Transcript (Textbook) Behavior in Organizations, 8ed (A. B. Shani)

Chapter 10
Demand Forecasting:
Building the Foundation for
Resource Planning
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc. 2008
Product and Service Life Cycles
Life Cycle: A pattern of demand growth and decline that
occurs from the introduction of a product to its
obsolescence.
The five stages of a life cycle:
Introduction
Exhibit 10.2 Product Life Cycle
Growth – Demand begins to
increase.
Maturation – Demand begins to
level off.
Saturation – Demand shifts to the
beginning of its decline.
Decline – Final stage as demand
disappears.
10-2
Looking into the Future:
The Planning Horizon
• Planning Horizon
–
The distance into the future one plans.
10-3
Types of Forecasts by Time Horizon
• Short-range forecast
–
usually < 3 months
– Job scheduling, worker assignments
• Medium-range forecast
–
–
3 months to 1 year
Sales & production planning, budgeting
• Long-range forecast
–
–
Up to 1 to 5+ years
New product planning, facility location
5-10
10-4
What is Forecasting?
¨ Process of predicting a
future event
¨ Underlying basis of
all business decisions
¨
¨
¨
¨
Sales will
be $200
Million!
Production
Inventory
Personnel
Facilities
10-5
Forecasting Approaches
Qualitative Methods
Quantitative Methods
¨ Used when situation is
vague & little data exist
¨ New products
¨ New technology
¨ Involves intuition,
experience, e.g.,
forecasting sales on
Internet
¨ Used when situation is
‘stable’ & historical data
exist
¨ Existing products
¨ Current technology
¨ Involves mathematical
techniques, e.g.,
forecasting sales of
color televisions
10-6
Overview of Qualitative Methods
• Jury of executive opinion
–
Pool opinions of high-level executives, sometimes
augment by statistical models
• Sales force composite
–
estimates from individual salespersons are reviewed for
reasonableness, then aggregated
• Delphi method
–
Panel of experts, queried iteratively
• Consumer Market Survey
–
Ask the customer
10-7
Jury of Executive Opinion
¨ Involves small group of high-level managers
¨ Group estimates demand by working
together
¨ Combines managerial experience with statistical
models
¨ Relatively quick
¨ ‘Group-think’
disadvantage
10-8
© 1995 Corel Corp.
Sales Force Composite
 Each salesperson projects
their sales
 Combined at district &
national levels
 Sales rep’s know
customers’ wants
 Tends to be overly
Pessimistic
Sales
© 1995 Corel Corp.
10-9
Delphi Method
• Iterative group process
• 3 types of people
Decision Makers
–
Decision makers
– Staff
– Respondents
• Reduces ‘group-think’
Staff
(Sales?)
(Sales will be 50!)
(What
will sales
be?
survey)
Respondents
(Sales will be 45, 50, 55)
10-10
Consumer Market Survey
¨ Ask customers about
purchasing plans
¨ What consumers say,
and what they
actually do are often
different
¨ Sometimes difficult
to answer
How many hours will you
use the Internet next week?
© 1995 Corel
Corp.
10-11
Seven Steps in Forecasting
•
•
•
•
•
•
•
Determine the use of the forecast
Select the items to be forecast
Determine the time horizon of the forecast
Select the forecasting model (s)
Gather the data
Make the forecast
Validate and implement results
10-12
Overview of Quantitative Approaches
•
•
•
•
Naïve approach
Moving averages
Exponential smoothing
Trend projection
• Linear regression
Time-series Models
Causal models
10-13
Demand Forecasting: Quantitative Analysis
• Time Series Techniques
– Use past demand to predict future demand
• Causal Techniques
– Uses external data to predict future demand
– Looking for the factors that “cause” demand
– Linear regression is often used.
10-14
Naive Approach
¨ Assumes demand in next
period is the same as demand
in most recent period
¨ e.g., If May sales were 48,
then June sales will be 48
¨ Sometimes cost effective &
efficient
© 1995 Corel Corp.
10-15
Quantitative Forecasting Methods (Non-Naive)
Quantitative
Forecasting
Causal
Models
Time Series
Models
Moving
Average
Exponential
Smoothing
Trend
Projection
Linear
Regression
10-16
What is a Time Series?
