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ã 2002 South-Western/Thomson Learning
2002 South-Western/Thomson Learning TM
TM
Slides prepared
Slides prepared
by John Loucks
by John Loucks
2
Chapter 3
Demand Forecasting
3
Overview
 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
4
Demand Management
 Independent demand items are the only
items demand for which needs to be
forecast
 These items include:
 Finished goods and
 Spare parts
5
Demand Management
A
Independent Demand
(finished goods and spare parts)
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
(components)
6
Demand Management
The importance of forecasting in OM
7
Introduction
 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.
8
Forecasting is an Integral Part
of Business Planning
Forecast
Method(s)
Demand
Estimates
Sales
Forecast
Management
Team
Inputs:
Market,
Economic,
Other
Business
Strategy
Production Resource
Forecasts
9
Some Reasons Why
Forecasting is Essential in OM
 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.
10
Examples of Production Resource Forecasts
Forecast
Horizon
Time Span Item Being Forecast
Units of
Measure
Long-Range Years
 Product lines
 Factory capacities
 Planning for new products
 Capital expenditures
 Facility location or expansion
 R&D
Dollars, tons, etc.
Medium-
Range
Months
 Product groups
 Department capacities
 Sales planning
 Production planning and budgeting
Dollars, tons, etc.
Short-Range Weeks
 Specific product quantities
 Machine capacities
 Planning
 Purchasing
 Scheduling
 Workforce levels
 Production levels
 Job assignments
Physical units of
products
11
Forecasting Methods
 Qualitative Approaches
 Quantitative Approaches
12
Qualitative Approaches
 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
13
Qualitative Methods
 Educated guess intuitive hunches
 Executive committee consensus
 Delphi method
 Survey of sales force
 Survey of customers
 Historical analogy
 Market research scientifically conducted surveys
14
Qualitative Forecasting Applications
Small and Large Firms
Technique Low Sales
(less than $100M)
High Sales
(more than $500M)
Manager’s Opinion 40.7% 39.6%
Executive’s
Opinion
40.7% 41.6%
Sales Force
Composite
29.6% 35.4%
Number of Firms 27 48
Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting
Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100.
Note: More than one response was permitted.
15
Quantitative Forecasting Approaches
 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
16
Quantitative Forecasting Applications
Small and Large Firms
Technique Low Sales
(less than $100M)
High Sales
(more than $500M)
Moving Average 29.6% 29.2
Simple Linear Regression 14.8% 14.6
Naive 18.5% 14.6
Single Exponential
Smoothing
14.8% 20.8
Multiple Regression 22.2% 27.1
Simulation 3.7% 10.4
Classical Decomposition 3.7% 8.3
Box-Jenkins 3.7% 6.3
Number of Firms 27 48
Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting
Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100.
Note: More than one response was permitted.
17
 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
Time Series Analysis
18
Components of Time Series
 Trends are noted by an upward or downward sloping
line
 Seasonality is a data pattern that repeats itself over
the period of one year or less
 Cycle is a data pattern that repeats itself... may take
years
 Irregular variations are jumps in the level of the series
due to extraordinary events
 Random fluctuation from random variation or
unexplained causes
19
Seasonal Patterns
Length of Time Number of
Before Pattern Length of Seasons
Is Repeated Season in Pattern
Year Quarter 4
Year Month 12
Year Week 52
Month Day 28-31
Week Day 7
20
Quantitative Forecasting Approaches
 Linear Regression
 Simple Moving Average
 Weighted Moving Average
 Exponential Smoothing (exponentially weighted
moving average)
 Exponential Smoothing with Trend (double
exponential smoothing)
21
Long-Range Forecasts
 Time spans usually greater than one year
 Necessary to support strategic decisions about
planning products, processes, and facilities
22
Simple Linear Regression
 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.
23
Simple Linear Regression
 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
24
Simple Linear Regression
 Constants a and b
The constants a and b are computed using the
following equations:
2
2 2
x y- x xy
a =
n x -( x)
   
 
2 2
xy- x y
b =
n x -( x)
n  
 
25
Simple Linear Regression
 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.
26
Example: College Enrollment
 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 2.8 5 3.3
3 2.9 6 3.4
27
Example: College Enrollment
 Simple Linear Regression
x y x2 xy
1 2.5 1 2.5
2 2.8 4 5.6
3 2.9 9 8.7
4 3.2 16 12.8
5 3.3 25 16.5
6 3.4 36 20.4
Sx=21 Sy=18.1 Sx2=91 Sxy=66.5
28
Example: College Enrollment
 Simple Linear Regression
Y = 2.387 + 0.180X
2
91(18.1) 21(66.5)
2.387
6(91) (21)
a

 

