05 forecasting

© 2008 Prentice-Hall, Inc.
Chapter 5
To accompany
Quantitative Analysis for Management, Tenth Edition,
by Render, Stair, and Hanna
Power Point slides created by Jeff Heyl
Forecasting
© 2009 Prentice-Hall, Inc.

© 2009 Prentice-Hall, Inc. 5 – 2
Introduction
 Managers are always trying to reduce
uncertainty and make better estimates of what
will happen in the future
 This is the main purpose of forecasting
 Some firms use subjective methods
 Seat-of-the pants methods, intuition,
experience
 There are also several quantitative techniques
 Moving averages, exponential smoothing,
trend projections, least squares regression
analysis

Introduction
 Eight steps to forecasting :
1. Determine the use of the forecast—what
objective are we trying to obtain?
2. Select the items or quantities that are to be
forecasted
3. Determine the time horizon of the forecast
4. Select the forecasting model or models
5. Gather the data needed to make the
forecast
6. Validate the forecasting model
7. Make the forecast
8. Implement the results

Introduction
 These steps are a systematic way of initiating,
designing, and implementing a forecasting
system
 When used regularly over time, data is
collected routinely and calculations performed
automatically
 There is seldom one superior forecasting
system
 Different organizations may use different
techniques
 Whatever tool works best for a firm is the one
they should use

Regression
Analysis
Multiple
Regression
Moving
Average
Exponential
Smoothing
Trend
Projections
Decomposition
Delphi
Methods
Jury of Executive
Opinion
Sales Force
Composite
Consumer
Market Survey
Time-Series
Methods
Qualitative
Models
Causal
Methods
Forecasting Models
Forecasting
Techniques
Figure 5.1

Time-Series Models
 Time-series models attempt to predict
the future based on the past
 Common time-series models are
 Moving average
 Exponential smoothing
 Trend projections
 Decomposition
 Regression analysis is used in trend
projections and one type of
decomposition model

Causal Models
 Causal modelsCausal models use variables or factors
that might influence the quantity being
forecasted
 The objective is to build a model with
the best statistical relationship between
the variable being forecast and the
independent variables
 Regression analysis is the most
common technique used in causal
modeling

Qualitative Models
 Qualitative modelsQualitative models incorporate judgmental
or subjective factors
 Useful when subjective factors are
thought to be important or when accurate
quantitative data is difficult to obtain
 Common qualitative techniques are
 Delphi method
 Jury of executive opinion
 Sales force composite
 Consumer market surveys

Qualitative Models
 Delphi MethodDelphi Method – an iterative group process where
(possibly geographically dispersed) respondentsrespondents
provide input to decision makersdecision makers
 Jury of Executive OpinionJury of Executive Opinion – collects opinions of a
small group of high-level managers, possibly
using statistical models for analysis
 Sales Force CompositeSales Force Composite – individual salespersons
estimate the sales in their region and the data is
compiled at a district or national level
 Consumer Market SurveyConsumer Market Survey – input is solicited from
customers or potential customers regarding their
purchasing plans

Scatter Diagrams
0
50
100
150
200
250
300
350
400
450
0 2 4 6 8 10 12
Time (Years)
AnnualSales
Radios
Televisions
Compact Discs
Scatter diagrams are helpful when forecasting time-series
data because they depict the relationship between variables.

Scatter Diagrams
 Wacker Distributors wants to forecast sales for
three different products
YEAR TELEVISION SETS RADIOS COMPACT DISC PLAYERS
1 250 300 110
2 250 310 100
3 250 320 120
4 250 330 140
5 250 340 170
6 250 350 150
7 250 360 160
8 250 370 190
9 250 380 200
10 250 390 190
Table 5.1

Scatter Diagrams
Figure 5.2
        
330 –
250 –
200 –
150 –
100 –
50 –
| | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10
Time (Years)
AnnualSalesofTelevisions
(a)
 Sales appear to be
constant over time
Sales = 250
 A good estimate of
sales in year 11 is
250 televisions

