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Forecasting Disney World Case
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© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 1
44 ForecastingForecasting
PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e
PowerPoint slides by Jeff Heyl
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 2
OutlineOutline
Global Company Profile: Disney World
What Is Forecasting? Forecasting Time Horizons
The Influence of Product Life Cycle
Types Of Forecasts
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 3
Outline – ContinuedOutline – Continued
The Strategic Importance of Forecasting Human Resources
Capacity
Supply Chain Management
Seven Steps in the Forecasting System
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 4
Outline – ContinuedOutline – Continued
Forecasting Approaches Overview of Qualitative Methods
Overview of Quantitative Methods
Time-Series Forecasting Decomposition of a Time Series
Naive Approach
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 5
Outline – ContinuedOutline – Continued
Time-Series Forecasting (cont.) Moving Averages
Exponential Smoothing
Exponential Smoothing with Trend Adjustment
Trend Projections
Seasonal Variations in Data
Cyclical Variations in Data
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 6
Outline – ContinuedOutline – Continued 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 7
Outline – ContinuedOutline – Continued
Monitoring and Controlling Forecasts Adaptive Smoothing
Focus Forecasting
Forecasting in the Service Sector
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 8
Learning ObjectivesLearning Objectives
When you complete this chapter you When you complete this chapter you should be able to :should be able to :
1. Understand the three time horizons and which models apply for each use
2. Explain when to use each of the four qualitative models
3. Apply the naive, moving average, exponential smoothing, and trend methods
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 9
Learning ObjectivesLearning Objectives
When you complete this chapter you When you complete this chapter you should be able to :should be able to :
4. Compute three measures of forecast accuracy
5. Develop seasonal indexes
6. Conduct a regression and correlation analysis
7. Use a tracking signal
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 10
Forecasting at Disney WorldForecasting 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 11
Forecasting at Disney WorldForecasting at Disney World
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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 12
Forecasting at Disney WorldForecasting at Disney World
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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 13
Forecasting at Disney WorldForecasting at Disney World
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%
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 14
What is Forecasting?What is Forecasting?
Process of predicting a future event
Underlying basis of all business decisions Production
Inventory
Personnel
Facilities
??
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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
Forecasting Time HorizonsForecasting Time Horizons
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Distinguishing DifferencesDistinguishing Differences
Medium/long rangeMedium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes
Short-termShort-term forecasting usually employs different methodologies than longer-term forecasting
Short-termShort-term forecasts tend to be more accurate than longer-term forecasts
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 17
Influence of Product Life Influence of Product Life CycleCycle
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
Introduction – Growth – Maturity – DeclineIntroduction – Growth – Maturity – Decline
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Product Life CycleProduct Life Cycle
Best period to increase market share
R&D engineering is critical
Practical to change price or quality image
Strengthen niche
Poor time to change image, price, or quality
Competitive costs become criticalDefend market position
Cost control critical
Introduction Growth Maturity Decline
Co
mp
an
y S
tra
teg
y/Is
sue
s
Figure 2.5
Internet search engines
Sales
Drive-through restaurants
CD-ROMs
Analog TVs
iPods
Boeing 787
LCD & plasma TVs
Avatars
Xbox 360
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Product Life CycleProduct Life Cycle
Product design and development critical
Frequent product and process design changes
Short production runs
High production costs
Limited models
Attention to quality
Introduction Growth Maturity Decline
OM
Str
ate
gy
/Issu
es
Forecasting critical
Product and process reliability
Competitive product improvements and options
Increase capacity
Shift toward product focus
Enhance distribution
Standardization
Fewer product changes, more minor changes
Optimum capacity
Increasing stability of process
Long production runs
Product improvement and cost cutting
Little product differentiation
Cost minimization
Overcapacity in the industry
Prune line to eliminate items not returning good margin
Reduce capacity
Figure 2.5
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 20
Types of ForecastsTypes 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 21
Strategic Importance of Strategic Importance of ForecastingForecasting
