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
© 2006 Prentice Hall, Inc.
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
© 2006 Prentice Hall, Inc.
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
© 2006 Prentice Hall, Inc.
4–4
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.
4–5
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
© 2006 Prentice Hall, Inc.
4–6
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
© 2006 Prentice Hall, Inc.
4–7
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
© 2006 Prentice Hall, Inc.
4–8
Overview of Qualitative
Methods
 Jury of executive opinion
 Delphi method
 Sales force composite
 Consumer Market Survey
© 2006 Prentice Hall, Inc.
4–9
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
© 2006 Prentice Hall, Inc.
4 – 10
Delphi Method
 Iterative group
process,
continues until
consensus is
reached
Staff
(Administering
 3 types of
survey)
participants
 Decision makers
 Staff
 Respondents
© 2006 Prentice Hall, Inc.
Decision Makers
(Evaluate
responses and
make decisions)
Respondents
(People who can
make valuable
judgments)
4 – 11
Sales Force Composite
 Each salesperson projects his or
her sales
 Combined at district and national
levels
 Sales reps know customers’ wants
 Tends to be overly optimistic
© 2006 Prentice Hall, Inc.
4 – 12
Consumer Market Survey
 Ask customers about purchasing
plans
 What consumers say, and what
they actually do are often different
 Sometimes difficult to answer
© 2006 Prentice Hall, Inc.
4 – 13
Overview of Quantitative
Approaches
1. Naive approach
2. Moving averages
3. Exponential
smoothing
Time-Series
Models
4. Trend projection
5. Linear regression
© 2006 Prentice Hall, Inc.
Associative
Model
4 – 14
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
© 2006 Prentice Hall, Inc.
4 – 15
Time Series Components
Trend
Cyclical
Seasonal
Random
© 2006 Prentice Hall, Inc.
4 – 16
Trend Component
 Persistent, overall upward or
downward pattern
 Changes due to population,
technology, age, culture, etc.
 Typically several years
duration
© 2006 Prentice Hall, Inc.
4 – 17
Seasonal Component
 Regular pattern of up and
down fluctuations
 Due to weather, customs, etc.
 Occurs within a single year
© 2006 Prentice Hall, Inc.
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
4 – 18
Cyclical Component
 Repeating up and down movements
 Affected by business cycle, political,
and economic factors
 Multiple years duration
0
© 2006 Prentice Hall, Inc.
5
10
15
20
4 – 19
Random Component
 Erratic, unsystematic, ‘residual’
fluctuations
 Due to random variation or
unforeseen events
 Short duration and
nonrepeating
M
© 2006 Prentice Hall, Inc.
T
W
T
F
4 – 20
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
© 2006 Prentice Hall, Inc.
4 – 21
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
© 2006 Prentice Hall, Inc.
4 – 22
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
© 2006 Prentice Hall, Inc.
4 – 23
Shed Sales
Graph of Moving Average
30
28
26
24
22
20
18
16
14
12
10
Moving
Average
Forecast
–
–
–
–
–
–
–
–
–
–
–
Actual
Sales
|
J
© 2006 Prentice Hall, Inc.
|
F
|
M
|
A
|
M
|
J
|
J
|
A
|
S
|
O
|
N
|
D
4 – 24
Weighted Moving Average
 Used when trend is present
 Older data usually less important
 Weights based on experience and
intuition
Weighted
moving average =
© 2006 Prentice Hall, Inc.
∑ (weight for period n)
x (demand in period n)
∑ weights
4 – 25
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 – 26
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
© 2006 Prentice Hall, Inc.
4 – 27
Moving Average And
Weighted Moving Average
Weighted
moving
average
Sales demand
30 –
25 –
20 –
Actual
sales
15 –
Moving
average
10 –
5 –
|
Figure 4.2
© 2006 Prentice Hall, Inc.
J
|
F
|
M
|
A
|
M
|
J
|
J
|
A
|
S
|
O
|
N
|
D
4 – 28
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
© 2006 Prentice Hall, Inc.
4 – 29
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
© 2006 Prentice Hall, Inc.
Ft = new forecast
Ft – 1 = previous forecast
 = smoothing (or weighting)
constant (0    1)
4 – 30
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
© 2006 Prentice Hall, Inc.
4 – 31
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
New forecast = 142 + .2(153 – 142)
© 2006 Prentice Hall, Inc.
4 – 32
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
© 2006 Prentice Hall, Inc.