Scatter Diagrams










increasing at a
constant rate of 10
radios per year
Sales = 290 + 10(Year)
 A reasonable
estimate of sales in
year 11 is 400
televisions
420 –
400 –
380 –
360 –
340 –
320 –
300 –
280 –
| | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10
Time (Years)
AnnualSalesofRadios
(b)
Figure 5.2

Scatter Diagrams







 
 This trend line may
not be perfectly
accurate because
of variation from
year to year
increasing
 A forecast would
probably be a
larger figure each
year
200 –
180 –
160 –
140 –
120 –
100 –
| | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10
Time (Years)
AnnualSalesofCDPlayers
(c)
Figure 5.2

Measures of Forecast Accuracy
 We compare forecasted values with actual values
to see how well one model works or to compare
models
Forecast error = Actual value – Forecast value
 One measure of accuracy is the mean absolutemean absolute
deviationdeviation (MADMAD)
n
∑=
errorforecast
MAD

 Using a naïvenaïve forecasting model
YEAR
ACTUAL
SALES OF CD
PLAYERS FORECAST SALES
ABSOLUTE VALUE OF
ERRORS (DEVIATION),
(ACTUAL – FORECAST)
1 110 — —
2 100 110 |100 – 110| = 10
3 120 100 |120 – 110| = 20
4 140 120 |140 – 120| = 20
5 170 140 |170 – 140| = 30
6 150 170 |150 – 170| = 20
7 160 150 |160 – 150| = 10
8 190 160 |190 – 160| = 30
9 200 190 |200 – 190| = 10
10 190 200 |190 – 200| = 10
11 — 190 —
Sum of |errors| = 160
MAD = 160/9 = 17.8
Table 5.2

 Using a naïvenaïve forecasting model
YEAR
ACTUAL
SALES OF CD
PLAYERS FORECAST SALES
ABSOLUTE VALUE OF
ERRORS (DEVIATION),
(ACTUAL – FORECAST)
1 110 — —
2 100 110 |100 – 110| = 10
3 120 100 |120 – 110| = 20
4 140 120 |140 – 120| = 20
5 170 140 |170 – 140| = 30
6 150 170 |150 – 170| = 20
7 160 150 |160 – 150| = 10
8 190 160 |190 – 160| = 30
9 200 190 |200 – 190| = 10
10 190 200 |190 – 200| = 10
11 — 190 —
Sum of |errors| = 160
MAD = 160/9 = 17.8
Table 5.2
817
9
160errorforecast
.MAD ===
∑
n

 There are other popular measures of forecast
accuracy
 The mean squared errormean squared error
n
∑=
2
error)(
MSE
 The mean absolute percent errormean absolute percent error
%MAPE 100
actual
error
n
∑
=
 And biasbias is the average error and tells whether the
forecast tends to be too high or too low and by
how much. Thus, it can be negative or positive.

Year Actual CD Sales Forecast Sales |Actual -Forecast|
1 110
2 100 110 10
3 120 100 20
4 140 120 20
5 170 140 30
6 150 170 20
7 160 150 10
8 190 160 30
9 200 190 10
10 190 200 10
11 190
Sum of |errors| 160
MAD 17.8

Hospital Days Forecast Error
Example
Ms. Smith forecasted
total hospital inpatient
days last year. Now
that the actual data are
known, she is
reevaluating her
forecasting model.
Compute the MAD,
MSE, and MAPE for her
forecast.
Month Forecast Actual
JAN 250 243
FEB 320 315
MAR 275 286
APR 260 256
MAY 250 241
JUN 275 298
JUL 300 292
AUG 325 333
SEP 320 326
OCT 350 378
NOV 365 382
DEC 380 396