•
Set of evenly spaced numerical data
–
•
Forecast based only on past values
–
•
Obtained by observing response variable at regular time
periods
Assumes that factors influencing past, present, & future
will continue
Example
Year:
Sales:
1993
78.7
1994
63.5
1995
89.7
1996
93.2
1997
92.1
10-17
Moving Average Method
•
MA is a series of arithmetic means
•
Used if little or no trend
•
Used often for smoothing
–
•
Provides overall impression of data over time
Equation
MA =
∑ Demand in Previous n Periods
n
10-18
Table 1
Sales Data
Month
1
2
3
4
5
6
7
8
Sales
(in millions)
6
8
10
5
3
9
6
7
19
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
Total
24 / 3
Moving
Average Forecast
=
8
10-20
Table 2
Moving Average
(3-period ) Forecast
Sales
Moving
Month (in millions) Total
Average Forecast
1
6
2
8
3
10
4
5
24 / 3 =
8
10-21
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
Total
24 / 3
23 / 3
Moving
Average Forecast
=
=
8
7.66
10-22
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
Total
24 / 3
23 / 3
Moving
Average Forecast
=
=
8
7.66
10-23
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
Total
24 / 3
23 / 3
18/3
Moving
Average Forecast
=
=
=
8
7.66
6
10-24
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
Total
1
6
2
8
3
10
4
5
24 / 3 =
5
3
23 / 3 =
6
9
18/3 =
Moving
Average Forecast
8
7.66
6
10-25
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
Total
1
6
2
8
3
10
4
5
24 / 3 =
5
3
23 / 3 =
6
9
18 / 3 =
7
17 / 3 =
Moving
Average Forecast
8
7.66
6
5.66
10-26
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
7
6
Total
24 / 3 =
23 / 3 =
18 / 3 =
17 / 3 =
Moving
Average Forecast
8
7.66
6
5.66
10-27
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
7
6
8
Total
24 / 3 =
23 / 3 =
18 / 3 =
17 / 3 =
18 / 3 =
Moving
Average Forecast
8
7.66
6
5.66
6
10-28
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
7
6
8
7
Total
24 / 3 =
23 / 3 =
18 / 3 =
17 / 3 =
18 / 3 =
Moving
Average Forecast
8
7.66
6
5.66
6
10-29
Table 2
Moving Average
(3-period ) Forecast
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
7
6
8
7
9
Total
24 / 3
23 / 3
18 / 3
17 / 3
18 / 3
22 / 3
=
=
=
=
=
=
Moving
Average Forecast
8
7.66
6
5.66
6
7.33
10-30
Table 2
Moving Average (3-period ) Smoothing Process
Sales
Month (in millions)
1
6
2
8
3
10
Moving
Average
Total
24 / 3
=
8
10-31
Table 2
Moving Average (3-period ) Smoothing Process
Sales
Month (in millions)
1
6
2
8
3
10
4
5
Total
24 / 3
23 / 3
Moving
Average
=
=
8
7.66
10-32
Table 2
Moving Average (3-period ) Smoothing Process
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
Total
24 / 3 =
23 / 3
18 / 3
Moving
Average
8
=
=
7.66
6
10-33
Table 2
Moving Average (3-period ) Smoothing Process
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
Total
24 / 3 =
23 / 3 =
18 / 3 =