6(66.5) 21(18.1)
0.180
105
b

 
29
Example: College Enrollment
 Simple Linear Regression
Y7 = 2.387 + 0.180(7) = 3.65 or 3,650 students
Y8 = 2.387 + 0.180(8) = 3.83 or 3,830 students
Y9 = 2.387 + 0.180(9) = 4.01 or 4,010 students
Note: Enrollment is expected to increase by 180
students per year.
30
Simple Linear Regression
 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.
31
Example: Railroad Products Co.
 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.
32
Example: Railroad Products Co.
 Simple Linear Regression – Causal Model
RPC Sales Car Loadings
Year ($millions) (millions)
1 9.5 120
2 11.0 135
3 12.0 130
4 12.5 150
5 14.0 170
6 16.0 190
7 18.0 220
33
Example: Railroad Products Co.
 Simple Linear Regression – Causal Model
x y x2 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
34
Example: Railroad Products Co.
 Simple Linear Regression – Causal Model
Y = 0.528 + 0.0801X
2
185,425(93) 1,115(15,440)
a 0.528
7(185,425) (1,115)

 

2
7(15,440) 1,115(93)
b 0.0801
7(185,425) (1,115)

 

35
Example: Railroad Products Co.
 Simple Linear Regression – Causal Model
Y8 = 0.528 + 0.0801(250) = $20.55 million
Y9 = 0.528 + 0.0801(270) = $22.16 million
Y10 = 0.528 + 0.0801(300) = $24.56 million
Note: RPC sales are expected to increase by
$80,100 for each additional million national freight
car loadings.
36
Multiple Regression Analysis
 Multiple regression analysis is used when there are
two or more independent variables.
 An example of a multiple regression equation is:
Y = 50.0 + 0.05X1 + 0.10X2 – 0.03X3
where: Y = firm’s annual sales ($millions)
X1 = industry sales ($millions)
X2 = regional per capita income ($thousands)
X3 = regional per capita debt ($thousands)
37
Coefficient of Correlation (r)
 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.
38
Coefficient of Correlation (r)
 Meanings of several values of r:
-1 a perfect negative relationship (as x goes up, y
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
39
Coefficient of Correlation (r)
 r is computed by:
2 2 2 2
( ) ( )
n xy x y
r
n x x n y y


   
 
   
  
   
40
Coefficient of Determination (r2)
 The coefficient of determination, r2, is the square of
the coefficient of correlation.
 The modification of r to r2 allows us to shift from
subjective measures of relationship to a more specific
measure.
 r2 is determined by the ratio of explained variation to
total variation:
2
2
2
( )
( )
Y y
r
y y





41
Example: Railroad Products Co.
 Coefficient of Correlation
x y x2 xy y2
120 9.5 14,400 1,140 90.25
135 11.0 18,225 1,485 121.00
130 12.0 16,900 1,560 144.00
150 12.5 22,500 1,875 156.25
170 14.0 28,900 2,380 196.00
190 16.0 36,100 3,040 256.00
220 18.0 48,400 3,960 324.00
1,115 93.0 185,425 15,440 1,287.50
42
Example: Railroad Products Co.
 Coefficient of Correlation
r = .9829
2 2
7(15,440) 1,115(93)
7(185,425) (1,115) 7(1,287.5) (93)
r


  
 
  
43
Example: Railroad Products Co.
 Coefficient of Determination
r2 = (.9829)2 = .966
96.6% of the variation in RPC sales is explained by
national freight car loadings.
44
Ranging Forecasts
 Forecasts for future periods are only estimates and are
subject to error.
 One way to deal with uncertainty is to develop best-
estimate forecasts and the ranges within which the
actual data are likely to fall.
 The ranges of a forecast are defined by the upper and
lower limits of a confidence interval.
45
Ranging Forecasts
 The ranges or limits of a forecast are estimated by:
Upper limit = Y + t(syx)
Lower limit = Y - t(syx)
where:
Y = best-estimate forecast
t = number of standard deviations from the mean
of the distribution to provide a given
probability of exceeding the limits through
chance
syx = standard error of the forecast
46
Ranging Forecasts
 The standard error (deviation) of the forecast is
computed as:
2
yx
y - a y - b xy
s =
n - 2
  
47
Example: Railroad Products Co.
 Ranging Forecasts
Recall that linear regression analysis provided a
forecast of annual sales for RPC in year 8 equal to
$20.55 million.
Set the limits (ranges) of the forecast so that there
is only a 5 percent probability of exceeding the limits
by chance.
48
Example: Railroad Products Co.
 Ranging Forecasts
 Step 1: Compute the standard error of the
forecasts, syx.
 Step 2: Determine the appropriate value for t.
n = 7, so degrees of freedom = n – 2 = 5.
Area in upper tail = .05/2 = .025
Appendix B, Table 2 shows t = 2.571.
1287.5 .528(93) .0801(15,440)
.5748
7 2
yx
s
 
 

