McGraw-Hill/Irwin
Demand
Forecasting
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

 Introduction
 Qualitative Forecasting Methods
 Quantitative Forecasting Models
 How to Have a Successful Forecasting System
 Computer Software for Forecasting
 Forecasting in Small Businesses and Start-Up
Ventures
 Wrap-Up: What World-Class Producers Do

 Demand estimates for products and services are the starting point for all the other planning in operations management.
 Management teams develop sales forecasts based in part on demand estimates.
 The sales forecasts become inputs to both business strategy and production resource forecasts.

Inputs:
Market,
Economic,
Other
Forecast
Method(s)
Demand
Estimates
Business
Strategy
Sales
Forecast
Management
Team
Production Resource
Forecasts

 New Facility Planning – It can take 5 years to design and build a new factory or design and implement a new production process.
 Production Planning – Demand for products vary from month to month and it can take several months to change the capacities of production processes.
 Workforce Scheduling – Demand for services (and the necessary staffing) can vary from hour to hour and employees weekly work schedules must be developed in advance.

Forecast
Horizon
Long
Range
Medium
Range
Short
Range
Time
Span
Years
Months
Days,
Weeks
Item Being
Forecasted
Product Lines,
Factory Capacities
Product Groups,
Depart. Capacities
Specific Products,
Machine Capacities
Unit of
Measure
Dollars,
Tons
Units,
Pounds
Units,
Hours




 Usually based on judgments about causal factors that underlie the demand of particular products or services
 Do not require a demand history for the product or service, therefore are useful for new products/services
 Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events
 The approach/method that is appropriate depends on a product’s life cycle stage

 Educated guess intuitive hunches
 Executive committee consensus
 Delphi method
 Survey of sales force
 Survey of customers
 Historical analogy
 Market research surveys scientifically conducted

 Based on the assumption that the “forces” that generated the past demand will generate the future demand, i.e., history will tend to repeat itself
 Analysis of the past demand pattern provides a good basis for forecasting future demand
 Majority of quantitative approaches fall in the category of time series analysis

 A time series is a set of numbers where the order or sequence of the numbers is important, e.g., historical demand
 Analysis of the time series identifies patterns
 Once the patterns are identified, they can be used to develop a forecast

 Trends are noted by an upward or downward sloping line.
 Cycle is a data pattern that may cover several years before it repeats itself.
 Seasonality is a data pattern that repeats itself over the period of one year or less.
 Random fluctuation (noise) results from random variation or unexplained causes.

Length of Time
Before Pattern Length of
Is Repeated Season
Year
Year
Year
Month
Week
Quarter
Month
Week
Day
Day
Number of
Seasons in Pattern
4
12
52
28-31
7

 Linear Regression
 Simple Moving Average
 Weighted Moving Average
 Exponential Smoothing (exponentially weighted moving average)
 Exponential Smoothing with Trend (double exponential smoothing)

 Time spans usually greater than one year
 Necessary to support strategic decisions about planning products, processes, and facilities

 Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables.
 In simple linear regression analysis there is only one independent variable.
 If the data is a time series, the independent variable is the time period.
 The dependent variable is whatever we wish to forecast.

 Regression Equation
This model is of the form:
Y = a + bX
Y = dependent variable
X = independent variable a = y-axis intercept b = slope of regression line

 Constants a and b
The constants a and b are computed using the following equations: a =
    n
 
2 b = n n
  
 
2

 Once the a and b values are computed, a future value of X can be entered into the regression equation and a corresponding value of Y (the forecast) can be calculated.

 Simple Linear Regression
At a small regional college enrollments have grown steadily over the past six years, as evidenced below.
Use time series regression to forecast the student enrollments for the next three years.
Students Students
Year Enrolled (1000s) Year Enrolled (1000s)
1 2.5
4 3.2
2
3
2.8
2.9
5
6
3.3
3.4

 Simple Linear Regression x y x 2 xy
3
4
1
2
2.5
2.8
2.9
3.2
1
4
9
16
2.5
5.6
8.7
12.8
5 3.3
25 16.5
6 3.4
36 20.4
S x=21
S y=18.1
S x 2 =91
S xy=66.5

 Simple Linear Regression a 
91(18.1)  21(66.5)
 2
 2.387
b 
105
 0.180
Y = 2.387 + 0.180X

 Simple Linear Regression
Y
7
Y
8
Y
9
= 2.387 + 0.180(7) = 3.65 or 3,650 students
= 2.387 + 0.180(8) = 3.83 or 3,830 students
= 2.387 + 0.180(9) = 4.01 or 4,010 students
Note: Enrollment is expected to increase by 180 students per year.

