
20
7.7
7
210
250
−40
1600
40
19.0
8
275
240
35
1225
35
12.7
Total
−15
5275
195
81.3%
=
−==
n
tt
ECFE
1
15
875.1
8
15 −=
−
== n
CFE
E
4.659
8
5275
1
2
===
=
n
E
MSE
n
tt
( )
4.27
1
1
2
=
−
−
=
=
n
EE
n
tt
4.24
8
195
1===
=
n
E
MAD
n
tt
( )
%2.10
8
%3.81
100
1===
=
n
E
MAPE
n
tt
5. 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
4. Judgment Methods
1. Salesforce estimates
a. Advantages: the salesforce is the 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.
b. Disadvantages: individual biases of the salespeople may taint the forecast
2. Executive opinion
a. Method in which opinions, experience, and technical knowledge of one or more
managers are summarized to arrive at a single forecast.
b. Can be used for technological forecasting.
3. Market research
a. A systematic approach to determine external customer interest in a service or product by
creating and testing hypotheses through data-gathering surveys.
4. Delphi method
a. A process of gaining consensus from a group of experts while maintaining their
anonymity.
b. 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.
c. The Delphi method can be used to develop long-range forecasts of product demand and
new-product sales projections, and it can also be used for technological forecasting.
5. Causal Methods: Linear Regression
TEACHING TIP
Some students may find this section difficult, especially if an introduction to statistics is not a
prerequisite for this course.
Causal methods are used when historical data are available and the relationship between the
factor to be forecasted and the other external or internal factors can be identified. These
relationships are expressed in mathematical terms and can be complex. Causal methods provide
the most sophisticated forecasting tools and are good predicting turning points in demand for
preparing long-range forecasts.
1. Linear regression
a. One variable, called a dependent variable, is related to one or more independent variables
by a linear equation.
b. The independent variables are assumed to affect the dependent variable and thereby
“cause” the results observed in the past.
c. Simplest linear regression models is a function of only one independent variable and
therefore, the theoretical relationship is a straight line
Y = a + bX
where
Y =
dependent variable
X =
independent variable
a =
Y-intercept of the line
b =
slope of the line
2. The sample correlation coefficient, r
a. Measures the direction and strength of the relationship between the independent variable
and the dependent variable.
b. The value of r can range from –1.00 to + 1.00.
• An r of +1.00 implies 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 –1.00 implies period-by-period changes in direction (increases or decreases)
of the independent variable are always accompanied by changes in the opposite
direction by the dependent variable.
• A zero value of r means no relationship exists between the variables.
c. The closer the value of r is to ±1.00, the better the relationship.
3. The sample coefficient of determination, r2
a. Measures the amount of variation in the dependent variable about its mean that is
explained by the regression line.
b. The coefficient of determination is the square of the correlation coefficient, or r2.
c. The values of r2 range from 0.00 to 1.00.
d. Regression equations with a value of r2 close to 1.00 are desired because the variations in
the dependent variable and the forecast generated by the regression equation are closely
related.
4. The standard error of the estimate, syx
a. Measures how closely the data on the dependent variable cluster around the regression
line.
b. 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.
c. When determining which independent variable to include in the regression line, one
should choose the one with the smallest standard error of the estimate.
5. Forecasting with linear regression
a. Example 8.2 Using Linear Regression to Forecast Product Demand
b. Active Model 8.1 in MyLab Operations Management provides insights on varying the
intercept and slope of the model
6. Time-Series Methods
1. Naive forecast
a. A method whereby the forecast for the next period equals the demand for the current
period (Forecast = Dt).
b. The advantages of this method are its simplicity and low cost.
c. The method works best when horizontal, trend, or seasonal patterns are stable and
random variation is small.
2. Horizontal Patterns: Estimating the average
a. Simple moving averages
• Used to estimate the average of a demand time series and thereby remove the effects
of random fluctuation.
• It is most useful when demand has no pronounced trend or seasonal influences.
• Applying a moving average simply involves calculating the average demand for the n
most recent time periods and using it as a forecast for the next time period. In this
way the averages “moves” from period to period.
• The stability of the demand series generally determines how many periods to include
(i.e., larger values of n should be used for demand series that are stable, and small
values for those susceptible to changes in the underlying average).
Large values of n should be used for demand series that are stable.
Small values of n should be used for those that are susceptible to changes in the
underlying average.
