Transcript Forecasting - University of Hawaii at Hilo

Operations
Management
Chapter 4 Forecasting
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 6e
Operations Management, 8e
© 2006
Prentice
Hall, Inc. Hall, Inc.
©
2006
Prentice
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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4–2
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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4–3
Influence of Product Life
Cycle
Introduction – Growth – Maturity – Decline
 Introduction and growth require longer
forecasts than maturity and decline
 As product passes through life cycle,
forecasts are useful in projecting
 Staffing levels
 Inventory levels
 Factory capacity
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4–4
Product Life Cycle
Company Strategy/Issues
Introduction
Growth
Maturity
Best period to
increase market
share
Practical to change
price or quality
image
Poor time to
change image,
price, or quality
R&D engineering is
critical
Strengthen niche
Competitive costs
become critical
Defend market
position
CD-ROM
Internet
Sales
Decline
Cost control
critical
Fax machines
Drive-through
restaurants
Color printers
Flat-screen
monitors
DVD
3 1/2”
Floppy
disks
Figure 2.5
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4–5
Product Life Cycle
OM Strategy/Issues
Introduction
Product design
and
development
critical
Frequent
product and
process design
changes
Growth
Forecasting
critical
Product and
process
reliability
Maturity
Standardization
Less rapid
product changes
– more minor
changes
Competitive
product
improvements
and options
Optimum
capacity
High production
costs
Shift toward
product focus
Long production
runs
Limited models
Enhance
distribution
Product
improvement
and cost cutting
Short production
runs
Attention to
quality
Increasing
stability of
Increase capacity process
Decline
Little product
differentiation
Cost
minimization
Overcapacity
in the
industry
Prune line to
eliminate
items not
returning
good margin
Reduce
capacity
Figure 2.5
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4–6
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 product
© 2006 Prentice Hall, Inc.
4–7
The Realities!
 Forecasts are seldom perfect
 Most techniques assume an
underlying stability in the system
 Product family and aggregated
forecasts are more accurate than
individual product forecasts
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4–8
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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4–9
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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4 – 10
Overview of Qualitative
Methods
 Jury of executive opinion
 Pool opinions of high-level
executives, sometimes augment by
statistical models
 Delphi method
 Panel of experts, queried iteratively
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4 – 11
Overview of Qualitative
Methods
 Sales force composite
 Estimates from individual
salespersons are reviewed for
reasonableness, then aggregated
 Consumer Market Survey
 Ask the customer
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4 – 12
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
4 – 13
Time Series Forecasting
 Set of evenly spaced numerical
data
 Obtained by observing response
variable at regular time periods
 Forecast based only on past
values
 Assumes that factors influencing
past and present will continue
influence in future
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4 – 14
Time Series Components
Trend
Cyclical
Seasonal
Random
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4 – 15
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 and
efficient
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4 – 16
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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4 – 17
Moving Average Example
Month
Actual
Shed Sales
3-Month
Moving Average
January
February
March
April
May
June
July
10
12
13
16
19
23
26
(10 + 12 + 13)/3 = 11 2/3
(12 + 13 + 16)/3 = 13 2/3
(13 + 16 + 19)/3 = 16
(16 + 19 + 23)/3 = 19 1/3
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4 – 18
Weighted Moving Average
 Used when trend is present
 Older data usually less important
 Weights based on experience and
intuition
Weighted
moving average =
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∑ (weight for period n)
x (demand in period n)
∑ weights
4 – 19
Weights Applied
3
2
1
6
Period
Last month
Two months ago
Three months ago
Sum of weights
Weighted Moving Average
Month
Actual
Shed Sales
January
February
March
April
May
June
July
10
12
13
16
19
23
26
© 2006 Prentice Hall, Inc.
