Transcript Ch. 4 Forecasting

4
Forecasting
PowerPoint presentation to accompany
Heizer and Render
Operations Management, 10e
Principles of Operations Management, 8e
PowerPoint slides by Jeff Heyl
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4-1
What is Forecasting?
 Process of predicting
a future event
 Underlying basis
of all business
decisions
??
 Production
 Inventory
 Personnel
 Facilities
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Forecasting Time Horizons
 Short-range forecast
 Up to 1 year, generally less than 3 months
 Purchasing, job scheduling, workforce
levels, job assignments, production levels
 Medium-range forecast
 3 months to 3 years
 Sales and production planning, budgeting
 Long-range forecast
 3+ years
 New product planning, facility location,
research and development
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Types of Forecasts
 Economic forecasts
 Address business cycle – inflation rate,
money supply, housing starts, etc.
 Technological forecasts
 Predict rate of technological progress
 Impacts development of new products
 Demand forecasts
 Predict sales of existing products and
services
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Forecasting Approaches
Qualitative Methods
 Used when situation is vague
and little data exist
 New products
 New technology
 Involves intuition, experience
 e.g., forecasting sales on
Internet
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Forecasting Approaches
Quantitative Methods
 Used when situation is ‘stable’ and
historical data exist
 Existing products
 Current technology
 Involves mathematical techniques
 e.g., forecasting sales of color
televisions
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Overview of Quantitative
Approaches
1. Naive approach
2. Moving averages
3. Exponential
smoothing
time-series
models
4. Trend projection
5. Linear regression
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associative
model
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Time Series Forecasting
 Set of evenly spaced numerical data
 Obtained by observing response
variable at regular time periods
 Forecast based only on past values,
no other variables important
 Assumes that factors influencing
past and present will continue
influence in future
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Time Series Components
Trend
Cyclical
Seasonal
Random
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Components of Demand
Demand for product or service
Trend
component
Seasonal peaks
Actual demand
line
Average demand
over 4 years
Random variation
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1
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2
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3
Time (years)
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Figure 4.1
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Trend Component
 Persistent, overall upward or
downward pattern
 Changes due to population,
technology, age, culture, etc.
 Typically several years
duration
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Seasonal Component
 Regular pattern of up and
down fluctuations
 Due to weather, customs, etc.
 Occurs within a single year
Period
Length
Number of
Seasons
Week
Month
Month
Year
Year
Year
Day
Week
Day
Quarter
Month
Week
7
4-4.5
28-31
4
12
52
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Cyclical Component
 Repeating up and down movements
 Affected by business cycle,
political, and economic factors
 Multiple years duration
 Often causal or
associative
relationships
0
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10
15
20
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Random Component
 Erratic, unsystematic, ‘residual’
fluctuations
 Due to random variation or unforeseen
events
 Short duration
and nonrepeating
M
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T
W
T
F
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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
∑ demand in previous n periods
Moving average =
n
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Exponential Smoothing
 Form of weighted moving average
 Weights decline exponentially
 Most recent data weighted most
 Requires smoothing constant ()
 Ranges from 0 to 1
 Subjectively chosen
 Involves little record keeping of past
data
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Exponential Smoothing
New forecast = Last period’s forecast
+  (Last period’s actual demand
– Last period’s forecast)
Ft = Ft – 1 + (At – 1 - Ft – 1)
where
Ft = new forecast
Ft – 1 = previous forecast
 = smoothing (or weighting)
constant (0 ≤  ≤ 1)
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Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |Actual - Forecast|
n
Mean Squared Error (MSE)
MSE =
∑ (Forecast Errors)2
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n
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Common Measures of Error
Mean Absolute Percent Error (MAPE)
n
∑100|Actuali - Forecasti|/Actuali
MAPE =
i=1
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n
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Trend Projections
Fitting a trend line to historical data points
to project into the medium to long-range
Linear trends can be found using the least
squares technique
y^ = a + bx
^ = computed value of the variable to
where y
be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable
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Seasonal Variations In Data
The multiplicative
seasonal model
can adjust trend
data for seasonal
variations in
demand
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Associative Forecasting
Used when changes in one or more
independent variables can be used to predict
the changes in the dependent variable
Most common technique is linear
regression analysis
We apply this technique just as we did
in the time series example
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Associative Forecasting
Forecasting an outcome based on
predictor variables using the least squares
technique
y^ = a + bx
^
where y
= computed value of the variable to
be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable though to
predict the value of the dependent
variable
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Associative Forecasting
Example
Area Payroll
($ billions), x
1
3
4
4.0 –
2
1
3.0 –
7
Sales
Sales
($ millions), y
2.0
3.0
2.5
2.0
2.0
3.5
2.0 –
1.0 –
0
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2
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5 6
Area payroll
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Associative Forecasting
Example
Sales, y
2.0
3.0
2.5
2.0
2.0
3.5
∑y = 15.0
Payroll, x
1
3
4
2
1
7
∑x = 18
x = ∑x/6 = 18/6 = 3
x2
1
9
16
4
1
49
∑x2 = 80
xy
2.0
9.0
10.0
4.0
2.0
24.5
∑xy = 51.5
51.5 - (6)(3)(2.5)
∑xy - nxy
b=
= 80 - (6)(32) = .25
∑x2 - nx2
y = ∑y/6 = 15/6 = 2.5
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a = y - bx = 2.5 - (.25)(3) = 1.75
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Associative Forecasting
Example
If payroll next year
is estimated to be
$6 billion, then:
Sales = 1.75 + .25(6)
Sales = $3,250,000
Sales = 1.75 + .25(payroll)
4.0 –
Nodel’s sales
y^ = 1.75 + .25x
3.25
3.0 –
2.0 –
1.0 –
0
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2
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Area payroll
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Standard Error of the
Estimate
 A forecast is just a point estimate of a
future value
4.0 –
Nodel’s sales
 This point is
actually the
mean of a
probability
distribution
3.25
3.0 –
2.0 –
1.0 –
0
Figure 4.9
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Area payroll
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Standard Error of the
Estimate
Sy,x =
∑(y - yc)2
n-2
where y = y-value of each data point
yc = computed value of the dependent
variable, from the regression
equation
n = number of data points
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Correlation
 How strong is the linear
relationship between the variables?
 Correlation does not necessarily
imply causality!
 Coefficient of correlation, r,
measures degree of association
 Values range from -1 to +1
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Correlation Coefficient
nSxy - SxSy
r=
[nSx2 - (Sx)2][nSy2 - (Sy)2]
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y
y
Correlation Coefficient
nSxy - SxSy
r=
2 - (Sx)2][nSy2 - (Sy)2]
[nSx
(a) Perfect positive x
(b) Positive
correlation:
0<r<1
correlation:
r = +1
y
x
y
(c) No correlation:
r=0
x
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(d) Perfect negative x
correlation:
r = -1
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Correlation
 Coefficient of Determination, r2,
measures the percent of change in
y predicted by the change in x
 Values range from 0 to 1
 Easy to interpret
For the Nodel Construction example:
r = .901
r2 = .81
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Multiple Regression
Analysis
If more than one independent variable is to be
used in the model, linear regression can be
extended to multiple regression to
accommodate several independent variables
y^ = a + b1x1 + b2x2 …
Computationally, this is quite
complex and generally done on the
computer
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Multiple Regression
Analysis
In the Nodel example, including interest rates in
the model gives the new equation:
y^ = 1.80 + .30x1 - 5.0x2
An improved correlation coefficient of r = .96
means this model does a better job of predicting
the change in construction sales
Sales = 1.80 + .30(6) - 5.0(.12) = 3.00
Sales = $3,000,000
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