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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 22
Seven Steps in ForecastingSeven Steps in Forecasting
1. Determine the use of the forecast
2. Select the items to be forecasted
3. Determine the time horizon of the forecast
4. Select the forecasting model(s)
5. Gather the data
6. Make the forecast
7. Validate and implement results
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 23
The Realities!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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 24
Forecasting ApproachesForecasting Approaches
Used when situation is vague and little data exist New products
New technology
Involves intuition, experience e.g., forecasting sales on
Internet
Qualitative MethodsQualitative Methods
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 25
Forecasting ApproachesForecasting Approaches
Used when situation is ‘stable’ and historical data exist Existing products
Current technology
Involves mathematical techniques e.g., forecasting sales of color
televisions
Quantitative MethodsQuantitative Methods
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 26
Overview of Qualitative Overview of Qualitative MethodsMethods
1. Jury of executive opinion Pool opinions of high-level experts,
sometimes augment by statistical models
2. Delphi method Panel of experts, queried iteratively
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 27
Overview of Qualitative Overview of Qualitative MethodsMethods
3. Sales force composite Estimates from individual
salespersons are reviewed for reasonableness, then aggregated
4. Consumer Market Survey Ask the customer
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 28
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
Jury of Executive OpinionJury of Executive Opinion
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 29
Sales Force CompositeSales 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 30
Delphi MethodDelphi Method Iterative group
process, continues until consensus is reached
3 types of participants Decision makers
Staff
Respondents
Staff(Administering
survey)
Decision Makers(Evaluate
responses and make decisions)
Respondents(People who can make valuable
judgments)
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 31
Consumer Market SurveyConsumer Market Survey
Ask customers about purchasing plans
What consumers say, and what they actually do are often different
Sometimes difficult to answer
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 32
Overview of Quantitative Overview of Quantitative ApproachesApproaches
1. Naive approach
2. Moving averages
3. Exponential smoothing
4. Trend projection
5. Linear regression
time-series models
associative model
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 33
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 ForecastingTime Series Forecasting
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 34
Trend
Seasonal
Cyclical
Random
Time Series ComponentsTime Series Components
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 35
Components of DemandComponents of DemandD
eman
d f
or
pro
du
ct o
r se
rvic
e
| | | |1 2 3 4
Time (years)
Average demand over 4 years
Trend component
Actual demand line
Random variation
Figure 4.1
Seasonal peaks
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 36
Persistent, overall upward or downward pattern
Changes due to population, technology, age, culture, etc.
Typically several years duration
Trend ComponentTrend Component
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Regular pattern of up and down fluctuations
Due to weather, customs, etc.
Occurs within a single year
Seasonal ComponentSeasonal Component
Number ofPeriod Length Seasons
Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 38
Repeating up and down movements
Affected by business cycle, political, and economic factors
Multiple years duration
Often causal or associative relationships
Cyclical ComponentCyclical Component
0 5 10 15 20
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Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events
Short duration and nonrepeating
Random ComponentRandom Component
M T W T F
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Naive ApproachNaive 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 41
MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing Provides overall impression of data
over time
Moving Average MethodMoving Average Method
Moving average =∑ demand in previous n periods
n
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 42
January 10February 12March 13April 16May 19June 23July 26
Actual 3-MonthMonth Shed Sales Moving Average
(12 + 13 + 16)/3 = 13 2/3
(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3
Moving Average ExampleMoving Average Example
101012121313
(1010 + 1212 + 1313)/3 = 11 2/3
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 43
Graph of Moving AverageGraph of Moving Average
| | | | | | | | | | | |
J F M A M J J A S O N D
Sh
ed S
ales
30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –
Actual Sales
Moving Average Forecast
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 44
Used when some trend might be present Older data usually less important
Weights based on experience and intuition
Weighted Moving AverageWeighted Moving Average
Weightedmoving average =
∑ (weight for period n) x (demand in period n)
∑ weights
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 45
January 10February 12March 13April 16May 19June 23July 26