3-Month Weighted
Moving Average
[(3 x 13) + (2 x 12) + (10)]/6 = 121/6
[(3 x 16) + (2 x 13) + (12)]/6 = 141/3
[(3 x 19) + (2 x 16) + (13)]/6 = 17
[(3 x 23) + (2 x 19) + (16)]/6 = 201/2
4 – 20
Potential Problems With
Moving Average
 Increasing n smooths the forecast
but makes it less sensitive to
changes
 Do not forecast trends well
 Require extensive historical data
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4 – 21
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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4 – 22
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
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Ft = new forecast
Ft – 1 = previous forecast
 = smoothing (or weighting)
constant (0    1)
4 – 23
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
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4 – 24
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
New forecast = 142 + .2(153 – 142)
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4 – 25
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
New forecast = 142 + .2(153 – 142)
= 142 + 2.2
= 144.2 ≈ 144 cars
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4 – 26
Choosing 
The objective is to obtain the most
accurate forecast no matter the
technique
We generally do this by selecting the
model that gives us the lowest forecast
error
Forecast error = Actual demand - Forecast value
= At - Ft
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4 – 27
Common Measure of Error
Mean Absolute Deviation (MAD)
MAD =
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∑ |actual - forecast|
n
4 – 28
Exponential Smoothing with
Trend Adjustment
When a trend is present, exponential
smoothing must be modified
Forecast
exponentially
exponentially
including (FITt) = smoothed (Ft) + (Tt) smoothed
trend
forecast
trend
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4 – 29
Exponential Smoothing with
Trend Adjustment
Ft = (At - 1) + (1 - )(Ft - 1 + Tt - 1)
Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1
Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt
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4 – 30
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Actual
Demand (At)
12
17
20
19
24
21
31
28
36
Smoothed
Forecast, Ft
11
Smoothed
Trend, Tt
2
Forecast
Including
Trend, FITt
13.00
Table 4.1
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4 – 31
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Forecast
Including
Trend, FITt
13.00
Actual
Smoothed
Smoothed
Demand (At) Forecast, Ft
Trend, Tt
12
11
2
17
20
19
Step 1: Forecast for Month 2
24
21
F2 = A1 + (1 - )(F1 + T1)
31
28
F2 = (.2)(12) + (1 - .2)(11 + 2)
36
= 2.4 + 10.4 = 12.8 units
Table 4.1
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4 – 32
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Forecast
Including
Trend, FITt
13.00
Actual
Smoothed
Smoothed
Demand (At) Forecast, Ft
Trend, Tt
12
11
2
17
12.80
20
19
Step 2: Trend for Month 2
24
21
T2 = b(F2 - F1) + (1 - b)T1
31
28
T2 = (.4)(12.8 - 11) + (1 - .4)(2)
36
= .72 + 1.2 = 1.92 units
Table 4.1
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4 – 33
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Forecast
Including
Trend, FITt
13.00
Actual
Smoothed
Smoothed
Demand (At) Forecast, Ft
Trend, Tt
12
11
2
17
12.80
1.92
20
19
Step 3: Calculate FIT for Month 2
24
21
FIT2 = F2 + T1
31
28
FIT2 = 12.8 + 1.92
36
= 14.72 units
Table 4.1
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4 – 34
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Actual
Demand (At)
12
17
20
19
24
21
31
28
36
Smoothed
Forecast, Ft
11
12.80
15.18
17.82
19.91
22.51
24.11
27.14
29.28
32.48
Smoothed
Trend, Tt
2
1.92
2.10
2.32
2.23
2.38
2.07
2.45
2.32
2.68
Forecast
Including
Trend, FITt
13.00
14.72
17.28
20.14
22.14
24.89
26.18
29.59
31.60
35.16
Table 4.1
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4 – 35
Exponential Smoothing with
Trend Adjustment Example
35 –
Product demand
30 –
Actual demand (At)
25 –
20 –
15 –
Forecast including trend (FITt)
10 –
5 –
0 – |
1
|
2
|
3
|
4
|
5
|
6
Time (month)
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|
7
|
8
|
9
Figure 4.3
4 – 36
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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4 – 37