Hospital Days Forecast Error
Example
Forecast Actual |error| error2
|error/actual|
JAN 250 243 7 49 0.03
FEB 320 315 5 25 0.02
MAR 275 286 11 121 0.04
APR 260 256 4 16 0.02
MAY 250 241 9 81 0.04
JUN 275 298 23 529 0.08
JUL 300 292 8 64 0.03
AUG 325 333 8 64 0.02
SEP 320 326 6 36 0.02
OCT 350 378 28 784 0.07
NOV 365 382 17 289 0.04
DEC 380 396 16 256 0.04
AVERAGE
MAD=
11.83
MSE=
192.83
MAPE=
.0381*100 =
3.81

Time-Series Forecasting Models
 A time series is a sequence of evenly
spaced events (weekly, monthly, quarterly,
etc.)
 Time-series forecasts predict the future
based solely of the past values of the
variable
 Other variables, no matter how potentially
valuable, are ignored

Decomposition of a Time-Series
 A time series typically has four components
1.1. TrendTrend (TT) is the gradual upward or
downward movement of the data over time
2.2. SeasonalitySeasonality (SS) is a pattern of demand
fluctuations above or below trend line that
repeats at regular intervals
3.3. CyclesCycles (CC) are patterns in annual data that
occur every several years
4.4. Random variationsRandom variations (RR) are “blips” in the
data caused by chance and unusual
situations

Average Demand
over 4 Years
Trend
Component
Actual
Demand
Line
Time
DemandforProductorService
| | | |
Year Year Year Year
1 2 3 4
Seasonal Peaks
Figure 5.3

 There are two general forms of time-series
models
 The multiplicative model
Demand = T x S x C x R
 The additive model
Demand = T + S + C + R
 Models may be combinations of these two
forms
 Forecasters often assume errors are
normally distributed with a mean of zero

Moving Averages
 Moving averagesMoving averages can be used when demand is
relatively steady over time
 The next forecast is the average of the most
recent n data values from the time series
 The most recent period of data is added and
the oldest is dropped
This methods tends to smooth out short-term
irregularities in the data series
n
n periodspreviousindemandsofSum
forecastaverageMoving =

Moving Averages
 Mathematically
n
YYY
F nttt
t
11
1
+−−
+
+++
=
...
where
= forecast for time period t + 1
= actual value in time period t
n = number of periods to average
tY
1+tF

Wallace Garden Supply Example
 Wallace Garden Supply wants to
forecast demand for its Storage Shed
 They have collected data for the past
year
 They are using a three-month moving
average to forecast demand (n = 3)

Table 5.3
MONTH ACTUAL SHED SALES THREE-MONTH MOVING AVERAGE
January 10
February 12
March 13
April 16
May 19
June 23
July 26
August 30
September 28
October 18
November 16
December 14
January —
(12 + 13 + 16)/3 = 13.67
(13 + 16 + 19)/3 = 16.00
(16 + 19 + 23)/3 = 19.33
(19 + 23 + 26)/3 = 22.67
(23 + 26 + 30)/3 = 26.33
(26 + 30 + 28)/3 = 28.00
(30 + 28 + 18)/3 = 25.33
(28 + 18 + 16)/3 = 20.67
(18 + 16 + 14)/3 = 16.00
(10 + 12 + 13)/3 = 11.67

Weighted Moving Averages
 Weighted moving averagesWeighted moving averages use weights to put
more emphasis on recent periods
 Often used when a trend or other pattern is
emerging
∑
∑=+
)(
))((
Weights
periodinvalueActualperiodinWeight
1
i
Ft
 Mathematically
n
ntntt
t
www
YwYwYw
F
+++
+++
= +−−
+
...
...
21
1121
1
ere
wi = weight for the ith observation

Weighted Moving Averages
 Both simple and weighted averages are
effective in smoothing out fluctuations in
the demand pattern in order to provide
stable estimates
 Problems
Increasing the size of n smoothes out
fluctuations better, but makes the method
less sensitive to real changes in the data
Moving averages can not pick up trends
very well – they will always stay within past
levels and not predict a change to a higher or
lower level

