Heizer 04

Operations
Management
Chapter 4 –
Forecasting

PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 7e
Operations Management, 9e
© 2008 Prentice Hall, Inc. 4–1

Outline
 Global Company Profile: Disney
World
 What Is Forecasting?
 Forecasting Time Horizons
 The Influence of Product Life Cycle
 Types Of Forecasts


Outline – Continued
 The Strategic Importance of
Forecasting
 Human Resources
 Capacity
 Supply Chain Management
 Seven Steps in the Forecasting
System


 Forecasting Approaches
 Overview of Qualitative Methods
 Overview of Quantitative Methods


 Time-Series Forecasting
 Decomposition of a Time Series
 Naive Approach
 Moving Averages
 Exponential Smoothing
 Exponential Smoothing with Trend
Adjustment
 Trend Projections
 Seasonal Variations in Data
 Cyclical Variations in Data

 Associative Forecasting Methods:
Regression and Correlation
Analysis
 Using Regression Analysis for
Forecasting
 Standard Error of the Estimate
 Correlation Coefficients for
Regression Lines
 Multiple-Regression Analysis


 Monitoring and Controlling
Forecasts
 Adaptive Smoothing
 Focus Forecasting
 Forecasting In The Service Sector


Learning Objectives
When you complete this chapter you
should be able to :

 Understand the three time horizons and
which models apply for each use
 Explain when to use each of the four
qualitative models
 Apply the naive, moving average,
exponential smoothing, and trend
methods


Learning Objectives
When you complete this chapter you
should be able to :

 Compute three measures of forecast
accuracy
 Develop seasonal indexes
 Conduct a regression and correlation
analysis
 Use a tracking signal


Forecasting at Disney World
 Global portfolio includes parks in Hong
Kong, Paris, Tokyo, Orlando, and
Anaheim
 Revenues are derived from people – how
many visitors and how they spend their
money
 Daily management report contains only
the forecast and actual attendance at
each park

© 2008 Prentice Hall, Inc. 4 – 10

 Disney generates daily, weekly, monthly,
annual, and 5-year forecasts
 Forecast used by labor management,
maintenance, operations, finance, and
park scheduling
 Forecast used to adjust opening times,
rides, shows, staffing levels, and guests
admitted


 20% of customers come from outside the
USA
 Economic model includes gross
domestic product, cross-exchange rates,
arrivals into the USA
 A staff of 35 analysts and 70 field people
survey 1 million park guests, employees,
and travel professionals each year


 Inputs to the forecasting model include
airline specials, Federal Reserve
policies, Wall Street trends,
vacation/holiday schedules for 3,000
school districts around the world
 Average forecast error for the 5-year
forecast is 5%
 Average forecast error for annual
forecasts is between 0% and 3%


What is Forecasting?
 Process of
predicting a future
event
 Underlying basis of
??
all business
decisions
 Production
 Inventory
 Personnel
 Facilities


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

Distinguishing Differences
 Medium/long range forecasts deal with
more comprehensive issues and support
management decisions regarding
planning and products, plants and
processes
 Short-term forecasting usually employs
different methodologies than longer-term
forecasting
 Short-term forecasts tend to be more
accurate than longer-term forecasts


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


Product Life Cycle
Introduction Growth Maturity Decline
Best period to Practical to change Poor time to Cost control
Company Strategy/Issues

increase market price or quality change image, critical
share image price, or quality

R&D engineering is Strengthen niche Competitive costs
critical become critical
Defend market
position
CD-ROMs
Internet search engines
Analog TVs
Drive-through
LCD & plasma TVs restaurants

Sales iPods

3 1/2”
Xbox 360 Floppy
disks

Figure 2.5

Product Life Cycle
Introduction Growth Maturity Decline
Product design Forecasting Standardization Little product
and critical Less rapid differentiation
development Product and product changes Cost
OM Strategy/Issues

critical process – more minor minimization
Frequent reliability changes Overcapacity
product and Competitive Optimum in the
process design product capacity industry
changes improvements Increasing Prune line to
Short production and options stability of eliminate
runs Increase capacity process items not
High production returning
Shift toward Long production
costs good margin
product focus runs
Limited models Reduce
Enhance Product
capacity
Attention to distribution improvement and
quality cost cutting

Figure 2.5

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


Strategic Importance of
Forecasting

 Human Resources – Hiring, training,
laying off workers
 Capacity – Capacity shortages can
result in undependable delivery, loss
of customers, loss of market share
 Supply Chain Management – Good
supplier relations and price
advantages


