1
Chapter 15
Demand Management
and Forecasting
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc., 2006
2
OBJECTIVES




Simple & Weighted Moving Average Forecasts
Exponential Smoothing
Simple Linear Regression
Multiple Regression
3
Types of Forecasts
 Qualitative (Judgmental)
 Quantitative

Time Series Analysis
Causal Relationships

Simulation

4
Components of Demand
 Average demand for a period of time
 Trend
 Seasonal element
 Cyclical elements
 Random variation
 Autocorrelation
5
Finding Components of Demand
Sales
Seasonal variation
xxx
x
x
x
x
x xx
xxxxx
x
x
x
x
x
x x x xx
x
x x
1
2
x
xx
x
x
x
x
x
x
x
x
3
Year
x xxx
x
x
4
Linear
x
x
Trend
6
Time Series Analysis
 Time series forecasting models try to predict the
future based on past data
 You can pick models based on:
1. Time horizon to forecast
2. Data availability
3. Accuracy required
4. Size of forecasting budget
5. Availability of qualified personnel
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Simple Moving Average Formula
 The simple moving average model assumes an average is a
good estimator of future behavior
 The formula for the simple moving average is:
A t -1 + A t -2 + A t -3 + ... + A t -n
Ft =
n
Ft = Forecast for the coming period
N = Number of periods to be averaged
A t-1 = Actual occurrence in the past period for up to “n” periods
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Simple Moving Average Problem (1)
Week
Demand
1
650
2
678
3
720
4
785
5
859
6
920
7
850
8
758
9
892
10
920
11
789
12
844
3 week
6 week
Ft =
A t -1 + A t -2 + A t -3 + ... + A t -n
n
Question: What are the 3week and 6-week moving
average forecasts for
demand?
Assume you only have 3
weeks and 6 weeks of
actual demand data for the
respective forecasts
9
Plotting the moving averages and comparing them shows how the
lines smooth out to reveal the overall upward trend in this example
950
900
850
Demand
800
750
700
Demand
650
3-Week
600
6-Week
550
500
1
2
3
4
5
6
Week
7
8
9
10
11
12
Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother
10
Simple Moving Average Problem (2) Data
Week
1
2
3
4
5
6
7
Demand
820
775
680
655
620
600
575
Question: What is the 3 week moving
average forecast for this data?
Assume you only have 3 weeks and 5
weeks of actual demand data for the
respective forecasts
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Simple Moving Average Problem (2) Solution
Week
1
2
3
4
5
6
7
Demand
820
775
680
655
620
600
575
3-Week
5-Week
12
Weighted Moving Average Formula
While the moving average formula implies an equal weight being placed on
each value that is being averaged, the weighted moving average permits an
unequal weighting on prior time periods
The formula for the moving average is:
Ft = w1A t -1 + w 2 A t -2 + w 3A t -3 + ... + w n A t -n
n
w
i =1
i
=1
wt = weight given to time period “t”
occurrence (weights must add to one)
13
Weighted Moving Average Problem (1) Data
Question: Given the weekly demand and weights, what is the forecast for the
4th period or Week 4?
Week
1
2
3
4
Demand
650
678
720
Weights:
t-3
.2
t-2
.3
t-1
.5
Note that the weights place more emphasis on the most recent data, that is time
period “t-1”
In Excel use the =SUMPRODUCT(…, …) function.
14
Weighted Moving Average Problem (1) Solution
Week
1
2
3
4
Demand Forecast
650
678
720
15
Weighted Moving Average Problem (2) Data
Question: Given the weekly demand information and weights, what is the three
week weighted moving average forecast of the 5th period or week?
Week
1
2
3
4
Demand
820
775
680
655
Weights:
t-3
.1
t-2
.2
t-1
.7
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Excel Example of Weighted Moving Average
1
2
3
4
5
6
A
Week
1
2
3
4
5
B
C
D
Demand Forecast
820
775
680
655
E
Weights
0.1
0.2
0.7
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Exponential Smoothing Model
Ft = Ft-1 + a(At-1 - Ft-1)
Where :
Ft  Forcast value for the coming t time period
Ft - 1  Forecast value in 1 past time period
At - 1  Actual occurance in the past t time period
a  Alpha smoothing constant
 Premise: The most recent observations might have the
highest predictive value
 Therefore, we should give more weight to the more recent
time periods when forecasting
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Exponential Smoothing Model – Alternate form
Ft  aAt 1  (1  a ) Ft 1
a  Alpha smoothing constant
1 - a  Dampening factor
Microsoft Excel uses the
dampening factor in the Data
Analysis Exponential Smoothing
routine
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Exponential Smoothing Problem (1) Data
Week
1
2
3
4
5
6
7
8
9
10
Demand
820
775
680
655
750
802
798
689
775
Question: Given the weekly demand
data, what are the exponential
smoothing forecasts for periods
2-10 using a=0.10 and a=0.60?
Assume F1=D1
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Answer: The respective alphas columns denote the forecast values. Note
that you can only forecast one time period into the future.
Week
1
2
3
4
5
6
7
8
9
10
Demand
820
775
680
655
750
802
798
689
775
0.1
820.00
820.00
815.50
801.95
787.26
783.53
785.38
786.64
776.88
776.69
0.6
820.00
820.00
793.00
725.20
683.08
723.23
770.49
787.00
728.20
756.28
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Exponential Smoothing Problem (1) Plotting
Note how that the smaller alpha results in a smoother line in this example
850
800
750
Demand
700
650
600
Demand
550
500
1
2
3
4
5
6
Week
7
8
9
10
The MAD Statistic to Determine
Forecasting Error
n
A
M AD =
t
- Ft
t =1
1 MAD  0.8 standard deviation
1 standard deviation  1.25 MAD
n
 The ideal MAD is zero which would mean there is no
forecasting error