 Wallace Garden Supply decides to try a
weighted moving average model to forecast
demand for its Storage Shed
 They decide on the following weighting
scheme
WEIGHTS APPLIED PERIOD
3 Last month
2 Two months ago
1 Three months ago
6
3 x Sales last month + 2 x Sales two months ago + 1 X Sales three months ago
Sum of the weights

Table 5.4
MONTH ACTUAL SHED SALES
THREE-MONTH WEIGHTED
MOVING AVERAGE
January 10
February 12
March 13
April 16
May 19
June 23
July 26
August 30
September 28
October 18
November 16
December 14
January —
[(3 X 13) + (2 X 12) + (10)]/6 = 12.17
[(3 X 16) + (2 X 13) + (12)]/6 = 14.33
[(3 X 19) + (2 X 16) + (13)]/6 = 17.00
[(3 X 23) + (2 X 19) + (16)]/6 = 20.50
[(3 X 26) + (2 X 23) + (19)]/6 = 23.83
[(3 X 30) + (2 X 26) + (23)]/6 = 27.50
[(3 X 28) + (2 X 30) + (26)]/6 = 28.33
[(3 X 18) + (2 X 28) + (30)]/6 = 23.33
[(3 X 16) + (2 X 18) + (28)]/6 = 18.67
[(3 X 14) + (2 X 16) + (18)]/6 = 15.33

Program 5.1A

Program 5.1B

Exponential Smoothing
 Exponential smoothingExponential smoothing is easy to use and
requires little record keeping of data
 It is a type of moving average
ecast = Last period’s forecast
+ α(Last period’s actual demand
– Last period’s forecast)
Where α is a weight (or smoothing constantsmoothing constant)
with a value between 0 and 1 inclusive
A larger α gives more importance to recent
data while a smaller value gives more
importance to past data

Exponential Smoothing
 Mathematically
)( tttt FYFF −+=+ α1
re
Ft+1 = new forecast (for time period t + 1)
Ft = pervious forecast (for time period t)
α = smoothing constant (0 ≤ α ≤ 1)
Yt = pervious period’s actual demand
 The idea is simple – the new estimate is the
old estimate plus some fraction of the error in
the last period

Exponential Smoothing Example
 In January, February’s demand for a certain
car model was predicted to be 142
 Actual February demand was 153 autos
 Using a smoothing constant of α = 0.20, what
is the forecast for March?
New forecast (for March demand) = 142 + 0.2(153 – 142)
= 144.2 or 144 autos
 If actual demand in March was 136 autos, the
April forecast would be
New forecast (for April demand) = 144.2 + 0.2(136 – 144.2)
= 142.6 or 143 autos

Selecting the Smoothing Constant
 Selecting the appropriate value for α is
key to obtaining a good forecast
 The objective is always to generate an
accurate forecast
 The general approach is to develop trial
forecasts with different values of α and
select the α that results in the lowest MAD

Port of Baltimore Example
QUARTER
ACTUAL
TONNAGE
UNLOADED
FORECAST
USING α =0.10
FORECAST
USING α =0.50
1 180 175 175
2 168 175.5 = 175.00 + 0.10(180 – 175) 177.5
3 159 174.75 = 175.50 + 0.10(168 – 175.50) 172.75
4 175 173.18 = 174.75 + 0.10(159 – 174.75) 165.88
5 190 173.36 = 173.18 + 0.10(175 – 173.18) 170.44
6 205 175.02 = 173.36 + 0.10(190 – 173.36) 180.22
7 180 178.02 = 175.02 + 0.10(205 – 175.02) 192.61
8 182 178.22 = 178.02 + 0.10(180 – 178.02) 186.30
9 ? 178.60 = 178.22 + 0.10(182 – 178.22) 184.15
Table 5.5
 Exponential smoothing forecast for two values of α

