44 ForecastingForecasting44 ForecastingForecasting
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OutlineOutlineOutlineOutline Gl b l C P fil Di Global Company Profile: Disney
World What Is Forecasting?
F ti Ti H i Forecasting Time Horizons The Influence of Product Life Cycley Types Of Forecasts
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OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued Th St t i I t f The Strategic Importance of
Forecasting Human Resources Capacity Capacity Supply Chain Management
Seven Steps in the Forecasting SystemSystem
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OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued F ti A h Forecasting Approaches
Overview of Qualitative Methods Overview of Qualitative Methods Overview of Quantitative Methods
Time-Series Forecasting Decomposition of a Time Series Decomposition of a Time Series Naive Approach
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OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued Ti S i F ti ( t ) Time-Series Forecasting (cont.)
Moving Averages Moving Averages Exponential Smoothing Exponential Smoothing with Trend
Adjustment Trend Projections Seasonal Variations in Data Seasonal Variations in Data Cyclical Variations in Data
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OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued A i ti F ti M th d Associative Forecasting Methods:
Regression and Correlation A l iAnalysis Using Regression Analysis for g g y
Forecasting Standard Error of the Estimate Standard Error of the Estimate Correlation Coefficients for
Regression LinesRegression Lines Multiple-Regression Analysis
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OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued Monitoring and Controlling
Forecasts Adaptive Smoothing F F ti Focus Forecasting
Forecasting in the Service Sectorg
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Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning ObjectivesWh l t thi h tWh l t thi h tWhen 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 useand which models apply for each use
2. Explain when to use each of the four lit ti d lqualitative models
3. Apply the naive, moving average, exponential smoothing, and trend methods
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Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning ObjectivesWh l t thi h tWh l t thi h tWhen 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 accuracyaccuracy
5. Develop seasonal indexes6. Conduct a regression and correlation
analysis7. Use a tracking signal
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Forecasting at Disney WorldForecasting at Disney WorldForecasting at Disney WorldForecasting at Disney World
Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and g, , y , ,Anaheim
Revenues are derived from people – how Revenues are derived from people how many visitors and how they spend their moneyy
Daily management report contains only the forecast and actual attendance atthe forecast and actual attendance at each park
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Forecasting at Disney WorldForecasting at Disney WorldForecasting at Disney WorldForecasting at Disney World
Disney generates daily, weekly, monthly, annual and 5-year forecastsannual, and 5 year forecasts
Forecast used by labor management, maintenance operations finance andmaintenance, operations, finance, and park scheduling
F t d t dj t i ti Forecast used to adjust opening times, rides, shows, staffing levels, and guests admittedadmitted
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Forecasting at Disney WorldForecasting at Disney WorldForecasting at Disney WorldForecasting at Disney World
20% of customers come from outside the USA
Economic model includes gross domestic product cross-exchange ratesdomestic product, cross-exchange rates, arrivals into the USA
A staff of 35 analysts and 70 field people A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each yearand travel professionals each year
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Forecasting at Disney WorldForecasting at Disney WorldForecasting at Disney WorldForecasting at Disney World
Inputs to the forecasting model include airline specials, Federal Reserve p ,policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world
Average forecast error for the 5-year g yforecast is 5%
Average forecast error for annual Average forecast error for annual forecasts is between 0% and 3%
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What is Forecasting?What is Forecasting?What is Forecasting?What is Forecasting? Process of predicting
a future event Underlying basis
of all business ??
decisions Production Production Inventory Personnel Personnel Facilities
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Forecasting Time HorizonsForecasting Time Horizons Short-range forecastForecasting Time HorizonsForecasting Time Horizons
Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce g, j g,
levels, job assignments, production levels Medium-range forecastg
3 months to 3 years Sales and production planning budgeting Sales and production planning, budgeting
Long-range forecast 3+ years New product planning, facility location,
h d d l4 - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall
research and development
Distinguishing DifferencesDistinguishing DifferencesDistinguishing DifferencesDistinguishing Differences
Medium/long rangeMedium/long range forecasts deal with more comprehensive issues and support
t d i i dimanagement decisions regarding planning and products, plants and processesprocesses
ShortShort--termterm forecasting usually employs diff t th d l i th l tdifferent methodologies than longer-term forecasting
ShortShort--termterm forecasts tend to be more accurate than longer-term forecasts
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Influence of Product LifeInfluence of Product LifeInfluence of Product Life Influence of Product Life CycleCycle
Introduction Introduction –– Growth Growth –– Maturity Maturity –– DeclineDecline
Introduction and growth require longer forecasts than maturity and declineforecasts than maturity and decline