49
Example: Railroad Products Co.
 Ranging Forecasts
 Step 3: Compute upper and lower limits.
Upper limit = 20.55 + 2.571(.5748)
= 20.55 + 1.478
= 22.028
Lower limit = 20.55 - 2.571(.5748)
= 20.55 - 1.478
= 19.072
We are 95% confident the actual sales for year 8
will be between $19.072 and $22.028 million.
50
Seasonalized Time Series Regression Analysis
 Select a representative historical data set.
 Develop a seasonal index for each season.
 Use the seasonal indexes to deseasonalize the data.
 Perform linear regression analysis on the
deseasonalized data.
 Use the regression equation to compute the forecasts.
 Use the seasonal indexes to reapply the seasonal
patterns to the forecasts.
51
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
An analyst at CPC wants to develop next year’s
quarterly forecasts of sales revenue for CPC’s line of
Epsilon Computers. She believes that the most recent
8 quarters of sales (shown on the next slide) are
representative of next year’s sales.
52
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Representative Historical Data Set
Year Qtr. ($mil.) Year Qtr. ($mil.)
1 1 7.4 2 1 8.3
1 2 6.5 2 2 7.4
1 3 4.9 2 3 5.4
1 4 16.1 2 4 18.0
53
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Compute the Seasonal Indexes
Quarterly Sales
Year Q1 Q2 Q3 Q4 Total
1 7.4 6.5 4.9 16.1 34.9
2 8.3 7.4 5.4 18.0 39.1
Totals 15.7 13.9 10.3 34.1 74.0
Qtr. Avg. 7.85 6.95 5.15 17.05 9.25
Seas.Ind. .849 .751 .557 1.843 4.000
54
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Deseasonalize the Data
Quarterly Sales
Year Q1 Q2 Q3 Q4
1 8.72 8.66 8.80 8.74
2 9.78 9.85 9.69 9.77
55
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Perform Regression on Deseasonalized Data
Yr. Qtr. x y x2 xy
1 1 1 8.72 1 8.72
1 2 2 8.66 4 17.32
1 3 3 8.80 9 26.40
1 4 4 8.74 16 34.96
2 1 5 9.78 25 48.90
2 2 6 9.85 36 59.10
2 3 7 9.69 49 67.83
2 4 8 9.77 64 78.16
Totals 36 74.01 204 341.39
56
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Perform Regression on Deseasonalized Data
Y = 8.357 + 0.199X
2
204(74.01) 36(341.39)
a 8.357
8(204) (36)

 

2
8(341.39) 36(74.01)
b 0.199
8(204) (36)

 

57
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Compute the Deseasonalized Forecasts
Y9 = 8.357 + 0.199(9) = 10.148
Y10 = 8.357 + 0.199(10) = 10.347
Y11 = 8.357 + 0.199(11) = 10.546
Y12 = 8.357 + 0.199(12) = 10.745
Note: Average sales are expected to increase by
.199 million (about $200,000) per quarter.
58
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 Seasonalize the Forecasts
Seas. Deseas. Seas.
Yr. Qtr. Index Forecast Forecast
3 1 .849 10.148 8.62
3 2 .751 10.347 7.77
3 3 .557 10.546 5.87
3 4 1.843 10.745 19.80
59
Short-Range Forecasts
 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
60
Evaluating Forecast-Model Performance
Short-range forecasting models are evaluated on the
basis of three characteristics:
 Impulse response
 Noise-dampening ability
 Accuracy
61
Evaluating Forecast-Model Performance
 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.
62
Evaluating Forecast-Model Performance
 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
63
Monitoring Accuracy
 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)
64
Monitoring Accuracy
 Mean Absolute Deviation (MAD)
n
periods
n
for
deviation
absolute
of
Sum
=
MAD
n
i i
i=1
Actual demand -Forecast demand
MAD =
n