4 – 33
Effect of
Smoothing Constants
Weight Assigned to
Smoothing
Constant
Most
Recent
Period
()
 = .1
.1
.09
.081
.073
.066
 = .5
.5
.25
.125
.063
.031
© 2006 Prentice Hall, Inc.
2nd Most 3rd Most 4th Most 5th Most
Recent
Recent
Recent
Recent
Period
Period
Period
Period
2
3
(1 - ) (1 - )
(1 - )
(1 - )4
4 – 34
Impact of Different 
Demand
225 –
 = .5
Actual
demand
200 –
175 –
 = .1
150 – |
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
Quarter
© 2006 Prentice Hall, Inc.
4 – 35
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
© 2006 Prentice Hall, Inc.
4 – 36
Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |actual - forecast|
n
Mean Squared Error (MSE)
MSE =
© 2006 Prentice Hall, Inc.
∑ (forecast errors)2
n
4 – 37
Comparison of Forecast
Error
Quarter
Actual
Tonnage
Unloaded
Rounded
Forecast
with
 = .10
Absolute
Deviation
for
 = .10
Rounded
Forecast
with
 = .50
1
2
3
4
5
6
7
8
180
168
159
175
190
205
180
182
175
176
175
173
173
175
178
178
5
8
16
2
17
30
2
4
84
175
178
173
166
170
180
193
186
© 2006 Prentice Hall, Inc.
Absolute
Deviation
for
 = .50
5
10
14
9
20
25
13
4
100
4 – 38
Comparison of Forecast
Error
∑ |deviations|
Rounded
Absolute
MADActual
=
Quarter
Tonage
Unloaded
Forecast
n
with
 = .10
Deviation
for
 = .10
For 180
= .10 175
168 = 84/8
176
= 10.50
1
2
3
4 For
5
6
7
8
© 2006 Prentice Hall, Inc.
159
175
175
= .50 173
190
173
205 = 100/8
175 =
180
178
182
178
5
8
16
2
17
12.5030
2
4
84
Rounded
Forecast
with
 = .50
175
178
173
166
170
180
193
186
Absolute
Deviation
for
 = .50
5
10
14
9
20
25
13
4
100
4 – 39
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
© 2006 Prentice Hall, Inc.
4 – 40
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
© 2006 Prentice Hall, Inc.
4 – 41
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
© 2006 Prentice Hall, Inc.
4 – 42
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
© 2006 Prentice Hall, Inc.
4 – 43
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
© 2006 Prentice Hall, Inc.
4 – 44
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
© 2006 Prentice Hall, Inc.
4 – 45
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
© 2006 Prentice Hall, Inc.
4 – 46
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)
© 2006 Prentice Hall, Inc.
|
7
|
8
|
9
Figure 4.3
4 – 47
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
© 2006 Prentice Hall, Inc.
4 – 48
Values of Dependent Variable
Least Squares Method
Actual observation
(y value)
Deviation7
Deviation5
Deviation3
Deviation4
Deviation1
Deviation2
Trend line, y^ = a + bx
Time period
© 2006 Prentice Hall, Inc.
Deviation6
Figure 4.4
4 – 49
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
© 2006 Prentice Hall, Inc.
Deviation6
Figure 4.4
4 – 50
Least Squares Method
Equations to calculate the regression variables
y^ = a + bx
b=
Sxy - nxy
Sx2 - nx2
a = y - bx
© 2006 Prentice Hall, Inc.
4 – 51
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
© 2006 Prentice Hall, Inc.
4 – 52
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
© 2006 Prentice Hall, Inc.
4 – 53
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
© 2006 Prentice Hall, Inc.
|
2000
|
2001
|
2002
|
2003
Year
|
2004
|
2005
|
2006
|
2007
4 – 54
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
© 2006 Prentice Hall, Inc.
4 – 56
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 – 57
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
© 2006 Prentice Hall, Inc.
Seasonal
Index
0.957
4 – 58
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
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 – 59
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
© 2006 Prentice Hall, Inc.
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 – 60
Seasonal Index Example
2006 Forecast
2005 Demand
2004 Demand
2003 Demand
140 –
130 –
Demand
120 –
110 –
100 –
90 –
80 –
70 –
|
J
|
F
|
M
|
A
|
M
|
J
|
J
|
A
|
S
|
O
|
N
|
D
Time
© 2006 Prentice Hall, Inc.
4 – 61