Actual 3-Month WeightedMonth Shed Sales Moving Average
[(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
Weighted Moving AverageWeighted Moving Average
101012121313
[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6
Weights Applied Period
33 Last month22 Two months ago11 Three months ago
6 Sum of weights
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 46
Increasing n smooths the forecast but makes it less sensitive to changes
Do not forecast trends well
Require extensive historical data
Potential Problems WithPotential Problems With Moving Average Moving Average
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Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average
30 –
25 –
20 –
15 –
10 –
5 –
Sa
les
de
man
d
| | | | | | | | | | | |
J F M A M J J A S O N D
Actual sales
Moving average
Weighted moving average
Figure 4.2
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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
Exponential SmoothingExponential Smoothing
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Exponential SmoothingExponential 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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Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20
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Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20
New forecast = 142 + .2(153 – 142)
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 52
Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20
New forecast = 142 + .2(153 – 142)
= 142 + 2.2
= 144.2 ≈ 144 cars
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Effect ofEffect of Smoothing Constants Smoothing Constants
Weight Assigned to
Most 2nd Most 3rd Most 4th Most 5th MostRecent Recent Recent Recent Recent
Smoothing Period Period Period Period PeriodConstant () (1 - ) (1 - )2 (1 - )3 (1 - )4
= .1 .1 .09 .081 .073 .066
= .5 .5 .25 .125 .063 .031
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Impact of Different Impact of Different
225 –
200 –
175 –
150 –| | | | | | | | |
1 2 3 4 5 6 7 8 9
Quarter
De
ma
nd
= .1
Actual demand
= .5
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 55
Impact of Different Impact of Different
225 –
200 –
175 –
150 –| | | | | | | | |
1 2 3 4 5 6 7 8 9
Quarter
De
ma
nd
= .1
Actual demand
= .5 Chose high values of when underlying average is likely to change
Choose low values of when underlying average is stable
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Choosing Choosing
The objective is to obtain the most accurate forecast no matter the technique
We generally do this by selecting the We generally do this by selecting the model that gives us the lowest forecast model that gives us the lowest forecast errorerror
Forecast error = Actual demand - Forecast value
= At - Ft
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Common Measures of ErrorCommon Measures of Error
Mean Absolute Deviation (MAD)
MAD =∑ |Actual - Forecast|
n
Mean Squared Error (MSE)
MSE =∑ (Forecast Errors)2
n
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Common Measures of ErrorCommon Measures of Error
Mean Absolute Percent Error (MAPE)
MAPE =∑100|Actuali - Forecasti|/Actuali
n
n
i = 1
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Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 60
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62
MAD =∑ |deviations|
n
= 82.45/8 = 10.31
For = .10
= 98.62/8 = 12.33
For = .50
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 61
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33
= 1,526.54/8 = 190.82
For = .10
= 1,561.91/8 = 195.24
For = .50
MSE =∑ (forecast errors)2
n
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 62
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33MSE 190.82 195.24
= 44.75/8 = 5.59%
For = .10
= 54.05/8 = 6.76%
For = .50
MAPE =∑100|deviationi|/actuali
n
n
i = 1
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 63
Comparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%
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Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment
When a trend is present, exponential smoothing must be modified
Forecast including (FITt) = trend
Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend
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Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment
Ft = (At - 1) + (1 - )(Ft - 1 + Tt - 1)
Tt = (Ft - Ft - 1) + (1 - )Tt - 1
Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 173 204 195 246 217 318 289 36
10
Table 4.1
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 173 204 195 246 217 318 289 36
10
Table 4.1
F2 = A1 + (1 - )(F1 + T1)
F2 = (.2)(12) + (1 - .2)(11 + 2)
= 2.4 + 10.4 = 12.8 units
Step 1: Forecast for Month 2
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17 12.803 204 195 246 217 318 289 36
10
Table 4.1
T2 = (F2 - F1) + (1 - )T1
T2 = (.4)(12.8 - 11) + (1 - .4)(2)
= .72 + 1.2 = 1.92 units
Step 2: Trend for Month 2
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17 12.80 1.923 204 195 246 217 318 289 36
10
Table 4.1
FIT2 = F2 + T2
FIT2 = 12.8 + 1.92
= 14.72 units
Step 3: Calculate FIT for Month 2
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastActual Smoothed Smoothed Including
Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt
1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 318 289 36
10
Table 4.1
15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
Figure 4.3
| | | | | | | | |
1 2 3 4 5 6 7 8 9
Time (month)
Pro
du
ct d
eman
d
35 –
30 –
25 –
20 –