65
 Mean Squared Error (MSE)
MSE = (Syx)2
A small value for Syx 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 syx are related:
MSE = 1.25(MAD)
Monitoring Accuracy
66
Short-Range Forecasting Methods
 (Simple) Moving Average
 Weighted Moving Average
 Exponential Smoothing
 Exponential Smoothing with Trend
67
Simple Moving Average
 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
68
Simple Moving Average
 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)
69
Weighted Moving Average
 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
70
Weighted Moving Average
 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.
71
 The weights used to compute the forecast (moving
average) are exponentially distributed.
 The forecast is the sum of the old forecast and a
portion (a) of the forecast error (A t-1 - Ft-1).
Ft = Ft-1 + a(A t-1 - Ft-1)
 . . . more
Exponential Smoothing
72
Exponential Smoothing
 The smoothing constant, a, must be between 0.0 and
1.0.
 A large a provides a high impulse response forecast.
 A small a provides a low impulse response forecast.
73
Example: Central Call Center
 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.
74
Example: Central Call Center
 Moving Average
 Representative Historical Data
Day Calls Day Calls
1 159 7 203
2 217 8 195
3 186 9 188
4 161 10 168
5 173 11 198
6 157 12 159
75
Example: Central Call Center
 Moving Average
Use the moving average method with an AP = 3
days to develop a forecast of the call volume in Day
13.
F13 = (168 + 198 + 159)/3 = 175.0 calls
76
Example: Central Call Center
 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.
F13 = .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).
77
Example: Central Call Center
 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?
F12 = 180.76 + .25(198 – 180.76) = 185.07
F13 = 185.07 + .25(159 – 185.07) = 178.55
78
Example: Central Call Center
 Forecast Accuracy - MAD
Which forecasting method (the AP = 3 moving
average or the a = .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.)
79
Example: Central Call Center
AP = 3 a = .25
Day Calls Forec. |Error| Forec. |Error|
4 161 187.3 26.3 186.0 25.0
5 173 188.0 15.0 179.8 6.8
6 157 173.3 16.3 178.1 21.1
7 203 163.7 39.3 172.8 30.2
8 195 177.7 17.3 180.4 14.6
9 188 185.0 3.0 184.0 4.0
10 168 195.3 27.3 185.0 17.0
11 198 183.7 14.3 180.8 17.2
12 159 184.7 25.7 185.1 26.1
MAD 20.5 18.0
80
Exponential Smoothing with Trend
 As we move toward medium-range forecasts, trend
becomes more important.
 Incorporating a trend component into exponentially
smoothed forecasts is called double exponential
smoothing.
 The estimate for the average and the estimate for the
trend are both smoothed.
81
Exponential Smoothing with Trend
 Model Form
FTt = St-1 + Tt-1
where:
FTt = forecast with trend in period t
St-1 = smoothed forecast (average) in period t-1
Tt-1 = smoothed trend estimate in period t-1
82
Exponential Smoothing with Trend
 Smoothing the Average
St = FTt + a (At – FTt)
 Smoothing the Trend
Tt = Tt-1 + b (FTt – FTt-1 - Tt-1)
where: a = smoothing constant for the average
b = smoothing constant for the trend
83
Criteria for Selecting
a Forecasting Method
 Cost
 Accuracy
 Data available
 Time span
 Nature of products and services
 Impulse response and noise dampening
84
Criteria for Selecting
a Forecasting Method
 Cost and Accuracy
 There is a trade-off between cost and accuracy;
generally, more forecast accuracy can be obtained
at a cost.
 High-accuracy approaches have disadvantages:
 Use more data
 Data are ordinarily more difficult to obtain
 The models are more costly to design,
implement, and operate
 Take longer to use
85
Criteria for Selecting
a Forecasting Method
 Cost and Accuracy
 Low/Moderate-Cost Approaches – statistical
models, historical analogies, executive-committee
consensus
 High-Cost Approaches – complex econometric
models, Delphi, and market research
86
Criteria for Selecting
a Forecasting Method
 Data Available
 Is the necessary data available or can it be
economically obtained?
 If the need is to forecast sales of a new product,
then a customer survey may not be practical;
instead, historical analogy or market research may
have to be used.
87
Criteria for Selecting
a Forecasting Method
 Time Span
 What operations resource is being forecast and for
what purpose?
 Short-term staffing needs might best be forecast
with moving average or exponential smoothing
models.
 Long-term factory capacity needs might best be
predicted with regression or executive-committee
consensus methods.
88
Criteria for Selecting
a Forecasting Method
 Nature of Products and Services
 Is the product/service high cost or high volume?
 Where is the product/service in its life cycle?
 Does the product/service have seasonal demand
fluctuations?
89
Criteria for Selecting
a Forecasting Method
 Impulse Response and Noise Dampening
 An appropriate balance must be achieved between:
 How responsive we want the forecasting model
to be to changes in the actual demand data
 Our desire to suppress undesirable chance
variation or noise in the demand data
90
Reasons for Ineffective Forecasting
 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
91
Monitoring and Controlling
a Forecasting Model
 Tracking Signal (TS)
 The TS measures the cumulative forecast error
over n periods in terms of 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.
n
i i
1
(Actual demand - Forecast demand )
TS =
MAD
i

92
Monitoring and Controlling
a Forecasting Model
 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 suffer.
93
Tracking Signal: What do you notice?
94
Computer Software for Forecasting
 Examples of computer software with forecasting
capabilities
 Forecast Pro
 Autobox
 SmartForecasts for Windows
 SAS
 SPSS
 SAP
 POM Software Library
Primarily for
forecasting
Have
Forecasting
modules
95
Forecasting in Small Businesses
and Start-Up Ventures
 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
96
Sources of Forecasting Data and Help
 Government agencies at the local, regional, state, and
federal levels
 Industry associations
 Consulting companies
97
Some Specific Forecasting Data
 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
98
Wrap-Up: World-Class Practice
 Predisposed to have effective methods of forecasting
because they have exceptional long-range 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
99
End of Chapter 3