• Forecasting formula:
n
DDDD
n
demands n last of Sum
Fntttt
t121
1+−−−
+
++++
==
where
Dt =
actual demand in period t
n =
total number of periods in the average
Ft+1 =
forecast for period t + 1
• Quickly illustrate the approach with Example 8.3, before trying out with
Application 8.1
• Estimating with Simple Moving Average. Use Application 8.1:
We will use the following customer-arrival data in this application.
Month
Customer arrivals
1
800
2
740
3
810
4
790
Use a three-month moving average to forecast customer arrivals for month 5.
780
3
740810790
3
234
5=
++
=
++
=DDD
F
Forecast for month 5 is 780 customer arrivals.
If the actual number of arrivals in month 5 is 805, what is the forecast for month 6?
667.801
3
810790805
3
345
6=
++
=
++
=DDD
F
Forecast for month 6 is 802 customer arrivals.
• Given the three–month moving average forecast for month 5, and the number of
patients that actually arrived (805), what is the forecast error?
• Active Model 8.2 in MyLab Operations Management provides insights on the impact
of varying n.
• Tutor 8.1 in MyLab Operations Management provides another example to practice
making forecasts with the moving average method.
b. Weighted moving averages
• Formula
Ft+1 = W1Dt + W2Dt–1 +…+WnDt –n+1
• Each historical demand in the average can have its own weight with the sum of the
weights = 1.00.
• The advantage of a weighted moving average is that it allows you to emphasize
recent demand over earlier demand.
• The forecast will be more responsive to changes in the underlying average of the
demand series than the simple moving average forecast.
• Solved Problem 8.2 provides an example.
• Use Application 8.2: Estimating with Weighted Moving Average
Revisiting the customer arrival data in Application 8.1. Let W1 = 0.50, W2 = 0.30,
and W3 = 0.20. Use the weighted moving average method to forecast arrivals for
month 5.
( ) ( ) ( )
78674020.081030.079050.0
2332415 =++=++= DWDWDWF
Forecast for month 5 is 786 customer arrivals.
• Given the number of patients that actually arrived (805), what is the forecast error?
E5 = 805 − 786 = 19
Forecast error for month 5 is 19.
If the actual number of arrivals in month 5 is 805, compute the forecast for month 6.
( ) ( ) ( )
5.80181020.079030.080550.0
3342516 =++=++= DWDWDWF
Forecast for month 6 is 802 customer arrivals.
• Tutor 8.2 in MyLab Operations Management provides a new practice example for
making forecasts with weighted moving average method.
c. Exponential smoothing
• A sophisticated weighted moving average that calculates the average of a time series
by giving recent demands more weight that earlier demands.
• Requires only three items of data
• The emphasis given to the most recent demand levels can be adjusted by changing
the smoothing parameter.
Larger α values emphasize recent levels of demand and result in forecasts more
responsive to changes in the underlying average.
Smaller α values treat past demand more uniformly and result in more stable
forecasts.
• Formula:
( ) ( )( )
tt
t
FD
period last calculated Forecastperiod this DemandF
)1(
1
1
−+=
−+=
+
• An equivalent formula is:
( )
tttt FDFF −+=
+
1
This form of the equation shows that the forecast for the next period equals the forecast
for the current period plus a proportion of the forecast error for the current period.
• Estimating with Exponential Smoothing. Use Example 8.4 to illustrate then
Application 8.3 to confirm technique by hand calculation
Suppose that there were 790 customer arrivals in month 4 (D4), whereas the forecast was for
783 arrivals. Use exponential smoothing with α=0.20 to compute the forecast for month 5.
( )
=−+=
+tttt FDFF
1
783+.2(790-783) = 784.4
Forecast for month 5 is 784 customer arrivals.
TEACHING TIP
Rounding is necessary in this case because you would not have a fraction of customer arrivals.
However, the actual forecast, and not the rounded forecast, needs to be included in the forecast
updates.
• Because exponential smoothing is simple and requires minimal data, it is inexpensive
and attractive to firms that make thousands of forecasts for each time period.
However, its simplicity also has a disadvantage when the underlying average is
changing, as in the case of demand series with a trend.
• Active Model 8.3 in MyLab Operations Management provides insight on the impact
of varying α.
• Tutor 8.3 in MyLab Operations Management provides a new example of how to
make forecasts with the exponential smoothing method.
3. Trend Patterns: Using Regression
a. 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 lag behind actual demand and tend to be below or
above the actual demand.
b. 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 t= 1, for the second period, let t = 2; and so on.