 Simple linear regression can also be used when the independent variable X represents a variable other than time.
 In this case, linear regression is representative of a class of forecasting models called causal forecasting models.

 Simple Linear Regression – Causal Model
The manager of RPC wants to project the firm’s sales for the next 3 years. He knows that
RPC’s long-range sales are tied very closely to national freight car loadings. On the next slide are 7 years of relevant historical data.
Develop a simple linear regression model between RPC sales and national freight car loadings. Forecast RPC sales for the next 3 years, given that the rail industry estimates car loadings of 250, 270, and 300 million.

 Simple Linear Regression – Causal Model
Year
5
6
7
1
2
3
4
RPC Sales Car Loadings
($millions)
9.5
11.0
12.0
12.5
14.0
16.0
18.0
(millions)
120
135
130
150
170
190
220

 Simple Linear Regression – Causal Model x y x 2 xy
120 9.5
14,400 1,140
135 11.0
18,225 1,485
130 12.0
16,900 1,560
150 12.5
22,500 1,875
170 14.0
28,900 2,380
190 16.0
36,100 3,040
220 18.0
48,400 3,960
1,115 93.0
185,425 15,440

 Simple Linear Regression – Causal Model a 
 2
 0.528
b 
 2
 0.0801
Y = 0.528 + 0.0801X

 Simple Linear Regression – Causal Model
Y
8
Y
9
Y
10
= 0.528 + 0.0801(250) = $20.55 million
= 0.528 + 0.0801(270) = $22.16 million
= 0.528 + 0.0801(300) = $24.56 million
Note: RPC sales are expected to increase by $80,100 for each additional million national freight car loadings.

l l
Multiple regression analysis is used when there are two or more independent variables.
An example of a multiple regression equation is:
Y = 50.0 + 0.05X
1
+ 0.10X
2
– 0.03X
3 where: Y = firm’s annual sales ($millions)
X
1
= industry sales ($millions)
X
2
= regional per capita income ($thousands)
X
3
= regional per capita debt ($thousands)

 The coefficient of correlation, r, explains the relative importance of the relationship between x and y.
 The sign of r shows the direction of the relationship.
 The absolute value of r shows the strength of the relationship.
 The sign of r is always the same as the sign of b.
 r can take on any value between –1 and +1.

 Meanings of several values of r: y
-1 a perfect negative relationship (as x goes up, goes down by one unit, and vice versa)
+1 a perfect positive relationship (as x goes up, y goes up by one unit, and vice versa)
0 no relationship exists between x and y
+0.3 a weak positive relationship
-0.8 a strong negative relationship

 r is computed by: r 
    y

2  (
 x ) 2

2  (
 y ) 2

 The coefficient of determination, r 2 , is the square of the coefficient of correlation.
 The modification of r to r 2 allows us to shift from subjective measures of relationship to a more specific measure.
 r 2 is determined by the ratio of explained variation to total variation: r 2 


( 
(
) 2
) 2

 Select a representative historical data set.
 Develop a seasonal index for each season.
 Use the seasonal indexes to deseasonalize the data.
 Perform lin. regr. analysis on the deseasonalized data.
 Use the regression equation to compute the forecasts.
 Use the seas. indexes to reapply the seasonal patterns to the forecasts.

 Seasonalized Times Series Regression Analysis
An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of
Epsilon Computers. She believes that the most recent
8 quarters of sales (shown on the next slide) are representative of next year’s sales.

 Seasonalized Times Series Regression Analysis
 Representative Historical Data Set
Year Qtr.
($mil.) Year Qtr. ($mil.)
1
1
1
1 1
2
3
4
7.4
6.5
4.9
16.1
2
2
2
2
1
2
3
4
8.3
7.4
5.4
18.0

 Seasonalized Times Series Regression Analysis
 Compute the Seasonal Indexes
Year
1
2
Totals
Qtr. Avg.
Seas.Ind.
Quarterly Sales
Q1 Q2 Q3 Q4 Total
7.4
6.5
4.9
16.1
8.3
7.4
5.4
18.0
34.9
39.1
15.7
13.9
10.3
34.1
74.0
7.85
6.95
5.15
17.05
9.25
.849
.751
.557
1.843
4.000