Selecting the Best Value of α
QUARTER
ACTUAL
TONNAGE
UNLOADED
FORECAST
WITH α =
0.10
ABSOLUTE
DEVIATIONS
FOR α = 0.10
FORECAST
WITH α = 0.50
ABSOLUTE
DEVIATIONS
FOR α = 0.50
1 180 175
5…..
175
5….
2 168 175.5
7.5..
177.5
9.5..
3 159 174.75
15.75
172.75
13.75
4 175 173.18
1.82
165.88
9.12
5 190 173.36
16.64
170.44
19.56
6 205 175.02
29.98
180.22
24.78
7 180 178.02
1.98
192.61
12.61
8 182 178.22
3.78
186.30
4.3..
Sum of absolute deviations 82.45 98.63
MAD =
Σ|deviations|
= 10.31 MAD = 12.33
Table 5.6
Best choiceBest choice

Program 5.2A

Program 5.2B

PM Computer: Moving Average
Example
 PM Computer assembles customized personal
computers from generic parts
 The owners purchase generic computer parts
in volume at a discount from a variety of
sources whenever they see a good deal.
 It is important that they develop a good
forecast of demand for their computers so
they can purchase component parts
efficiently.

PM Computers: Data
Period Month Actual Demand
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 June 50
7 July 43
8 Aug 47
9 Sept 56
 Compute a 2-month moving average
 Compute a 3-month weighted average using weights of
4,2,1 for the past three months of data
 Compute an exponential smoothing forecast using α =
0.7, previous forecast of 40
 Using MAD, what forecast is most accurate?

PM Computers: Moving Average
Solution
2 month
MA Abs. Dev 3 month WMA Abs. Dev Exp.Sm. Abs. Dev
37.00
37.00 3.00
38.50 2.50 39.10 1.90
40.50 3.50 40.14 3.14 40.43 3.43
39.00 6.00 38.57 6.43 38.03 6.97
41.00 9.00 42.14 7.86 42.91 7.09
47.50 4.50 46.71 3.71 47.87 4.87
46.50 0.50 45.29 1.71 44.46 2.54
45.00 11.00 46.29 9.71 46.24 9.76
51.50 51.57 53.07
5.29 5.43 4.95MAD
Exponential smoothing resulted in the lowest MAD.

Exponential Smoothing with
Trend Adjustment
 Like all averaging techniques, exponential
smoothing does not respond to trends
 A more complex model can be used that
adjusts for trends
 The basic approach is to develop an
exponential smoothing forecast then adjust it
for the trend
t) = New forecast (Ft)
+ Trend correction (Tt)

Exponential Smoothing with
Trend Adjustment
 The equation for the trend correction uses a
new smoothing constant β
 Tt is computed by
)()1( 11 tttt FFTT −+−= ++ ββ
where
Tt+1 = smoothed trend for period t + 1
Tt = smoothed trend for preceding period
β = trend smooth constant that we select
Ft+1 = simple exponential smoothed
forecast for period t + 1
Ft = forecast for pervious period

Selecting a Smoothing Constant
 As with exponential smoothing, a high value of β
makes the forecast more responsive to changes
in trend
 A low value of β gives less weight to the recent
trend and tends to smooth out the trend
 Values are generally selected using a trial-and-
error approach based on the value of the MAD for
different values of β
 Simple exponential smoothing is often referred to
as first-order smoothingfirst-order smoothing
 Trend-adjusted smoothing is called second-second-
orderorder, double smoothingdouble smoothing, or Holt’s methodHolt’s method

Trend Projection
 Trend projection fits a trend line to a
series of historical data points
 The line is projected into the future for
medium- to long-range forecasts
 Several trend equations can be
developed based on exponential or
quadratic models
 The simplest is a linear model developed
using regression analysis

Trend Projection
 Trend projections are used to forecast time-
series data that exhibit a linear trend.
 A trend line is simply a linear regression
equation in which the independent variable (X)
is the time period
 Least squares may be used to determine a
trend projection for future forecasts.
 Least squares determines the trend line forecast by
minimizing the mean squared error between the
trend line forecasts and the actual observed values.
 The independent variable is the time period
and the dependent variable is the actual
observed value in the time series.