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Ch3. Demand Forecasting.ppt

  • 1. 1 1 ã ã 2002 South-Western/Thomson Learning 2002 South-Western/Thomson Learning TM TM Slides prepared Slides prepared by John Loucks by John Loucks
  • 3. 3 Overview  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
  • 4. 4 Demand Management  Independent demand items are the only items demand for which needs to be forecast  These items include:  Finished goods and  Spare parts
  • 5. 5 Demand Management A Independent Demand (finished goods and spare parts) B(4) C(2) D(2) E(1) D(3) F(2) Dependent Demand (components)
  • 6. 6 Demand Management The importance of forecasting in OM
  • 7. 7 Introduction  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.
  • 8. 8 Forecasting is an Integral Part of Business Planning Forecast Method(s) Demand Estimates Sales Forecast Management Team Inputs: Market, Economic, Other Business Strategy Production Resource Forecasts
  • 9. 9 Some Reasons Why Forecasting is Essential in OM  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.
  • 10. 10 Examples of Production Resource Forecasts Forecast Horizon Time Span Item Being Forecast Units of Measure Long-Range Years  Product lines  Factory capacities  Planning for new products  Capital expenditures  Facility location or expansion  R&D Dollars, tons, etc. Medium- Range Months  Product groups  Department capacities  Sales planning  Production planning and budgeting Dollars, tons, etc. Short-Range Weeks  Specific product quantities  Machine capacities  Planning  Purchasing  Scheduling  Workforce levels  Production levels  Job assignments Physical units of products
  • 11. 11 Forecasting Methods  Qualitative Approaches  Quantitative Approaches
  • 12. 12 Qualitative Approaches  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
  • 13. 13 Qualitative Methods  Educated guess intuitive hunches  Executive committee consensus  Delphi method  Survey of sales force  Survey of customers  Historical analogy  Market research scientifically conducted surveys
  • 14. 14 Qualitative Forecasting Applications Small and Large Firms Technique Low Sales (less than $100M) High Sales (more than $500M) Manager’s Opinion 40.7% 39.6% Executive’s Opinion 40.7% 41.6% Sales Force Composite 29.6% 35.4% Number of Firms 27 48 Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100. Note: More than one response was permitted.
  • 15. 15 Quantitative Forecasting Approaches  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
  • 16. 16 Quantitative Forecasting Applications Small and Large Firms Technique Low Sales (less than $100M) High Sales (more than $500M) Moving Average 29.6% 29.2 Simple Linear Regression 14.8% 14.6 Naive 18.5% 14.6 Single Exponential Smoothing 14.8% 20.8 Multiple Regression 22.2% 27.1 Simulation 3.7% 10.4 Classical Decomposition 3.7% 8.3 Box-Jenkins 3.7% 6.3 Number of Firms 27 48 Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100. Note: More than one response was permitted.
  • 17. 17  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 Time Series Analysis
  • 18. 18 Components of Time Series  Trends are noted by an upward or downward sloping line  Seasonality is a data pattern that repeats itself over the period of one year or less  Cycle is a data pattern that repeats itself... may take years  Irregular variations are jumps in the level of the series due to extraordinary events  Random fluctuation from random variation or unexplained causes
  • 19. 19 Seasonal Patterns Length of Time Number of Before Pattern Length of Seasons Is Repeated Season in Pattern Year Quarter 4 Year Month 12 Year Week 52 Month Day 28-31 Week Day 7
  • 20. 20 Quantitative Forecasting Approaches  Linear Regression  Simple Moving Average  Weighted Moving Average  Exponential Smoothing (exponentially weighted moving average)  Exponential Smoothing with Trend (double exponential smoothing)
  • 21. 21 Long-Range Forecasts  Time spans usually greater than one year  Necessary to support strategic decisions about planning products, processes, and facilities
  • 22. 22 Simple Linear Regression  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.
  • 23. 23 Simple Linear Regression  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
  • 24. 24 Simple Linear Regression  Constants a and b The constants a and b are computed using the following equations: 2 2 2 x y- x xy a = n x -( x)       2 2 xy- x y b = n x -( x) n    
  • 25. 25 Simple Linear Regression  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.
  • 26. 26 Example: College Enrollment  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 2.8 5 3.3 3 2.9 6 3.4
  • 27. 27 Example: College Enrollment  Simple Linear Regression x y x2 xy 1 2.5 1 2.5 2 2.8 4 5.6 3 2.9 9 8.7 4 3.2 16 12.8 5 3.3 25 16.5 6 3.4 36 20.4 Sx=21 Sy=18.1 Sx2=91 Sxy=66.5