Seven Steps in Forecasting
 Determine the use of the forecast
 Select the items to be forecasted
 Determine the time horizon of the
forecast
 Select the forecasting model(s)
 Gather the data
 Make the forecast
 Validate and implement results

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


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


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


Overview of Qualitative
Methods
 Jury of executive opinion
 Pool opinions of high-level experts,
sometimes augment by statistical
models
 Delphi method
 Panel of experts, queried iteratively


Overview of Qualitative
Methods
 Sales force composite
 Estimates from individual
salespersons are reviewed for
reasonableness, then aggregated
 Consumer Market Survey
 Ask the customer


Jury of Executive Opinion
 Involves small group of high-level experts
and managers
 Group estimates demand by working
together
 Combines managerial experience with
statistical models
 Relatively quick
 ‘Group-think’
disadvantage


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


Delphi Method
 Iterative group Decision Makers
(Evaluate
process, responses and
continues until make decisions)
consensus is
reached Staff
 3 types of (Administering
survey)
participants
 Decision makers
 Staff Respondents
(People who can
 Respondents make valuable
judgments)

Consumer Market Survey
 Ask customers about purchasing
plans
 What consumers say, and what
they actually do are often different
 Sometimes difficult to answer


Overview of Quantitative
Approaches
1. Naive approach
2. Moving averages
Time-Series
3. Exponential Models
smoothing
4. Trend projection
Associative
5. Linear regression Model


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


Time Series Components

Trend Cyclical

Seasonal Random


Components of Demand
Trend
component
Demand for product or service

Seasonal peaks

Actual
demand

Average
demand over
Random four years
variation
| | | |
1 2 3 4
Year Figure 4.1

Trend Component
 Persistent, overall upward or
downward pattern
 Changes due to population,
technology, age, culture, etc.
 Typically several years
duration


Seasonal Component
 Regular pattern of up and
down fluctuations
 Due to weather, customs, etc.
 Occurs within a single year
Number of
Period Length Seasons
Week Day 7
Month Week 4-4.5
Month Day 28-31
Year Quarter 4
Year Month 12
Year Week 52

Cyclical Component
 Repeating up and down movements
 Affected by business cycle,
political, and economic factors
 Multiple years duration
 Often causal or
associative
relationships

0 5 10 15 20

Random Component
 Erratic, unsystematic, ‘residual’
fluctuations
 Due to random variation or
unforeseen events
 Short duration and
nonrepeating

M T W T F

Naive Approach
 Assumes demand in next
period is the same as
demand in most recent period
 e.g., If January sales were 68, then
February sales will be 68
 Sometimes cost effective and
efficient
 Can be good starting point


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


Moving Average Example
Actual 3-Month
Month Shed Sales Moving Average
January 10
February 12
March 13
April 16 (10 + 12 + 13)/3 = 11 2/3
May 19 (12 + 13 + 16)/3 = 13 2/3
June 23 (13 + 16 + 19)/3 = 16
July 26 (16 + 19 + 23)/3 = 19 1/3


Graph of Moving Average
Moving
Average
30 –
28 –
Forecast
26 – Actual
24 – Sales
Shed Sales

22 –
20 –
18 –
16 –
14 –
12 –
10 –
| | | | | | | | | | | |
J F M A M J J A S O N D


Weighted Moving Average
 Used when trend is present
 Older data usually less important
 Weights based on experience and
intuition

∑ (weight for period n)
Weighted x (demand in period n)
moving average = ∑ weights


Weights Applied Period
Weighted Moving Last month
3 Average
2 Two months ago
1 Three months ago
6 Sum of weights

Actual 3-Month Weighted
Month Shed Sales Moving Average
January 10
February 12
March 13
April 16 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6
May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3
June 23 [(3 x 19) + (2 x 16) + (13)]/6 = 17
July 26 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2


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


Moving Average And
Weighted Moving Average
Weighted
moving
30 – average
25 –
Sales demand

20 – Actual
sales
15 –
Moving
10 – average

5 –
| | | | | | | | | | | |
Figure 4.2


Exponential Smoothing
 Form of weighted moving average
 Weights decline exponentially
 Most recent data weighted most
 Requires smoothing constant (α )
 Ranges from 0 to 1
 Subjectively chosen
 Involves little record keeping of past
data


t = Last period’s forecast
+ α (Last period’s actual demand
– Last period’s forecast)