Trend Projection
 The mathematical form is
XbbY 10 +=ˆ
where
= predicted value
b0 = intercept
b1 = slope of the line
X = time period (i.e., X = 1, 2, 3, …, n)
Yˆ

Trend Projection
ValueofDependentVariable
Time
*
*
*
*
*
*
*Dist2
Dist4
Dist6
Dist1
Dist3
Dist5
Dist7
Figure 5.4

Midwestern Manufacturing
Company Example
 Midwestern Manufacturing Company has
experienced the following demand for it’s electrical
generators over the period of 2001 – 2007
YEAR ELECTRICAL GENERATORS SOLD
2001 74
2002 79
2003 80
2004 90
2005 105
2006 142
2007 122
Table 5.7

Company Example
Program 5.3A
Notice code
instead of
actual years

Company Example
Program 5.3B
r2
says model predicts
about 80% of the
variability in demand
Significance level for
F-test indicates a
definite relationship

Company Example
 The forecast equation is
XY 54107156 ..ˆ +=
 To project demand for 2008, we use the coding
system to define X = 8
(sales in 2008) = 56.71 + 10.54(8)
= 141.03, or 141 generators
 Likewise for X = 9
(sales in 2009) = 56.71 + 10.54(9)
= 151.57, or 152 generators

Company Example

 




GeneratorDemand
Year
160 –
150 –
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –
60 –
50 –
| | | | | | | | |
2001 2002 2003 2004 2005 2006 2007 2008 2009

Actual Demand Line
Trend Line
XY 54107156 ..ˆ +=
Figure 5.5

Company Example
Program 5.4A

Company Example
Program 5.4B

Seasonal Variations
 Recurring variations over time may
indicate the need for seasonal
adjustments in the trend line
 A seasonal index indicates how a
particular season compares with an
average season
 When no trend is present, the seasonal
index can be found by dividing the
average value for a particular season by
the average of all the data

Seasonal Variations
 Eichler Supplies sells telephone
answering machines
 Data has been collected for the past two
years sales of one particular model
 They want to create a forecast that
includes seasonality

Seasonal Variations
MONTH
SALES DEMAND
AVERAGE TWO-
YEAR DEMAND
MONTHLY
DEMAND
AVERAGE
SEASONAL
INDEXYEAR 1 YEAR 2
January 80 100
90
94 0.957
February 85 75
80
94 0.851
March 80 90
85
94 0.904
April 110 90
100
94 1.064
May 115 131
123
94 1.309
June 120 110
115
94 1.223
July 100 110
105
94 1.117
August 110 90
100
94 1.064
September 85 95
90
94 0.957
Seasonal index =
Average two-year demand
Average monthly demand
Average monthly demand = = 94
1,128
12 months
Table 5.8

Seasonal Variations
 The calculations for the seasonal indices are
Jan. July969570
12
2001
=× .
,
1121171
12
2001
=× .
,
Feb. Aug.858510
12
2001
=× .
,
1060641
12
2001
=× .
,
Mar. Sept.909040
12
2001
=× .
,
969570
12
2001
=× .
,
Apr. Oct.1060641
12
2001
=× .
,
858510
12
2001
=× .
,
May Nov.1313091
12
2001
=× .
,
858510
12
2001
=× .
,
June Dec.1222231
12
2001
=× .
,
858510
12
2001
=× .
,

Regression with Trend and
Seasonal Components
 Multiple regressionMultiple regression can be used to forecast both
trend and seasonal components in a time series
 One independent variable is time
 Dummy independent variables are used to represent the
seasons
 The model is an additive decomposition model
where
X1 = time period
X2 = 1 if quarter 2, 0 otherwise
44332211 XbXbXbXbaY ++++=ˆ