17 / 3 =
Moving
Average
8
7.66
6
5.66
10-34
Table 2
Moving Average (3-period ) Smoothing Process
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
7
6
Total
24 / 3 =
23 / 3 =
18 / 3 =
17 / 3 =
18 / 3 =
Moving
Average
8
7.66
6
5.66
6
10-35
Table 2
Moving Average (3-period ) Smoothing Process
Sales
Month (in millions)
1
6
2
8
3
10
4
5
5
3
6
9
7
6
8
7
Total
24 / 3 =
23 / 3 =
18 / 3 =
17 / 3 =
18 / 3 =
22 / 3 =
Moving
Average
8
7.66
6
5.66
6
7.33
10-36
Sales Data
Month
1
2
3
4
5
6
7
8
Sales
(in millions)
6
8
10
5
3
9
6
7
10-37
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
3
10
4
5
5
3
6
9
7
6
8
7
10-38
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
29/4 = 7.25
3
10
4
5
10-39
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
29/4 = 7.25
3
10
26/4 = 6.5
4
5
5
3
10-40
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
29/4 = 7.25
3
10
26/4 = 6.5
4
5
5
3
10-41
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
29/4 = 7.25
3
10
26/4 = 6.5
4
5
27/4 = 6.75
5
3
6
9
10-42
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
3
4
5
6
7
Sales
Moving
(in millions) Average
6
8
29/4 = 7.25
10
26/4 = 6.5
5
27/4 = 6.75
3
23/4 = 5.75
9
6
10-43
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
29/4 = 7.25
3
10
26/4 = 6.5
4
5
27/4 = 6.75
5
3
23/4 = 5.75
6
9
25/4 = 6.25
7
8
6
7
10-44
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
Centered
Moving
Average
29/4 = 7.25
3
10
(7.25+6.5)/2=6.87
26/4 = 6.5
4
5
27/4 = 6.75
5
3
23/4 = 5.75
6
9
25/4 = 6.25
7
8
6
7
10-45
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
Centered
Moving
Average
29/4 = 7.25
3
10
(7.25+6.5)/2=6.87
26/4 = 6.5
4
5
(6.5+6.75)/2=6.63
27/4 = 6.75
5
3
23/4 = 5.75
6
9
25/4 = 6.25
7
8
6
7
10-46
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
6
8
Moving
Average
Centered
Moving
Average
29/4 = 7.25
3
10
(7.25+6.5)/2=6.87
26/4 = 6.5
4
5
(6.5+6.75)/2=6.63
27/4 = 6.75
5
3
(6.75+5.75)/2=6.25
23/4 = 5.75
6
9
25/4 = 6.25
7
8
6
7
10-47
Table 1 -Sales Data
(4-period) Moving Average- Smoothing Process
Month
1
2
Sales
(in millions)
Moving
Average
Centered
Moving
Average
6
8
29/4 = 7.25
3
10
(7.25+6.5)/2=6.87
26/4 = 6.5
4
5
(6.5+6.75)/2=6.63
27/4 = 6.75
5
3
(6.75+5.75)/2=6.25
23/4 = 5.75
6
9
(5.75+6.25)/2=6.00
25/4 = 6.25
7
8
6
7
10-48
Disadvantages of
Moving Average Method
• Increasing n makes forecast less sensitive to
changes
• Does not forecast trend well
• Requires much historical
data
10-49
Time Series Techniques:
Exponential Smoothing
• A variant of moving average (weighted average):
– Premise: More recent observations are better indicators of future demand
than past observations.
– Reduces the need to hold lots of data.
• Uses a smoothing constant, ‘alpha’ () to weight the previous
demand and establish the responsiveness of the forecast.