• The regression equation is Ft = a + b t
c. The Trend Projection with Regression model can be solved with a solver in OM
Explorer. It provides the regression coefficients, coefficient of determination r2, error
measures, forecasts into the future, and a graph.
d. Using Trend Projection with Regression to Forecast a Demand Series with a Trend
use Example 8.5 to illustrate then move on to Application 8.4
Use OM Explorer to project the following weekly demand data using trend projection
with regression. What is the forecasted demand for periods 11-14
Week
Demand
Week
Demand
1
2
3
4
5
24
34
29
27
39
6
7
8
9
10
42
39
56
45
43
Copyright © 2019 Pearson Education, Inc.
4. Seasonal patterns: Using Seasonal Factors
a. Seasonal patterns are regularly repeated upward or downward movements in demand
measured in periods of less than one year (hours, days, weeks, months, or quarters). In
this content the time periods are called seasons.
• 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 periods in the same season.
• Example: day-of-the week seasonal effect, then 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.
b. Multiplicative seasonal method, whereby seasonal factors are multiplied by an estimate
of the average demand to arrive at a seasonal forecast.
• Step 1: For each year, calculate the average demand per season by dividing annual
demand by the number of seasons per year.
• Step 2: For each year, divide the actual demand for each season by the average
demand per season. The result is a seasonal index for each season in the year, which
indicates the level of demand relative to the average demand.
• Step 3: Calculate the average seasonal index for each season using the results from
step 2. Add the seasonal indices for each season and divide by the number of years
of data.
• Step 4: Calculate each season’s forecast for next year.
c. Forecasting Using the Multiplicative Seasonal Method Use Application 8.5:
Suppose the multiplicative seasonal method is being used to forecast customer demand. The
actual demand and seasonal indices are shown below.
Quarter
Year 1 _
Year 2 _
Average
Index
Demand
Index
Demand
Index
1
100
0.40
192
0.64
0.52
2
400
1.60
408
1.36
1.48
3
300
1.20
384
1.28
1.24
4
200
0.80
216
0.72
0.76
Avg.
250
300
If the projected demand for Year 3 is 1320 units, what is the forecast for each quarter of that
year?
unitsquartersunits 33041320 =
Forecast for Quarter 1 =
( )
units17233052.0
• An alternative to the multiplicative seasonal method is the additive seasonal method,
whereby seasonal forecasts are generated by adding or subtracting a seasonal
constant to the estimate of the average demand per season.
5. Criteria for Selecting Time-Series Methods
a. Forecast error measures provide important information for choosing the best
forecasting method for a service or product.
b. 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:
• For projections of more stable demand patterns, use lower values or larger n
values to emphasize historical experience.
• 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 emphasized.
c. Using a Holdout Sample:
• 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
d. Using a Tracking Signal = CFE/MAD
• A measure that indicates whether a method of forecasting is accurately predicting
actual changes in demand.
• Useful when forecast systems are computerized because it alerts analysts when
forecast are getting far from desirable limits.
7. Insights into Effective Demand Forecasting
1. Big Data
a. Data sets that are so large and complex that traditional data processing applications are
inadequate to deal with them.
b. Big Data is characterized by 3 Vs
• Volume: Exponential increase in data especially due to the internet
• Variety: Variety of sources, mobile phones, social networks, GPS etc.
• Velocity: Speed at which data is created and analyzed is critical
TEACHING TIP
Use Managerial Practice 8.1: Big Data and Health Care Forecasting to illustrate use of data
2. A typical forecasting process
a. Informational Inputs
• History file on past demand.
• Clarifying notes and adjustments are made to the database to explain unusual demand
behavior, such as the impact of special promotions and closeouts.
• 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.
b. Outputs of the process are forecasts for multiple time periods into the future.
c. The forecast process itself, typically done on a monthly basis, consists of structured steps.
• Step 1. Update the history file and review forecast accuracy
• Step 2. Prepare initial forecasts using some forecasting software package and
judgment.
3. Using multiple forecasting methods
• 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.
4. Adding collaboration to the process. Collaborative planning, forecasting, and replenishment
(CPFR) involves four interactive activities:
a. Strategy and Planning: establishing the ground rules for the collaborative relationship
5. Forecasting as a nested process. Forecasting is not a stand-alone activity, but instead part of a
larger process that encompasses:
a. Chapter 10, “Operations Planning and Scheduling”
b. Chapter 11, “Resource Planning”