Ft = Ft – 1 + α (At – 1 - Ft – 1)

where Ft = new forecast
Ft – 1 = previous forecast
α = smoothing (or weighting)
constant (0 ≤ α ≤ 1)

Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant α = .20


Example
Actual demand = 153

New forecast = 142 + .2(153 – 142)


Example
Actual demand = 153

New forecast = 142 + .2(153 – 142)
= 142 + 2.2
= 144.2 ≈ 144 cars


Effect of
Smoothing Constants

Weight Assigned to
Most 2nd Most 3rd Most 4th Most 5th Most
Recent Recent Recent Recent Recent
Smoothing Period Period Period Period Period
Constant (α ) α (1 - α ) α (1 - α ) α (1 - α ) α (1 - α )4
2 3

α = .1 .1 .09 .081 .073 .066

α = .5 .5 .25 .125 .063 .031


Impact of Different α
225 –

Actual α = .5
200 – demand
Demand

175 –

150 – α = .1
| | | | | | | | |
1 2 3 4 5 6 7 8 9
Quarter


Impact of Different α
225 –

Actual α = .5
 Chose high values of α
200 – demand
when underlying average
Demand

is likely to change
175 –
 Choose low values of α
when underlying average
150 – α = .1
is stable|
| | | | | | | |
1 2 3 4 5 6 7 8 9
Quarter


Choosing α
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 - F t


Common Measures of Error

Mean Absolute Deviation (MAD)
∑ |Actual - Forecast|
MAD =
n

Mean Squared Error (MSE)
∑ (Forecast Errors)2
MSE =
n

Common Measures of Error

Mean Absolute Percent Error (MAPE)

n

∑ 100|Actuali
i=1 - Forecasti|/Actuali
MAPE =
n


Comparison of Forecast
Error
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded α = .10 α = .10 α = .50 α = .50
1 180 175 5.00 175 5.00
2 168 175.5 7.50 177.50 9.50
3 159 174.75 15.75 172.75 13.75
4 175 173.18 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56
6 205 175.02 29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30
82.45 98.62


Error
∑ |deviations|
MAD =
Tonnage n
with for with for
1
For α180.10 175
= 5.00 175 5.00
2 168 = 82.45/8 = 10.31
175.5 7.50 177.50 9.50
3 159 174.75 15.75 172.75 13.75
4 For α175.50 173.18
= 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56
6 205 = 98.62/8
175.02 = 12.33
29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30
82.45 98.62


Error
∑ (forecast errors)2
MSE = Actual Forecast Deviation Forecast Deviation
Tonnage n
with for with for
1
For α180.10 175
= 5.00 175 5.00
2 168 1,526.54/8 = 190.82
= 175.5 7.50 177.50 9.50
3 159 174.75 15.75 172.75 13.75
4 For α175.50 173.18
= 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56
6 2051,561.91/8
= 175.02 = 195.24
29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30
82.45 98.62
MAD 10.31 12.33


n Error
i=1 ∑
100|deviationi|/actuali
MAPE = Actual Forecast Deviation Forecast Deviation
Tonnage with
Quarter Unloaded α = .10 n α for
= .10
with
α = .50
for
α = .50
1
α
For 180= .10 175 5.00 175 5.00
2 168 = 44.75/8 = 7.50
175.5 5.59% 177.50 9.50
3 159 174.75 15.75 172.75 13.75
4 For α=
175 .50 173.18 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56
6 205 = 54.05/8 = 6.76%
175.02 29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30
82.45 98.62
MAD 10.31 12.33
MSE 190.82 195.24


Error
Tonnage with for with for
1 180 175 5.00 175 5.00
2 168 175.5 7.50 177.50 9.50
3 159 174.75 15.75 172.75 13.75
4 175 173.18 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56
6 205 175.02 29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30
82.45 98.62
MAD 10.31 12.33
MSE 190.82 195.24
MAPE 5.59% 6.76%

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


Trend Adjustment

Ft = α (At - 1) + (1 - α )(Ft - 1 + Tt - 1)

Tt = β (Ft - Ft - 1) + (1 - β )Tt - 1

Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt

Trend Adjustment Example
Forecast
Actual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.00
2 17
3 20
4 19
5 24
6 21
7 31
8 28
9 36
10
Table 4.1

Forecast
1 12 11 2 13.00
2 17
3 20
4 19
5 24 Step 1: Forecast for Month 2
6 21
7 31 F2 = αA1 + (1 - α)(F1 + T1)
8 28
9 36
F2 = (.2)(12) + (1 - .2)(11 + 2)
10 = 2.4 + 10.4 = 12.8 units
Table 4.1