Ft+1 = Xt + (1- )Ft
Where:
Ft+1 = The forecast for the next time period

Xt
Ft
= A smoothing constant, between 0 and 1
= The actual demand for the most recent period
= The forecast for the most recent period
10-50
FORECASTING
• EXPONENTIAL SMOOTHING
Ft-1
= α X t + ( 1 - α ) Ft
10-51
Forecasting using
Exponential Smoothing
Steps in Exponential smoothing
1. choose alpha (α ) ( 0 < α < 1)
2. choose a number as a forecast for the first month
3. Forecast for the second month using first
month’s forecast, the actual, and the alpha
10-52
Time Series Techniques:
Exponential Smoothing
• A higher alpha makes the forecast more responsive to
changes:
Exhibit 10 .13 Comparison of .1 and .4 Alpha Values for Exponential Smoothing
10-53
Table 6
Monthly Sales in Dollars (000)
Time
t
1
2
3
4
5
6
7
8
9
10
11
12
Sales
X
10
12
13
16
19
23
26
30
28
18
16
14
10-54
Table 6
Monthly Sales in Dollars (000)
Time
t
1
α = .4
Sales
X
10
10-55
Table 6
Monthly Sales in Dollars (000)
α = .4
Time
t
1
Sales
X
10
F
10
10-56
Table 6
Monthly Sales in Dollars (000)
Time
t
1
2
α = .4
Sales
X
10
Ft = α X t + ( 1 - α ) Ft-1
10
10 = .4 (10) + (1-.4) 10
10-57
Table 6
Monthly Sales in Dollars (000)
α = .4
Time Actual Sales Forecast
t
X
Ft = α X t + ( 1 - α ) Ft-1
1
10
10
2
12
10 = .4 (10) + (1-.4) 10
10-58
Table 6
Monthly Sales in Dollars (000)
α = .4
Time Actual Sales Forecast
t
X
Ft = α X t + ( 1 - α ) Ft-1
1
10
10
2
12
10 = .4 (10) + (1-.4) 10
3
10.8 = .4 (12) + (1-.4) 10
10-59
Table 6
Monthly Sales in Dollars (000)
α = .4
Time Actual Sales Forecast
t
X
Ft = α X t + ( 1 - α ) Ft-1
1
10
10
2
12
10 = .4 (10) + (1-.4) 10
3
13
10.8 = .4 (12) + (1-.4) 10
10-60
Table 6
Monthly Sales in Dollars (000)
α = .4
Time Actual Sales Forecast
t
X
Ft = α X t + ( 1 - α ) Ft-1
1
10
10
2
12
10 = .4 (10) + (1-.4) 10
3
13
10.8 = .4 (12) + (1-.4) 10
4
11.68 = .4 (13) + (1-.4) 10.8
10-61
Table 6
Monthly Sales in Dollars (000)
α = .4
Time Actual Sales Forecast
t
X
Ft = α X t + ( 1 - α ) Ft-1
1
10
10
2
12
10
= .4 (10) + (1-.4) 10
3
13
10.8 = .4 (12) + (1-.4) 10
4
16
11.68 = .4 (13) + (1-.4) 10.8
10-62
Table 6
Monthly Sales in Dollars (000)
Time
Sales
Forecast
t
X
F
================================
1
10
10
2
12
10
3
13
10.8
4
16
11.68
5
19
13.41
6
23
15.64
7
26
18.59
8
30
21.55
9
28
24.93
10
18
26.15
11
16
22.90
12
14
20.14
13
17.68
10-63
Forecast Accuracy
• Forecast error is the actual demand minus the forecast
demand.
• Absolute Error: how far “off” are we, in absolute terms?
– Measured by mean absolute deviation (MAD) or mean squared
error (MSE)
• Forecast Bias: Are we consistently high or low?
– A forecast should be unbiased (low forecasts are as frequent as
high forecasts)
– Bias is measured by mean forecast error (MFE) or running sum
of forecast error (RSFE)
10-64
Forecast Accuracy
Two similar approaches are used to measure absolute forecast error
MAD is the mean of the absolute values of the forecast errors
n
A t - Ft
t =1
n
MAD = 
MSE is the mean of the squared values of the forecast errors
n
A t  Ft 2
t =1
n -1
MSE = 
•
•
The ideal value for both is zero, which would mean there is no forecasting error
The larger the MAD or MSE, the less the accurate the model
10-65
Table 6
Monthly Sales in Dollars (000)
Time
t
1
2
3
4
5
6
7
8
9
10
11
12
13
Sum of errors
Sales
X
10
12
13
16
19
23
26
30
28
18
16
14
Forecast
F
10
10
10.8
11.68
13.41
15.64
18.59
21.55
24.93
26.15
22.90
20.14
17.68
Error
2
2.20
4.32
5.60
7.36
7.41
8.45
3.07
- 8.16
- 6.90
- 6.14
-----------61.62
10-66
Table 6
Monthly Sales in Dollars (000)
Mean Absolute Deviation (MAD)
61.62
--------- = 5.60
11
10-67
Table 6
Monthly Sales in Dollars (000)
Time
Sales
Forecast
Error
Squared Error
t
X
F
(X-F )
(X-F)2
1
10
10
2
12
10
2
4
3
13
10.8
2.20
4.84
4
16
11.68
4.32
18.66
5
19
13.41
5.60
31.27
6
23
15.64
7.36
54.10
7
26
18.59
7.41
54.95
8
30
21.55
8.45
71.37
9
28
24.93
3.07
9.42
10
18
26.15
- 8.16
66.57
11
16
22.90
- 6.90
47.54
12
14
20.14
- 6.14
37.66
13
17.68
--------------------------------------------------------------------------------------Sum of Squared Error
400.37
10-68
Table 6
Monthly Sales in Dollars (000)
Mean Squared Error (MSE)
400.38
--------- = 36.40
11
Standard Error = sqrt (MSE) = sqrt (36.40) = 6.03
10-69
Classical Time Series Components
Trend
Cyclical
Seasonal
Random
10-70
10-71
Demand Forecasting:
Components of a Time Series
• There are four potential components of a time series:
– Cycles
• A pattern that repeats over a long period of time (such as 20 years).