 Seasonalized Times Series Regression Analysis
 Deseasonalize the Data
Year
1
2
Quarterly Sales
Q1 Q2
8.72
8.66
9.78
9.85
Q3
8.80
9.69
Q4
8.74
9.77

 Seasonalized Times Series Regression Analysis
 Perform Regression on Deseasonalized Data
Yr.
Qtr.
x y x 2 xy
2
2
1
1
1
1
2 3
2 4
1
2
1
2
3
4
1
2
3 8.80
4 8.74
5 9.78
6 9.85
7
8
8.72
8.66
9.69
9.77
1
4
64
8.72
17.32
9 26.40
16 34.96
25 48.90
36 59.10
49 67.83
78.16
Totals 36 74.01
204 341.39

a  b 
 2
 8.357
 2
 0.199
Y = 8.357 + 0.199X

 Seasonalized Times Series Regression Analysis
 Compute the Deseasonalized Forecasts
Y
9
Y
10
= 8.357 + 0.199(9) = 10.148
= 8.357 + 0.199(10) = 10.347
Y
11
Y
12
= 8.357 + 0.199(11) = 10.546
= 8.357 + 0.199(12) = 10.745
Note: Average sales are expected to increase by
.199 million (about $200,000) per quarter.

 Seasonalized Times Series Regression Analysis
 Seasonalize the Forecasts
Seas.
Deseas.
Seas.
Yr.
Qtr.
Index Forecast Forecast
3 1 .849
3
3
2
3
.751
.557
3 4 1.843
10.148
10.347
10.546
10.745
8.62
7.77
5.87
19.80

 Time spans ranging from a few days to a few weeks
 Cycles, seasonality, and trend may have little effect
 Random fluctuation is main data component

Short-range forecasting models are evaluated on the basis of three characteristics:



Impulse response
Noise-dampening ability
Accuracy

 Impulse Response and Noise-Dampening Ability




If forecasts have little period-to-period fluctuation, they are said to be noise dampening.
Forecasts that respond quickly to changes in data are said to have a high impulse response.
A forecast system that responds quickly to data changes necessarily picks up a great deal of random fluctuation
(noise).
Hence, there is a trade-off between high impulse response and high noise dampening.

 Accuracy


Accuracy is the typical criterion for judging the performance of a forecasting approach
Accuracy is how well the forecasted values match the actual values

 Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in its forecasts and changes in the market may require reevaluation of the approach
 Accuracy can be measured in several ways



Standard error of the forecast (covered earlier)
Mean absolute deviation (MAD)
Mean squared error (MSE)

 Mean Absolute Deviation (MAD)
MAD = n
 i=1 n i

 Mean Squared Error (MSE)
MSE = (S yx
) 2
A small value for S yx means data points are tightly grouped around the line and error range is small.
When the forecast errors are normally distributed, the values of MAD and s related: yx are
MSE = 1.25(MAD)

 (Simple) Moving Average
 Weighted Moving Average
 Exponential Smoothing
 Exponential Smoothing with Trend

 An averaging period (AP) is given or selected
 The forecast for the next period is the arithmetic average of the AP most recent actual demands
 It is called a “simple” average because each period used to compute the average is equally weighted
 . . . more

 It is called “moving” because as new demand data becomes available, the oldest data is not used
 By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and high noise dampening)
 By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and low noise dampening)

 Technique that averages a number of the most recent actual values in generating a forecast
F t

MA n
 i n 

1
A t
 i n where
F t

Forecast for time period t
MA n
 n period moving average
A t

1

Actual value in period t

1 n

Number of periods in the moving average
Student Slides
3-54

 This is a variation on the simple moving average where the weights used to compute the average are not equal.
 This allows more recent demand data to have a greater effect on the moving average, therefore the forecast.
 . . . more

 The weights must add to 1.0 and generally decrease in value with the age of the data.
 The distribution of the weights determine the impulse response of the forecast.

 The most recent values in a time series are given more weight in computing a forecast
 The choice of weights, w, is somewhat arbitrary and involves some trial and error
F t
 w t
( A t
)
 w t

1
( A t

1
)

...
 w t
 n
( A t
 n
) where w
A t t
 weight for period t , w t

1
 weight
 the actual value for period t , A t

1
 for period t

1 , etc.
the actual value for period t

1 , etc.
Student Slides
3-57

 A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error
F t

F t

1
 
( A t

1

F t

1
) where
F t
F t

1


Forecast for period t

Forecast for the previous period
= Smoothing constant
A t

1

Actual demand or sales from the previous period
Student Slides
3-58




The smoothing constant,

, must be between 0.0 and 1.0.
A large
 provides a high impulse response forecast.
A small
 provides a low impulse response forecast.