  • 28. 28 Example: College Enrollment  Simple Linear Regression Y = 2.387 + 0.180X 2 91(18.1) 21(66.5) 2.387 6(91) (21) a     6(66.5) 21(18.1) 0.180 105 b   
  • 29. 29 Example: College Enrollment  Simple Linear Regression Y7 = 2.387 + 0.180(7) = 3.65 or 3,650 students Y8 = 2.387 + 0.180(8) = 3.83 or 3,830 students Y9 = 2.387 + 0.180(9) = 4.01 or 4,010 students Note: Enrollment is expected to increase by 180 students per year.
  • 30. 30 Simple Linear Regression  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.
  • 31. 31 Example: Railroad Products Co.  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.
  • 32. 32 Example: Railroad Products Co.  Simple Linear Regression – Causal Model RPC Sales Car Loadings Year ($millions) (millions) 1 9.5 120 2 11.0 135 3 12.0 130 4 12.5 150 5 14.0 170 6 16.0 190 7 18.0 220
  • 33. 33 Example: Railroad Products Co.  Simple Linear Regression – Causal Model x y x2 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
  • 34. 34 Example: Railroad Products Co.  Simple Linear Regression – Causal Model Y = 0.528 + 0.0801X 2 185,425(93) 1,115(15,440) a 0.528 7(185,425) (1,115)     2 7(15,440) 1,115(93) b 0.0801 7(185,425) (1,115)    
  • 35. 35 Example: Railroad Products Co.  Simple Linear Regression – Causal Model Y8 = 0.528 + 0.0801(250) = $20.55 million Y9 = 0.528 + 0.0801(270) = $22.16 million Y10 = 0.528 + 0.0801(300) = $24.56 million Note: RPC sales are expected to increase by $80,100 for each additional million national freight car loadings.
  • 36. 36 Multiple Regression Analysis  Multiple regression analysis is used when there are two or more independent variables.  An example of a multiple regression equation is: Y = 50.0 + 0.05X1 + 0.10X2 – 0.03X3 where: Y = firm’s annual sales ($millions) X1 = industry sales ($millions) X2 = regional per capita income ($thousands) X3 = regional per capita debt ($thousands)
  • 37. 37 Coefficient of Correlation (r)  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.
  • 38. 38 Coefficient of Correlation (r)  Meanings of several values of r: -1 a perfect negative relationship (as x goes up, y 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
  • 39. 39 Coefficient of Correlation (r)  r is computed by: 2 2 2 2 ( ) ( ) n xy x y r n x x n y y                   
  • 40. 40 Coefficient of Determination (r2)  The coefficient of determination, r2, is the square of the coefficient of correlation.  The modification of r to r2 allows us to shift from subjective measures of relationship to a more specific measure.  r2 is determined by the ratio of explained variation to total variation: 2 2 2 ( ) ( ) Y y r y y     
  • 41. 41 Example: Railroad Products Co.  Coefficient of Correlation x y x2 xy y2 120 9.5 14,400 1,140 90.25 135 11.0 18,225 1,485 121.00 130 12.0 16,900 1,560 144.00 150 12.5 22,500 1,875 156.25 170 14.0 28,900 2,380 196.00 190 16.0 36,100 3,040 256.00 220 18.0 48,400 3,960 324.00 1,115 93.0 185,425 15,440 1,287.50
  • 42. 42 Example: Railroad Products Co.  Coefficient of Correlation r = .9829 2 2 7(15,440) 1,115(93) 7(185,425) (1,115) 7(1,287.5) (93) r          
  • 43. 43 Example: Railroad Products Co.  Coefficient of Determination r2 = (.9829)2 = .966 96.6% of the variation in RPC sales is explained by national freight car loadings.
  • 44. 44 Ranging Forecasts  Forecasts for future periods are only estimates and are subject to error.  One way to deal with uncertainty is to develop best- estimate forecasts and the ranges within which the actual data are likely to fall.  The ranges of a forecast are defined by the upper and lower limits of a confidence interval.
  • 45. 45 Ranging Forecasts  The ranges or limits of a forecast are estimated by: Upper limit = Y + t(syx) Lower limit = Y - t(syx) where: Y = best-estimate forecast t = number of standard deviations from the mean of the distribution to provide a given probability of exceeding the limits through chance syx = standard error of the forecast
  • 46. 46 Ranging Forecasts  The standard error (deviation) of the forecast is computed as: 2 yx y - a y - b xy s = n - 2   
  • 47. 47 Example: Railroad Products Co.  Ranging Forecasts Recall that linear regression analysis provided a forecast of annual sales for RPC in year 8 equal to $20.55 million. Set the limits (ranges) of the forecast so that there is only a 5 percent probability of exceeding the limits by chance.
  • 48. 48 Example: Railroad Products Co.  Ranging Forecasts  Step 1: Compute the standard error of the forecasts, syx.  Step 2: Determine the appropriate value for t. n = 7, so degrees of freedom = n – 2 = 5. Area in upper tail = .05/2 = .025 Appendix B, Table 2 shows t = 2.571. 1287.5 .528(93) .0801(15,440) .5748 7 2 yx s     
  • 49. 49 Example: Railroad Products Co.  Ranging Forecasts  Step 3: Compute upper and lower limits. Upper limit = 20.55 + 2.571(.5748) = 20.55 + 1.478 = 22.028 Lower limit = 20.55 - 2.571(.5748) = 20.55 - 1.478 = 19.072 We are 95% confident the actual sales for year 8 will be between $19.072 and $22.028 million.