• Cycles are less important for demand forecasting, since we rarely have 20
years’ worth of data.
– Trend
– Seasonality
– Randomness
10-72
General Time Series Models
Any observed value in a time series is the product (or
sum) of time series components
Multiplicative model
Yi = Ti · Si · Ci · Ri (if quarterly or mo. data)
Additive model
Yi = Ti + Si + Ci + Ri (if quarterly or mo. data)
10-73
Dealing with Seasonality and Trend
Using Regression
The regression analysis determines the best-fitting line through the
deseasonalized demand. The general equation for that line is:
Y=a+bt
Where:
Y = a point on the trend line
a = Y intercept
b = slope
t = time period
10-74
Demand Forecasting:
Components of a Time Series
• Trend – Component of a time series that causes demand to
increase or decrease.
Exhibit 10.6 Example of a Time Series with Trend
10-75
Time Series Techniques:
Dealing with Seasonality and Trend
• A regression-based approach (Multiplicative model)
– Compute seasonal indexes for each period
– Remove seasonal component from the time series
• “Deseasonalize” the data
– Model the trend using linear regression on the
deseasonalized data
– Determine the forecast by using the trend equation and seasonal
indexes
10-76
Seasonal Component
• Regular pattern of up & down fluctuations
• Due to weather, customs etc.
• Occurs within 1 year
Summer
Response
© 1984-1994 T/Maker Co.
Mo., Qtr.
10-77
Demand Forecasting:
Components of a Time Series
• Seasonality – A pattern in a time series that repeats itself at
least once a year.
Exhibit 10.7 Time Series with Seasonality
10-78
Cyclical Component
• Repeating up & down movements
• Due to interactions of factors influencing economy
• Usually 2-10 years duration
Cycle
Response
B
Mo., Qtr., Yr.
10-79
Random Component
• Erratic, unsystematic, ‘residual’ fluctuations
• Due to random variation or unforeseen events
–
–
Union strike
Tornado
© 1984-1994 T/Maker Co.
• Short duration &
non-repeating
10-80
Multiplicative Seasonal Model





Find average historical demand for each “season” by
summing the demand for that season in each year, and
dividing by the number of years for which you have data.
Compute the average demand over all seasons by dividing
the total average annual demand by the number of seasons.
Compute a seasonal index by dividing that season’s historical
demand (from step 1) by the average demand over all
seasons.
Estimate next year’s total demand
Divide this estimate of total demand by the number of
seasons then multiply it by the seasonal index for that
season. This provides the seasonal forecast.
81
Linear Trend Projection
• Used for forecasting linear trend line
• Assumes relationship between response variable, Y,
and time, X, is a linear function
$
Y = a + bX
i
i
• Estimated by least squares method
–
Minimizes sum of squared errors
10-82
Linear Regression Model
• Shows linear relationship between dependent &
explanatory variables
–
Example: Sales & advertising (not time)
Y-intercept
Slope
^
Yi = a + b X i
Dependent
(response) variable
Independent
(explanatory) variable
10-83
Interpretation of Coefficients
• Slope (b)
–
Estimated Y changes by b for each 1 unit increase in X
•
If b = 2, then sales (Y) is expected to increase by 2 for each 1 unit
increase in advertising (X)
• Y-intercept (a)
–
Average value of Y when X = 0
•
If a = 4, then average sales (Y) is expected to be 4 when advertising
(X) is 0
10-85
Least Squares Equations
Equation:
Yˆ i = a + bx i
n
 x i y i  nx y
Slope:
b = i =n
 x i  n x 
i =
Y-Intercept:
Transparency Masters to accompany Operations
Management, 5E (Heizer & Render)
a = y  bx
5-69
© 1998 by Prentice Hall, Inc.