Forecast
1 12 11 2 13.00
2 17 12.80
3 20
4 19
5 24 Step 2: Trend for Month 2
6 21
7 31 T2 = β(F2 - F1) + (1 - β)T1
8 28
9 36
T2 = (.4)(12.8 - 11) + (1 - .4)(2)
10 = .72 + 1.2 = 1.92 units
Table 4.1

Forecast
1 12 11 2 13.00
2 17 12.80 1.92
3 20
4 19
5 24 Step 3: Calculate FIT for Month 2
6 21
7 31 FIT2 = F2 + T1
8 28
FIT2 = 12.8 + 1.92
9 36
10 = 14.72 units
Table 4.1

Forecast
1 12 11 2 13.00
2 17 12.80 1.92 14.72
3 20 15.18 2.10 17.28
4 19 17.82 2.32 20.14
5 24 19.91 2.23 22.14
6 21 22.51 2.38 24.89
7 31 24.11 2.07 26.18
8 28 27.14 2.45 29.59
9 36 29.28 2.32 31.60
10 32.48 2.68 35.16

Table 4.1

35 –
Actual demand (At)
30 –
Product demand

25 –

20 –

15 –

10 –
Forecast including trend (FITt)
with α = .2 and β = .4
5 –

0 – | | | | | | | | |
1 2 3 4 5 6 7 8 9
Figure 4.3
Time (month)

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
^ where y = computed value of
the variable to be predicted
(dependent variable)
a = y-axis intercept
b = slope of the regression line
© 2008 Prentice Hall, Inc. x = the independent variable 4 – 72

Values of Dependent Variable
Least Squares Method

Actual observation Deviation7
(y value)

Deviation5 Deviation6

Deviation3

Deviation4

Deviation1
(error) Deviation2 ^
Trend line, y = a + bx

Time period Figure 4.4

Values of Dependent Variable

Actual observation Deviation7
(y value)

Deviation5 Deviation6

Deviation3 Least squares method
minimizes the sum of the
Deviation
squared errors (deviations)
4

Deviation1
Deviation2 ^
Trend line, y = a + bx

Time period Figure 4.4

Equations to calculate the regression variables

^
y = a + bx

Σ xy - nxy
b=
Σ x2 - nx2

a = y - bx


Least Squares Example
Time Electrical Power
Year Period (x) Demand x2 xy
2001 1 74 1 74
2002 2 79 4 158
2003 3 80 9 240
2004 4 90 16 360
2005 5 105 25 525
2005 6 142 36 852
2007 7 122 49 854
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063
x=4 y = 98.86

∑xy - nxy 3,063 - (7)(4)(98.86)
b= = = 10.54
∑x - nx
2 2 140 - (7)(4 )
2

a = y - bx = 98.86 - 10.54(4) = 56.70

Time Electrical Power
Year Period (x) Demand x2 xy
1999 1 74 1 74
2000 2 79 4 158
The trend line is 80
2001 3 9 240
2002 4 90 16 360
2003 ^=
y 5 56.70 + 10.54x
105 25 525
2004 6 142 36 852
2005 7 122 49 854
Σ x = 28 Σ y = 692 Σ x2 = 140 Σ xy = 3,063
x=4 y = 98.86

Σ xy - nxy 3,063 - (7)(4)(98.86)
b= = = 10.54
Σ x - nx
2 2 140 - (7)(4 )
2

a = y - bx = 98.86 - 10.54(4) = 56.70

Trend line,
160 – ^
150 –
y = 56.70 + 10.54x
140 –
Power demand

130 –
120 –
110 –
100 –
90 –
80 –
70 –
60 –
50 –
| | | | | | | | |
2001 2002 2003 2004 2005 2006 2007 2008 2009
Year

Seasonal Variations In Data

The multiplicative
seasonal model
can adjust trend
data for seasonal
variations in
demand


Seasonal Variations In Data
Steps in the process:
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


Seasonal Index Example
Demand Average Average Seasonal
Month 2005 2006 2007 2005-2007 Monthly Index
Jan 80 85 105 90 94
Feb 70 85 85 80 94
Mar 80 93 82 85 94
Apr 90 95 115 100 94
May 113 125 131 123 94
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

Jan 80 85 105 90 94 0.957
Feb 70 85 85 80 94
Mar 80 93 average 2005-2007 monthly demand
82 85 94
Seasonal index = 115
Apr 90 95 100 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