  • 50. 50 Seasonalized Time Series Regression Analysis  Select a representative historical data set.  Develop a seasonal index for each season.  Use the seasonal indexes to deseasonalize the data.  Perform linear regression analysis on the deseasonalized data.  Use the regression equation to compute the forecasts.  Use the seasonal indexes to reapply the seasonal patterns to the forecasts.
  • 51. 51 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales.
  • 52. 52 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Representative Historical Data Set Year Qtr. ($mil.) Year Qtr. ($mil.) 1 1 7.4 2 1 8.3 1 2 6.5 2 2 7.4 1 3 4.9 2 3 5.4 1 4 16.1 2 4 18.0
  • 53. 53 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Compute the Seasonal Indexes Quarterly Sales Year Q1 Q2 Q3 Q4 Total 1 7.4 6.5 4.9 16.1 34.9 2 8.3 7.4 5.4 18.0 39.1 Totals 15.7 13.9 10.3 34.1 74.0 Qtr. Avg. 7.85 6.95 5.15 17.05 9.25 Seas.Ind. .849 .751 .557 1.843 4.000
  • 54. 54 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Deseasonalize the Data Quarterly Sales Year Q1 Q2 Q3 Q4 1 8.72 8.66 8.80 8.74 2 9.78 9.85 9.69 9.77
  • 55. 55 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Perform Regression on Deseasonalized Data Yr. Qtr. x y x2 xy 1 1 1 8.72 1 8.72 1 2 2 8.66 4 17.32 1 3 3 8.80 9 26.40 1 4 4 8.74 16 34.96 2 1 5 9.78 25 48.90 2 2 6 9.85 36 59.10 2 3 7 9.69 49 67.83 2 4 8 9.77 64 78.16 Totals 36 74.01 204 341.39
  • 56. 56 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Perform Regression on Deseasonalized Data Y = 8.357 + 0.199X 2 204(74.01) 36(341.39) a 8.357 8(204) (36)     2 8(341.39) 36(74.01) b 0.199 8(204) (36)    
  • 57. 57 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Compute the Deseasonalized Forecasts Y9 = 8.357 + 0.199(9) = 10.148 Y10 = 8.357 + 0.199(10) = 10.347 Y11 = 8.357 + 0.199(11) = 10.546 Y12 = 8.357 + 0.199(12) = 10.745 Note: Average sales are expected to increase by .199 million (about $200,000) per quarter.
  • 58. 58 Example: Computer Products Corp.  Seasonalized Times Series Regression Analysis  Seasonalize the Forecasts Seas. Deseas. Seas. Yr. Qtr. Index Forecast Forecast 3 1 .849 10.148 8.62 3 2 .751 10.347 7.77 3 3 .557 10.546 5.87 3 4 1.843 10.745 19.80
  • 59. 59 Short-Range Forecasts  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
  • 60. 60 Evaluating Forecast-Model Performance Short-range forecasting models are evaluated on the basis of three characteristics:  Impulse response  Noise-dampening ability  Accuracy
  • 61. 61 Evaluating Forecast-Model Performance  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.
  • 62. 62 Evaluating Forecast-Model Performance  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
  • 63. 63 Monitoring Accuracy  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)
  • 64. 64 Monitoring Accuracy  Mean Absolute Deviation (MAD) n periods n for deviation absolute of Sum = MAD n i i i=1 Actual demand -Forecast demand MAD = n 
  • 65. 65  Mean Squared Error (MSE) MSE = (Syx)2 A small value for Syx 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 syx are related: MSE = 1.25(MAD) Monitoring Accuracy
  • 66. 66 Short-Range Forecasting Methods  (Simple) Moving Average  Weighted Moving Average  Exponential Smoothing  Exponential Smoothing with Trend
  • 67. 67 Simple Moving Average  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
  • 68. 68 Simple Moving Average  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)
  • 69. 69 Weighted Moving Average  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
  • 70. 70 Weighted Moving Average  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.
  • 71. 71  The weights used to compute the forecast (moving average) are exponentially distributed.  The forecast is the sum of the old forecast and a portion (a) of the forecast error (A t-1 - Ft-1). Ft = Ft-1 + a(A t-1 - Ft-1)  . . . more Exponential Smoothing
  • 72. 72 Exponential Smoothing  The smoothing constant, a, must be between 0.0 and 1.0.  A large a provides a high impulse response forecast.  A small a provides a low impulse response forecast.
  • 73. 73 Example: Central Call Center  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.
  • 74. 74 Example: Central Call Center  Moving Average  Representative Historical Data Day Calls Day Calls 1 159 7 203 2 217 8 195 3 186 9 188 4 161 10 168 5 173 11 198 6 157 12 159
  • 75. 75 Example: Central Call Center  Moving Average Use the moving average method with an AP = 3 days to develop a forecast of the call volume in Day 13. F13 = (168 + 198 + 159)/3 = 175.0 calls
  • 76. 76 Example: Central Call Center  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. F13 = .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).