A Simon & Schuster Company
Upper Saddle River, N.J. 07458
10-86
Demand Forecasting:
Components of a Time Series
• Random Fluctuation – Unpredictable variation in demand that
is not due to trend, seasonality, or cycle.
Exhibit 10.8 Time Series with Random Fluctuation
10-87
Collaborative Planning, Forecasting, and
Replenishment (CPFR)
• A shared process of creation between two or more parties
with diverse skills and knowledge delivering a unified
approach that provides the optimal framework for
customer satisfaction.
• CPFR requires that data be shared among supply chain
partners and that partners collaborate on developing
demand forecasts..
10-88
Causal Models
Some external variable is a leading indicator (independent
variable) for the demand you want to predict (dependent
variable)
• The example (10.1) uses temperature as the
independent variable, but you could use others as well.
• e.g., exam schedule, promotions, sporting events, day of the week,
etc.
10-89
Demand Forecasting:
Simple Linear Regression Example
Underlying model:
Y = a + bx
Regression analysis
provides the
formula for the line
that best fits through
the data points.
X2, Y2
X1, Y1
10-90
Linear Regression Equations
Equation:
ˆ i = a + bx i
Y
n
 x i y i  nx y
Slope:
b = i =n
 x i  n x 
i =
Y-Intercept:
Transparency Masters to accompany Operations
Management, 5E (Heizer & Render)
a = y  bx
5-76
© 1998 by Prentice Hall, Inc.
A Simon & Schuster Company
Upper Saddle River, N.J. 07458
10-91
Correlation
• Answers: ‘how strong is the linear relationship between the
variables?’
• Coefficient of correlation Sample correlation coefficient
denoted r
–
–
Values range from -1 to +1
Measures degree of association
• Used mainly for understanding
10-92
Pattern of Forecast Error
Trend Not Fully
Accounted for
Desired Pattern
Error
Error
0
0
Time (Years)
Transparency Masters to accompany Operations
Management, 5E (Heizer & Render)
Time (Years)
5-87
© 1998 by Prentice Hall, Inc.
A Simon & Schuster Company
Upper Saddle River, N.J. 07458
10-93
Coefficient of Correlation and Regression
Model
Y
r=1
Y
r = -1
^=a +b X
Y
i
i
^=a +b X
Y
i
i
X
Y
X
r = .89
Y
^=a +b X
Y
i
i
^=a +b X
Y
i
i
X
X
Transparency Masters to accompany Operations
Management, 5E (Heizer & Render)
r=0
5-85
© 1998 by Prentice Hall, Inc.
A Simon & Schuster Company
Upper Saddle River, N.J. 07458
10-95
Guidelines for Selecting Forecasting Model
• You want to achieve:
–
No pattern or direction in forecast error
•
•
–
Error = (Yi - Yi) =^(Actual - Forecast)
Seen in plots of errors over time
Smallest forecast error
•
•
Mean square error (MSE)
Mean absolute deviation (MAD)
Transparency Masters to accompany Operations
Management, 5E (Heizer & Render)
5-86
© 1998 by Prentice Hall, Inc.
A Simon & Schuster Company
Upper Saddle River, N.J. 07458
10-96
Pattern of Forecast Error
Trend Not Fully
Accounted for
Desired Pattern
Error
Error
0
0
Time (Years)
Transparency Masters to accompany Operations
Management, 5E (Heizer & Render)
Time (Years)
5-87
© 1998 by Prentice Hall, Inc.
A Simon & Schuster Company
Upper Saddle River, N.J. 07458
10-97