 Moving Average
CCC wishes to forecast the number of incoming calls it receives in a day from the customers of one of its clients, BMI. CCC schedules the appropriate number of telephone operators based on projected call volumes.
CCC believes that the most recent 12 days of call volumes (shown on the next slide) are representative of the near future call volumes.

 Moving Average
 Representative Historical Data
Day
3
4
1
2
5
6
Calls
159
217
186
161
173
157
Day
7
8
9
10
11
12
Calls
203
195
188
168
198
159

 Moving Average
Use the moving average method with an AP =
3 days to develop a forecast of the call volume in
Day 13.
F
13
= (168 + 198 + 159)/3 = 175.0 calls

 Weighted Moving Average
Use the weighted moving average method with an AP = 3 days and weights of .1 (for oldest datum), .3, and .6 to develop a forecast of the call volume in Day 13.
F
13
= .1(168) + .3(198) + .6(159) = 171.6 calls
Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA
(.60) as it does in the MA (.33).

l
Exponential Smoothing
If a smoothing constant value of .25 is used and the exponential smoothing forecast for Day 11 was
180.76 calls, what is the exponential smoothing forecast for Day 13?
F
12
= 180.76 + .25(198 – 180.76) = 185.07
F
13
= 185.07 + .25(159 – 185.07) = 178.55

 Forecast Accuracy - MAD
Which forecasting method (the AP = 3 moving average or the

= .25 exponential smoothing) is preferred, based on the MAD over the most recent
9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)

AP = 3

= .25
Day Calls Forec. |Error| Forec. |Error|
4 161
5 173
6 157
7 203
8 195
9 188
10 168
11 198
12 159
MAD
187.3
26.3
188.0
15.0
173.3
16.3
163.7
39.3
177.7
17.3
185.0
3.0
195.3
27.3
183.7
14.3
184.7
25.7
20.5
186.0
25.0
179.8
6.8
178.1
21.1
172.8
30.2
180.4
14.6
184.0
4.0
185.0
17.0
180.8
17.2
185.1
26.1
18.0

 Cost
 Accuracy
 Data available
 Time span
 Nature of products and services
 Impulse response and noise dampening

 Not involving a broad cross section of people
 Not recognizing that forecasting is integral to business planning
 Not recognizing that forecasts will always be wrong
 Not forecasting the right things
 Not selecting an appropriate forecasting method
 Not tracking the accuracy of the forecasting models

 Tracking Signal (TS)
 The TS measures the cumulative forecast error over n


 i  1 i
TS =
MAD
If the forecasting model is performing well, the TS should be around zero
The TS indicates the direction of the forecasting error; if the TS is positive -- increase the forecasts, if the TS is negative -- decrease the forecasts.

 Tracking Signal
 The value of the TS can be used to automatically trigger new parameter values of a model, thereby correcting model performance.


If the limits are set too narrow, the parameter values will be changed too often.
If the limits are set too wide, the parameter values will not be changed often enough and accuracy will suffe r.

 Examples of computer software with forecasting capabilities







Forecast Pro
Autobox
SmartForecasts for Windows
SAS
SPSS
SAP
POM Software Libary
Primarily for forecasting
Have
Forecasting modules

 Forecasting for these businesses can be difficult for the following reasons:




Not enough personnel with the time to forecast
Personnel lack the necessary skills to develop good forecasts
Such businesses are not data-rich environments
Forecasting for new products/services is always difficult, even for the experienced forecaster

 Government agencies at the local, regional, state, and federal levels
 Industry associations
 Consulting companies

 Consumer Confidence Index
 Consumer Price Index (CPI)
 Gross Domestic Product (GDP)
 Housing Starts
 Index of Leading Economic Indicators
 Personal Income and Consumption
 Producer Price Index (PPI)
 Purchasing Manager’s Index
 Retail Sales

 Predisposed to have effective methods of forecasting because they have exceptional longrange business planning
 Formal forecasting effort
 Develop methods to monitor the performance of their forecasting models
 Do not overlook the short run.... excellent short range forecasts as well

MAD


Actual t

Forecast t n
MSE

 
Actual t n


1
Forecast t

2
MAD weights all errors evenly
MSE weights errors according to their squared values
MAPE

 Actual t

Forecast t
Actual t n

100
Student Slides
MAPE weights errors according to relative error
3-76