  • 77. 77 Example: Central Call Center  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? F12 = 180.76 + .25(198 – 180.76) = 185.07 F13 = 185.07 + .25(159 – 185.07) = 178.55
  • 78. 78 Example: Central Call Center  Forecast Accuracy - MAD Which forecasting method (the AP = 3 moving average or the a = .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.)
  • 79. 79 Example: Central Call Center AP = 3 a = .25 Day Calls Forec. |Error| Forec. |Error| 4 161 187.3 26.3 186.0 25.0 5 173 188.0 15.0 179.8 6.8 6 157 173.3 16.3 178.1 21.1 7 203 163.7 39.3 172.8 30.2 8 195 177.7 17.3 180.4 14.6 9 188 185.0 3.0 184.0 4.0 10 168 195.3 27.3 185.0 17.0 11 198 183.7 14.3 180.8 17.2 12 159 184.7 25.7 185.1 26.1 MAD 20.5 18.0
  • 80. 80 Exponential Smoothing with Trend  As we move toward medium-range forecasts, trend becomes more important.  Incorporating a trend component into exponentially smoothed forecasts is called double exponential smoothing.  The estimate for the average and the estimate for the trend are both smoothed.
  • 81. 81 Exponential Smoothing with Trend  Model Form FTt = St-1 + Tt-1 where: FTt = forecast with trend in period t St-1 = smoothed forecast (average) in period t-1 Tt-1 = smoothed trend estimate in period t-1
  • 82. 82 Exponential Smoothing with Trend  Smoothing the Average St = FTt + a (At – FTt)  Smoothing the Trend Tt = Tt-1 + b (FTt – FTt-1 - Tt-1) where: a = smoothing constant for the average b = smoothing constant for the trend
  • 83. 83 Criteria for Selecting a Forecasting Method  Cost  Accuracy  Data available  Time span  Nature of products and services  Impulse response and noise dampening
  • 84. 84 Criteria for Selecting a Forecasting Method  Cost and Accuracy  There is a trade-off between cost and accuracy; generally, more forecast accuracy can be obtained at a cost.  High-accuracy approaches have disadvantages:  Use more data  Data are ordinarily more difficult to obtain  The models are more costly to design, implement, and operate  Take longer to use
  • 85. 85 Criteria for Selecting a Forecasting Method  Cost and Accuracy  Low/Moderate-Cost Approaches – statistical models, historical analogies, executive-committee consensus  High-Cost Approaches – complex econometric models, Delphi, and market research
  • 86. 86 Criteria for Selecting a Forecasting Method  Data Available  Is the necessary data available or can it be economically obtained?  If the need is to forecast sales of a new product, then a customer survey may not be practical; instead, historical analogy or market research may have to be used.
  • 87. 87 Criteria for Selecting a Forecasting Method  Time Span  What operations resource is being forecast and for what purpose?  Short-term staffing needs might best be forecast with moving average or exponential smoothing models.  Long-term factory capacity needs might best be predicted with regression or executive-committee consensus methods.
  • 88. 88 Criteria for Selecting a Forecasting Method  Nature of Products and Services  Is the product/service high cost or high volume?  Where is the product/service in its life cycle?  Does the product/service have seasonal demand fluctuations?
  • 89. 89 Criteria for Selecting a Forecasting Method  Impulse Response and Noise Dampening  An appropriate balance must be achieved between:  How responsive we want the forecasting model to be to changes in the actual demand data  Our desire to suppress undesirable chance variation or noise in the demand data
  • 90. 90 Reasons for Ineffective Forecasting  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
  • 91. 91 Monitoring and Controlling a Forecasting Model  Tracking Signal (TS)  The TS measures the cumulative forecast error over n periods in terms of 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. n i i 1 (Actual demand - Forecast demand ) TS = MAD i 
  • 92. 92 Monitoring and Controlling a Forecasting Model  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 suffer.
  • 93. 93 Tracking Signal: What do you notice?
  • 94. 94 Computer Software for Forecasting  Examples of computer software with forecasting capabilities  Forecast Pro  Autobox  SmartForecasts for Windows  SAS  SPSS  SAP  POM Software Library Primarily for forecasting Have Forecasting modules
  • 95. 95 Forecasting in Small Businesses and Start-Up Ventures  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
  • 96. 96 Sources of Forecasting Data and Help  Government agencies at the local, regional, state, and federal levels  Industry associations  Consulting companies
  • 97. 97 Some Specific Forecasting Data  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
  • 98. 98 Wrap-Up: World-Class Practice  Predisposed to have effective methods of forecasting because they have exceptional long-range 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