15 –
10 –
5 –
0 –
Actual demand (At)
Forecast including trend (FITt)with = .2 and = .4
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Trend ProjectionsTrend 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 interceptb= slope of the regression linex= the independent variable
^
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 73
Least Squares MethodLeast Squares Method
Time period
Va
lue
s o
f D
ep
end
en
t V
ari
able
Figure 4.4
Deviation1
(error)
Deviation5
Deviation7
Deviation2
Deviation6
Deviation4
Deviation3
Actual observation (y-value)
Trend line, y = a + bx^
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Least Squares MethodLeast Squares Method
Time period
Va
lue
s o
f D
ep
end
en
t V
ari
able
Figure 4.4
Deviation1
(error)
Deviation5
Deviation7
Deviation2
Deviation6
Deviation4
Deviation3
Actual observation (y-value)
Trend line, y = a + bx^
Least squares method minimizes the sum of the
squared errors (deviations)
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 75
Least Squares MethodLeast Squares Method
Equations to calculate the regression variables
b =xy - nxy
x2 - nx2
y = a + bx^
a = y - bx
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Least Squares ExampleLeast Squares Example
b = = = 10.54∑xy - nxy
∑x2 - nx2
3,063 - (7)(4)(98.86)
140 - (7)(42)
a = y - bx = 98.86 - 10.54(4) = 56.70
Time Electrical Power Year Period (x) Demand x2 xy
2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86
© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 - 77
b = = = 10.54∑xy - nxy
∑x2 - nx2
3,063 - (7)(4)(98.86)
140 - (7)(42)
a = y - bx = 98.86 - 10.54(4) = 56.70
Time Electrical Power Year Period (x) Demand x2 xy
2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86
Least Squares ExampleLeast Squares Example
The trend line is
y = 56.70 + 10.54x^
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Least Squares ExampleLeast Squares Example
| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011
160 –150 –140 –130 –120 –110 –100 –90 –80 –70 –60 –50 –
Year
Po
wer
dem
and
Trend line,y = 56.70 + 10.54x^
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Seasonal Variations In DataSeasonal Variations In Data
The multiplicative seasonal model can adjust trend data for seasonal variations in demand
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Seasonal Variations In DataSeasonal Variations In Data
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
Steps in the process:Steps in the process:
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Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
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Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
0.957
Seasonal index = Average 2007-2009 monthly demand
Average monthly demand
= 90/94 = .957
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Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
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Seasonal Index ExampleSeasonal Index Example
Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851
Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index
Expected annual demand = 1,200
Jan x .957 = 961,200
12
Feb x .851 = 851,200
12
Forecast for 2010
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Seasonal Index ExampleSeasonal Index Example
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –| | | | | | | | | | | |J F M A M J J A S O N D
Time
Dem
and
2010 Forecast
2009 Demand
2008 Demand
2007 Demand
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San Diego HospitalSan Diego Hospital
10,200 –
10,000 –
9,800 –
9,600 –
9,400 –
9,200 –
9,000 –| | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78
Month
Inp
atie
nt
Day
s
9530
9551
9573
9594
9616
9637
9659
9680
9702
9724
9745
9766
Figure 4.6
Trend Data
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San Diego HospitalSan Diego Hospital
1.06 –
1.04 –
1.02 –
1.00 –
0.98 –
0.96 –
0.94 –
0.92 – | | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78
Month
Ind
ex f
or
Inp
atie
nt
Day
s 1.04
1.021.01
0.99
1.031.04
1.00
0.98
0.97
0.99
0.970.96
Figure 4.7
Seasonal Indices
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San Diego HospitalSan Diego Hospital
10,200 –
10,000 –
9,800 –
9,600 –
9,400 –
9,200 –
9,000 –| | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78
Month
Inp
atie
nt
Day
s
Figure 4.8
9911
9265
9764
9520
9691
9411
9949
9724
9542
9355
10068
9572
Combined Trend and Seasonal Forecast
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Associative ForecastingAssociative 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 We apply this technique just as we did in the time series examplein the time series example
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Associative ForecastingAssociative ForecastingForecasting 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 interceptb= slope of the regression linex= the independent variable though to predict the value of the dependent variable
^
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Associative Forecasting Associative Forecasting ExampleExample
Sales Area Payroll($ millions), y ($ billions), x
2.0 13.0 32.5 42.0 22.0 13.5 7
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sal
es
Area payroll
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Associative Forecasting Associative Forecasting ExampleExample
Sales, y Payroll, x x2 xy
2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5
x = ∑x/6 = 18/6 = 3
y = ∑y/6 = 15/6 = 2.5
b = = = .25∑xy - nxy
∑x2 - nx2
51.5 - (6)(3)(2.5)
80 - (6)(32)