Values of Dependent Variable
Least Squares Method
Actual observation
(y value)
Deviation7
Deviation5
Deviation3
Deviation4
Deviation1
Deviation2
Trend line, y^ = a + bx
Time period
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Deviation6
Figure 4.4
4 – 38
Values of Dependent Variable
Least Squares Method
Actual observation
(y value)
Deviation7
Deviation5
Deviation3
Least squares method
minimizes the sum of the
Deviation
squared
errors (deviations)
4
Deviation1
Deviation2
Trend line, y^ = a + bx
Time period
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Deviation6
Figure 4.4
4 – 39
Least Squares Method
Equations to calculate the regression variables
y^ = a + bx
b=
Sxy - nxy
Sx2 - nx2
a = y - bx
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4 – 40
Least Squares Example
Year
1999
2000
2001
2002
2003
2004
2005
Time
Period (x)
1
2
3
4
5
6
7
∑x = 28
x=4
Electrical Power
Demand
74
79
80
90
105
142
122
∑y = 692
y = 98.86
x2
xy
1
4
9
16
25
36
49
∑x2 = 140
74
158
240
360
525
852
854
∑xy = 3,063
3,063 - (7)(4)(98.86)
∑xy - nxy
b=
=
= 10.54
2)
2
2
140
(7)(4
∑x - nx
a = y - bx = 98.86 - 10.54(4) = 56.70
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4 – 41
Least Squares Example
Time
Period (x)
Electrical Power
Demand
x2
xy
1999
1
74
1
2000
2
79
4
line is 80
2001The trend
3
9
2002
4
90
16
2003
105
25
y^ 5= 56.70 + 10.54x
2004
6
142
36
2005
7
122
49
Sx = 28
Sy = 692
Sx2 = 140
x=4
y = 98.86
74
158
240
360
525
852
854
Sxy = 3,063
Year
3,063 - (7)(4)(98.86)
Sxy - nxy
b=
=
= 10.54
2)
2
2
140
(7)(4
Sx - nx
a = y - bx = 98.86 - 10.54(4) = 56.70
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4 – 42
Power demand
Least Squares Example
160
150
140
130
120
110
100
90
80
70
60
50
Trend line,
y^ = 56.70 + 10.54x
–
–
–
–
–
–
–
–
–
–
–
–
|
1999
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|
2000
|
2001
|
2002
|
2003
Year
|
2004
|
2005
|
2006
|
2007
4 – 43
Seasonal Variations In Data
The multiplicative seasonal model can
modify trend data to accommodate
seasonal variations in demand
1. Find average historical demand for each season
2. Compute the average demand over all seasons
3. Compute a seasonal index for each season
4. Estimate next year’s total demand
5. Divide this estimate of total demand by the
number of seasons, then multiply it by the
seasonal index for that season
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4 – 45
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
© 2006 Prentice Hall, Inc.
Demand
2003 2004 2005
80
70
80
90
113
110
100
88
85
77
75
82
85
85
93
95
125
115
102
102
90
78
72
78
105
85
82
115
131
120
113
110
95
85
83
80
Average
2003-2005
Average
Monthly
90
80
85
100
123
115
105
100
90
80
80
80
94
94
94
94
94
94
94
94
94
94
94
94
Seasonal
Index
4 – 46
Seasonal Index Example
Month
Demand
2003 2004 2005
Average
2003-2005
Average
Monthly
Jan
80
85 105
90
94
Feb
70
85
85
80
94
Mar
80
93 average
82
85 monthly demand
94
2003-2005
Seasonal90index95= 115
Apr
100
94
average monthly
demand
May
113 125 131
123
94
= 90/94 = .957
Jun
110 115 120
115
94
Jul
100 102 113
105
94
Aug
88 102 110
100
94
Sept
85
90
95
90
94
Oct
77
78
85
80
94
Nov
75
72
83
80
94
Dec
82
78
80
80
94
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Seasonal
Index
0.957
4 – 47
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
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Demand
2003 2004 2005
80
70
80
90
113
110
100
88
85
77
75
82
85
85
93
95
125
115
102
102
90
78
72
78
105
85
82
115
131
120
113
110
95
85
83
80
Average
2003-2005
Average
Monthly
Seasonal
Index
90
80
85
100
123
115
105
100
90
80
80
80
94
94
94
94
94
94
94
94
94
94
94
94
0.957
0.851
0.904
1.064
1.309
1.223
1.117
1.064
0.957
0.851
0.851
0.851
4 – 48
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
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Demand
2003 2004 2005
Average
2003-2005
Average
Monthly
80
85 105
90
94
for802006
70
85 Forecast
85
94
80
93
82
85
94
annual demand
= 1,200
90Expected
95 115
100
94
113 125 131
123
94
110 115 120 1,200 115
94
Jan 113
x
.957 = 96 94
100 102
105
12
88 102 110
100
94
1,200
85
90
95
Feb
x90
.851 = 85 94
77
78
85 12
80
94
75
72
83
80
94
82
78
80
80
94
Seasonal
Index
0.957
0.851
0.904
1.064
1.309
1.223
1.117
1.064
0.957
0.851
0.851
0.851
4 – 49