Jan 80 85 105 90 94 0.957
Feb 70 85 85 80 94 0.851
Mar 80 93 82 85 94 0.904
Apr 90 95 115 100 94 1.064
May 113 125 131 123 94 1.309
Jun 110 115 120 115 94 1.223
Jul 100 102 113 105 94 1.117
Aug 88 102 110 100 94 1.064
Sept 85 90 95 90 94 0.957
Oct 77 78 85 80 94 0.851
Nov 75 72 83 80 94 0.851
Dec 82 78 80 80 94 0.851

Jan 80 85 105 90 94 0.957
Feb 70 85 Forecast for 2008
85 80 94 0.851
Mar 80 93 82 85 94 0.904
Apr 90Expected annual demand = 1,200
95 115 100 94 1.064
May 113 125 131 123 94 1.309
Jun 110 115 120 1,200 115 94 1.223
Jul
Jan
100 102 113 12
x .957 = 96 94
105 1.117
Aug 88 102 110 100 94 1.064
1,200
Sept 85 Feb
90 95 x90
.851 = 85 94 0.957
Oct 77 78 85 12 80 94 0.851
Nov 75 72 83 80 94 0.851
Dec 82 78 80 80 94 0.851

2008 Forecast
140 – 2007 Demand
130 – 2006 Demand
2005 Demand
120 –
Demand

110 –
100 –
90 –
80 –
70 –
| | | | | | | | | | | |
Time

San Diego Hospital
Trend Data

10,200 –

10,000 –
Inpatient Days

9745
9,800 – 9702
9616 9659
9573 9724 9766
9,600 – 9530 9680
9594 9637
9551
9,400 –

9,200 –
| | | | | | | | | | | |
9,000 –
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
67 68 69 70 71 72 73 74 75 76 77 78
Month
Figure 4.6

San Diego Hospital
Seasonal Indices

1.06 –
1.04 1.04
Index for Inpatient Days

1.04 – 1.03
1.02
1.02 – 1.01
1.00
1.00 – 0.99
0.98
0.98 – 0.99
0.96 – 0.97 0.97
0.96
0.94 –
| | | | | | | | | | | |
0.92 –
67 68 69 70 71 72 73 74 75 76 77 78
Month
Figure 4.7

San Diego Hospital
Combined Trend and Seasonal Forecast

10,200 – 10068
9949
10,000 – 9911
Inpatient Days

9764 9724
9,800 – 9691
9572
9,600 –
9520 9542
9,400 –
9411
9265 9355
9,200 –
| | | | | | | | | | | |
9,000 –
67 68 69 70 71 72 73 74 75 76 77 78
Month
Figure 4.8

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


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

Example
Sales Local Payroll
($ millions), y ($ billions), x
2.0 1
3.0 3
2.5 4 4.0 –
2.0 2
2.0 1 3.0 –
3.5 7 Sales
2.0 –

1.0 –

| | | | | | |
0 1 2 3 4 5 6 7
Area payroll


Example
Sales, y Payroll, x x2 xy
2.0 1 1 2.0
3.0 3 9 9.0
2.5 4 16 10.0
2.0 2 4 4.0
2.0 1 1 2.0
3.5 7 49 24.5
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5

∑xy - nxy 51.5 - (6)(3)(2.5)
x = ∑x/6 = 18/6 = 3 b= = = .25
∑x - nx
2 2 80 - (6)(32)

y = ∑y/6 = 15/6 = 2.5 a = y - bx = 2.5 - (.25)(3) = 1.75


Example
^
y = 1.75 + .25x Sales = 1.75 + .25(payroll)

If payroll next year
4.0 –
is estimated to be
$6 billion, then: 3.25 –
3.0
Sales
2.0 –
Sales = 1.75 + .25(6) 1.0 –
Sales = $3,250,000
| | | | | | |
0 1 2 3 4 5 6 7
Area payroll

Standard Error of the
Estimate
 A forecast is just a point estimate of a
future value
 This point is 4.0 –
actually the 3.25 –
3.0
mean of a Sales
probability 2.0 –

distribution 1.0 –

| | | | | | |
0 1 2 3 4 5 6 7
Area payroll
Figure 4.9

Estimate

∑(y - yc)2
Sy,x =
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
© 2008 Prentice Hall, Inc.
points 4 – 96