Seasonal Components
Program 5.6A

Seasonal Components
Program 5.6B (partial)

Seasonal Components
 The resulting regression equation is
4321 130738715321104 XXXXY .....ˆ ++++=
 Using the model to forecast sales for the first two
quarters of next year
 These are different from the results obtained
using the multiplicative decomposition method
 Use MAD and MSE to determine the best model
13401300738071513321104 =++++= )(.)(.)(.)(..ˆY
15201300738171514321104 =++++= )(.)(.)(.)(..ˆY

Seasonal Components
 American Airlines original spare parts inventory
system used only time-series methods to
forecast the demand for spare parts
 This method was slow to responds to even moderate
changes in aircraft utilization let alone major fleet
expansions
 They developed a PC-based system named RAPS
which uses linear regression to establish a
relationship between monthly part removals and
various functions of monthly flying hours
 The computation now takes only one hour instead of
the days the old system needed
 Using RAPS provided a one time savings of $7 million
and a recurring annual savings of nearly $1 million

Monitoring and Controlling Forecasts
 Tracking signalsTracking signals can be used to monitor
the performance of a forecast
 Tacking signals are computed using the
following equation
MAD
RSFE
=signalTracking
n
∑=
errorforecast
MAD
where

Acceptable
Range
Signal Tripped
Upper Control Limit
Lower Control Limit
0 MADs
+
–
Time
Figure 5.7
Tracking Signal

 Positive tracking signals indicate demand is
greater than forecast
 Negative tracking signals indicate demand is less
than forecast
 Some variation is expected, but a good forecast
will have about as much positive error as
negative error
 Problems are indicated when the signal trips
either the upper or lower predetermined limits
 This indicates there has been an unacceptable
amount of variation
 Limits should be reasonable and may vary from
item to item

Seasonal Components
 How do you decide on the upper and lower
limits?
 Too small a value will trip the signal too often and
too large will cause a bad forecast
 Plossl & Wight – use maximums of ±4 MADs for
high volume stock items and ±8 MADs for lower
volume items
 One MAD is equivalent to approximately 0.8
standard deviation so that ±4 MADs =3.2 s.d.
 For a forecast to be “in control”, 89% of the errors
are expected to fall within ±2 MADs, 98% with ±3
MADs or 99.9% within ±4 MADs whenever the
errors are approximately normally distributed

Kimball’s Bakery Example
 Tracking signal for quarterly sales of croissants
TIME
PERIOD
FORECAST
DEMAND
ACTUAL
DEMAND ERROR RSFE
|FORECAST |
| ERROR |
CUMULATIVE
ERROR MAD
TRACKING
SIGNAL
1 100 90 –10 –10 10 10 10.0 –1
2 100 95 –5 –15 5 15 7.5 –2
3 100 115 +15 0 15 30 10.0 0
4 110 100 –10 –10 10 40 10.0 –1
5 110 125 +15 +5 15 55 11.0 +0.5
6 110 140 +30 +35 30 85 14.2 +2.5
214
6
85errorforecast
.MAD ===
∑
n
sMAD.
.MAD
RSFE
52
214
35
signalTracking ===

Forecasting at Disney
 The Disney chairman receives a dailyThe Disney chairman receives a daily
report from his main theme parks thatreport from his main theme parks that
contains only two numbers – thecontains only two numbers – the forecastforecast
of yesterday’s attendance at the parks andof yesterday’s attendance at the parks and
thethe actualactual attendanceattendance
 An error close to zero (using MAPE as the
measure) is expected
 The annual forecast of total volume
conducted in 1999 for the year 2000
resulted in a MAPE of 0

Using The Computer to Forecast
 Spreadsheets can be used by small and
medium-sized forecasting problems
 More advanced programs (SAS, SPSS,
Minitab) handle time-series and causal
models
 May automatically select best model
parameters
 Dedicated forecasting packages may be
fully automatic
 May be integrated with inventory planning
and control

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