 The larger the MAD, the less the accurate the
resulting model
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23
MAD Problem Data
Question: What is the MAD value given the forecast values in the table below?
Month
Sales
1
2
3
4
5
220
250
210
300
325
Forecast
n/a
255
205
320
315
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MAD Problem Solution
Month
1
2
3
4
5
Sales
220
250
210
300
325
Forecast
n/a
255
205
320
315
Abs Error
5
5
20
10
n
A
MAD =
t
t =1
n
- Ft
=
40
= 10
4
40
Note that by itself, the MAD only lets us know the mean error in a
set of forecasts
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Tracking Signal Formula
 The Tracking Signal or TS is a measure that indicates whether the
forecast average is keeping pace with any genuine upward or
downward changes in demand.
 Depending on the number of MAD’s selected, the TS can be used like a
quality control chart indicating when the model is generating too much
error in its forecasts.
 The TS formula is:
RSFE Running sum of forecast errors
TS =
=
MAD
Mean absolute deviation
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Tracking Signal
Month
Forecast
Actual
Deviation
RSFE
Abs. Dev.
Sum of AD
MAD
TS
1
1000
950
-50
-50
50
50
50
-1
2
1000
1070
70
20
70
120
60
0.33
3
1000
1100
100
120
100
220
73.33
1.64
4
1000
960
-40
80
40
260
65
1.23
5
1000
1090
90
170
90
350
70
2.43
6
1000
1050
50
220
50
400
66.67
3.30
Simple Linear Regression Model
The simple linear regression model
seeks to fit a line through various
data over time
Y
a
0 1 2 3 4 5
Yt = a + bx
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x
Is the linear regression model
Yt is the regressed forecast value or dependent variable in the model, a is
the intercept value of the the regression line, and b is similar to the slope
of the regression line. However, since it is calculated with the variability
of the data in mind, its formulation is not as straight forward as our
usual notion of slope.
Multiple Regression:
Using time series data
 Forecasting based on many pieces of information that are
historically related.
 Independent data (data used to forecast another set of data) is
generally lagged in time.
 Examination of the “errors” reveals model structure
weaknesses.
 Errors should be random and unpredictable.
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29
Algebra 1 Review
Draw a line between two points
y  mx  b
(x2,y2)
( x, y)
(x1,y1)
x  x2  x1
Intercept b
General line equation
y 
y2  y1
where,
m is the slope
m
y
y  y1
 2
x
x2  x1
b is the intercept
(you need the slope and one point)
b  y  mx
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Simple Linear Regression
Draw a line among many points
General line equation
ˆi  b0  b1xi
y
where,
b1 is the estimated slope
cov(x, y ) sxy
b1 
 2
var( x)
sx
Intercept b
b0 is the intercept
(you need the slope and one point)
b0  y  b1x
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Simple Regression - example
 The owner of Best of Beans Café believes that the
store sells more coffee in the morning hours when
the temperature is cold and fewer cups of coffee
when the temperature is warm.
 Develop a regression to help forecast the sales any
day based on the morning temperature.
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Date
1/1/2009
1/15/2009
1/29/2009
2/12/2009
2/26/2009
3/12/2009
3/26/2009
4/9/2009
4/23/2009
5/7/2009
Temperature
7:00AM
20
-3
14
-2
15
34
28
40
42
50
Cups of
Coffee Sold
(7-9AM)
187
305
276
296
238
159
190
150
133
127
Cups of Coffee old
Example: Best of Beans Café
Temperature (F)
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SUMMARY OUTPUT
Regression Statistics
Multiple R
0.95105994
R Square
0.90451501
Adjusted R Square
0.89257939
Standard Error
21.9427493
Observations
10
ANOVA
df
SS
MS
Regression
1 36488.23 36488.23
Residual
8 3851.874
Total
9
Coefficients
F
75.7828
Significance F
2.36537E-05
481.4842
40340.1
Standard
Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
300.670433
11.8265
25.42344
6.14E-09
273.3984671
327.9424
Temperature 7:00AM
-3.5029594 0.402392
-8.70533
2.37E-05
-4.43087791
-2.57504
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Simple Regression - example
How many cups of coffee would the owner of Best of Beans
Café estimate will be sold if the morning temperature is 32
degrees?
How many cups of coffee would the owner of Best of Beans
Café estimate will be sold if the morning temperature is -15
degrees?
35
Multiple Regression - example
 You are working for General Motors in the light truck
division. Your responsibilities include forecasting the
number of units to produce in the next six months.
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14
12
12
10
10
8
8
6
6
Autos and light truck assemblies
(millions)
4
4
Average majority prime rate charged
by banks on short-term loans to
business, quoted on an investment
basis (lagged 6 months)
2
2
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
0
1986
0
Prime Rate
Iraq War
9/11/01
Taliban
G.W.Bu
Clinton
Iraq War
Berlin
14
1984
Millions of units
Reagan
H.W.Bus
Interest Rates & Light Vechicles
2006
2004
2002
2000
1998
6
1996
8
1994
1992
1990
1988
1986
1984
Millions of units
14
10
Autos and light truck assemblies
(millions)
Gasoline price (cents per gallon
2000 prices)
150
100
4
50
2
0
0
cents per gallon of gasoline
Iraq War
9/11/01
Taliban
G.W.Bu
Clinton
Iraq War
Berlin
H.W.Bus
Reagan
37
Gasoline Price & Units Produced
250
12
200
38
Ferengi Rules of Acquisition
34. War is good for business. ("Destiny")
35. Peace is good for business. ("Destiny")
Download the “Forecasting Spreadsheet.xls”