Estimate
Computationally, this equation is
considerably easier to use

∑y2 - a∑y - b∑xy
Sy,x =
n-2

We use the standard error to set up
prediction intervals around the
point estimate


Estimate
∑y2 - a∑y - b∑xy = 39.5 - 1.75(15) - .25(51.5)
Sy,x =
n-2 6-2

Sy,x = .306 4.0 –
3.25 –
3.0
Sales
The standard error 2.0 –
of the estimate is 1.0 –
$306,000 in sales

| | | | | | |
0 1 2 3 4 5 6 7
Area payroll

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


Correlation Coefficient
nΣ xy - Σ xΣ y
r=
[nΣ x2 - (Σ x)2][nΣ y2 - (Σ y)2]


y
Correlation Coefficient y

nΣ xy - Σ xΣ y
r=
[nΣ x2 - (Σ x)2][nΣ y2 - (Σ y)2]
(a) Perfect positive x (b) Positive x
correlation: correlation:
r = +1 0<r<1

y y

(c) No correlation: x (d) Perfect negative x
r=0 correlation:
r = -1

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

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
^=a+bx +bx …
y 1 1 2 2

Computationally, this is quite
complex and generally done on the
computer

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

Monitoring and Controlling
Forecasts
Tracking Signal
 Measures how well the forecast is
predicting actual values
 Ratio of running sum of forecast errors
(RSFE) to mean absolute deviation (MAD)
 Good tracking signal has low values
 If forecasts are continually high or low, the
forecast has a bias error


Monitoring and Controlling
Forecasts

Tracking RSFE
signal =
MAD

∑(Actual demand in
period i -
Forecast demand
Tracking in period i)
signal = ( ∑|Actual - Forecast|/n)


Tracking Signal
Signal exceeding limit
Tracking signal
Upper control limit
+

0 MADs Acceptable
range
–

Lower control limit

Time


Tracking Signal Example
Cumulative
Absolute Absolute
Actual Forecast Forecast Forecast
Qtr Demand Demand Error RSFE Error Error MAD

1 90 100 -10 -10 10 10 10.0
2 95 100 -5 -15 5 15 7.5
3 115 100 +15 0 15 30 10.0
4 100 110 -10 -10 10 40 10.0
5 125 110 +15 +5 15 55 11.0
6 140 110 +30 +35 30 85 14.2


Tracking Signal Example
Cumulative
Tracking Absolute Absolute
Actual Signal
Forecast Forecast Forecast
(RSFE/MAD)
Qtr Demand Demand Error RSFE Error Error MAD

1 90 100 -1 -10
-10/10 = -10 10 10 10.0
2 95 100 -2 -5
-15/7.5 = -15 5 15 7.5
3 115 0/10 = 0 +15
100 0 15 30 10.0
4 100 110 -1 -10
-10/10 = -10 10 40 10.0
5 125 110 +15
+5/11 = +0.5 +5 15 55 11.0
6 140 110 +2.5
+35/14.2 = +30 +35 30 85 14.2

The variation of the tracking signal
between -2.0 and +2.5 is within acceptable
limits

Adaptive Forecasting

It’s possible to use the computer to
continually monitor forecast error and
adjust the values of the α and β
coefficients used in exponential
smoothing to continually minimize
forecast error
This technique is called adaptive
smoothing


Focus Forecasting
Developed at American Hardware Supply,
focus forecasting is based on two principles:
1. Sophisticated forecasting models are not
always better than simple ones
2. There is no single technique that should
be used for all products or services
This approach uses historical data to test
multiple forecasting models for individual items
The forecasting model with the lowest error is
then used to forecast the next demand


Forecasting in the Service
Sector
 Presents unusual challenges
 Special need for short term records
 Needs differ greatly as function of
industry and product
 Holidays and other calendar events
 Unusual events


Fast Food Restaurant
Forecast
20% –
Percentage of sales

15% –

10% –

5% –

11-12 1-2 3-4 5-6 7-8 9-10
12-1 2-3 4-5 6-7 8-9 10-11
(Lunchtime) (Dinnertime)
Hour of day Figure 4.12

FedEx Call Center Forecast
12% –

10% –

8% –

6% –

4% –

2% –

0% –

2 4 6 8 10 12 2 4 6 8 10 12
A.M. P.M.
Hour of day
Figure 4.12

Heizer 04

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Ähnlich wie Heizer 04

Ähnlich wie Heizer 04 (20)

Mehr von Rizwan Khurram

Mehr von Rizwan Khurram (20)

Heizer 04