a = y - bx = 2.5 - (.25)(3) = 1.75
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Associative Forecasting Associative Forecasting ExampleExample
y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)
If payroll next year is estimated to be $6 billion, then:
Sales = 1.75 + .25(6)Sales = $3,250,000
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
No
del
’s s
ales
Area payroll
3.25
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Standard Error of the Standard Error of the EstimateEstimate
A forecast is just a point estimate of a future value
This point is actually the mean of a probability distribution
Figure 4.9
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
No
del
’s s
ales
Area payroll
3.25
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Standard Error of the Standard Error of the EstimateEstimate
where y = y-value of each data point
yc = computed value of the dependent variable, from the regression equation
n = number of data points
Sy,x =∑(y - yc)2
n - 2
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Standard Error of the Standard Error of the EstimateEstimate
Computationally, this equation is considerably easier to use
We use the standard error to set up prediction intervals around the
point estimate
Sy,x =∑y2 - a∑y - b∑xy
n - 2
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Standard Error of the Standard Error of the EstimateEstimate
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
No
del
’s s
ales
Area payroll
3.25
Sy,x = =∑y2 - a∑y - b∑xyn - 2
39.5 - 1.75(15) - .25(51.5)6 - 2
Sy,x = .306
The standard error of the estimate is $306,000 in sales
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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
CorrelationCorrelation
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Correlation CoefficientCorrelation Coefficient
r = nxy - xy
[nx2 - (x)2][ny2 - (y)2]
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Correlation CoefficientCorrelation Coefficient
r = nxy - xy
[nx2 - (x)2][ny2 - (y)2]
y
x(a) Perfect positive correlation: r = +1
y
x(b) Positive correlation: 0 < r < 1
y
x(c) No correlation: r = 0
y
x(d) Perfect negative correlation: r = -1
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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
CorrelationCorrelation
For the Nodel Construction example:
r = .901
r2 = .81
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Multiple Regression Multiple Regression AnalysisAnalysis
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 Computationally, this is quite complex and generally done on the complex and generally done on the
computercomputer
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Multiple Regression Multiple Regression AnalysisAnalysis
y = 1.80 + .30x1 - 5.0x2^
In the Nodel example, including interest rates in the model gives the new equation:
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) = 3.00Sales = $3,000,000
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Measures how well the forecast is predicting actual values
Ratio of cumulative forecast errors 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 Monitoring and Controlling ForecastsForecasts
Tracking SignalTracking Signal
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Monitoring and Controlling Monitoring and Controlling ForecastsForecasts
Tracking signal
Cumulative errorMAD
=
Tracking signal =
∑(Actual demand in period i -
Forecast demand in period i)
∑|Actual - Forecast|/n)
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Tracking SignalTracking Signal
Tracking signal
+
0 MADs
–
Upper control limit
Lower control limit
Time
Signal exceeding limit
Acceptable range
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Tracking Signal ExampleTracking Signal Example
CumulativeAbsolute Absolute
Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD
1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
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CumulativeAbsolute Absolute
Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD
1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
Tracking Signal ExampleTracking Signal Example
TrackingSignal
(Cumm Error/MAD)
-10/10 = -1-15/7.5 = -2
0/10 = 0-10/10 = -1
+5/11 = +0.5+35/14.2 = +2.5
The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits
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Adaptive ForecastingAdaptive Forecasting
It’s possible to use the computer to continually monitor forecast error and adjust the values of the and coefficients used in exponential smoothing to continually minimize forecast error
This technique is called adaptive smoothing
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Focus ForecastingFocus Forecasting Developed at American Hardware Supply,
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
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Forecasting in the Service Forecasting in the Service SectorSector
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
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Fast Food Restaurant Fast Food Restaurant ForecastForecast
20% –
15% –
10% –
5% –
11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11
(Lunchtime) (Dinnertime)Hour of day
Per
cen
tag
e o
f sa
les
Figure 4.12
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FedEx Call Center ForecastFedEx Call Center Forecast
Figure 4.12
12% –
10% –
8% –
6% –
4% –
2% –
0% –
Hour of dayA.M. P.M.
2 4 6 8 10 12 2 4 6 8 10 12
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