As product passes through life cycle, f t f l i j tiforecasts are useful in projecting Staffing levels Inventory levels Factory capacity
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y p y
Product Life CycleProduct Life CycleProduct Life CycleProduct Life CycleIntroduction Growth Maturity Decline
Best period to increase market share
Practical to change price or quality image
Poor time to change image, price, or quality
Cost control critical
Introduction Growth Maturity Decline
ues
R&D engineering is critical
Strengthen niche Competitive costs become criticalDefend market eg
y/Is
s
position
ny S
trat
e
Internet search enginesDrive-through
restaurantsCD-ROMs
iPods LCD &
Com
pan
Sales
LCD & plasma TVs
Avatars
Xbox 360
C
Analog TVs
Boeing 787
4 - 18© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 2.5
Product Life CycleProduct Life CycleProduct Life CycleProduct Life CycleIntroduction Growth Maturity Decline
Product design and development
Introduction Growth Maturity Decline
s
Forecasting criticalProduct and
StandardizationFewer product changes more
Little product differentiationCostcritical
Frequent product and process designy/
Issu
es
Product and process reliabilityCompetitive
d t
changes, more minor changesOptimum capacity
Cost minimizationOvercapacity in the i d tprocess design
changesShort production runs
Stra
tegy product
improvements and optionsIncrease capacity
Increasing stability of processLong production
industryPrune line to eliminate items not
High production costsLimited modelsAtt ti t
OM
S
p yShift toward product focusEnhance di t ib ti
Long production runsProduct improvement
d t tti
returning good marginReduce capacityAttention to
qualitydistribution and cost cutting capacity
4 - 19© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 2.5
Types of ForecastsTypes of ForecastsTypes of ForecastsTypes of Forecasts
Economic forecasts Address business cycle – inflation rate Address business cycle – inflation rate,
money supply, housing starts, etc. Technological forecasts Technological forecasts
Predict rate of technological progress I t d l t f d t Impacts development of new products
Demand forecasts Predict sales of existing products and
services
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St t i I t fSt t i I t fStrategic Importance of Strategic Importance of ForecastingForecastingForecastingForecasting
Human Resources Hiring training Human Resources – Hiring, training, laying off workers
C it C it h t Capacity – Capacity shortages can result in undependable delivery, loss of customers loss of market shareof customers, loss of market share
Supply Chain Management – Good li l ti d isupplier relations and price
advantages
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Seven Steps in ForecastingSeven Steps in ForecastingSeven Steps in ForecastingSeven Steps in Forecasting1 Determine the use of the forecast1. Determine the use of the forecast2. Select the items to be forecasted3. Determine the time horizon of the
forecastforecast4. Select the forecasting model(s)5. Gather the data6. Make the forecast6. Make the forecast7. Validate and implement results
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The Realities!The Realities!
Forecasts are seldom perfect Most techniques assume an
underlying stability in the systemunderlying stability in the system Product family and aggregated
forecasts are more accurate than individual product forecasts
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Forecasting ApproachesForecasting ApproachesForecasting ApproachesForecasting Approaches
U d h i i iQualitative MethodsQualitative Methods
Used when situation is vague and little data exist New products New technology New technology
Involves intuition, experience e.g., forecasting sales on
Internet
4 - 24© 2011 Pearson Education, Inc. publishing as Prentice Hall
Internet
Forecasting ApproachesForecasting ApproachesForecasting ApproachesForecasting Approaches
Quantitative MethodsQuantitative Methods
Used when situation is ‘stable’ and historical data exist Existing products C t t h l Current technology
Involves mathematical techniquesq e.g., forecasting sales of color
televisions4 - 25© 2011 Pearson Education, Inc. publishing as Prentice Hall
televisions
Overview of QualitativeOverview of QualitativeOverview of Qualitative Overview of Qualitative MethodsMethods
1 Jury of executive opinion1. Jury of executive opinion Pool opinions of high-level experts,
sometimes augment by statisticalsometimes augment by statistical models
2. Delphi method Panel of experts, queried iteratively Panel of experts, queried iteratively
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Overview of QualitativeOverview of QualitativeOverview of Qualitative Overview of Qualitative MethodsMethods
3 Sales force composite3. Sales force composite Estimates from individual
l i d fsalespersons are reviewed for reasonableness, then aggregated
4. Consumer Market Survey Ask the customer Ask the customer
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Jury of Executive OpinionJury of Executive Opinion
Jury of Executive OpinionJury 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 ‘G thi k’ ‘Group-think’
disadvantage
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Sales Force CompositeSales Force CompositeSales Force CompositeSales Force Composite
Each salesperson projects his or her salesher sales
Combined at district and national levels
Sales reps know customers’ wants Sales reps know customers wants Tends to be overly optimistic
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Delphi MethodDelphi MethodDelphi MethodDelphi Method Iterative group te at e g oup
process, continues until
Decision Makers(Evaluate
responses andcontinues until consensus is reached
responses and make decisions)
reached 3 types of
ti i t
Staff(Administering
survey)participants Decision makers
survey)
Staff Respondents
Respondents(People who can
k l bl4 - 30© 2011 Pearson Education, Inc. publishing as Prentice Hall
Respondents make valuable judgments)
Consumer Market SurveyConsumer Market SurveyConsumer Market SurveyConsumer Market Survey
Ask customers about purchasing plansplans
What consumers say, and what they actually do are often different
Sometimes difficult to answer Sometimes difficult to answer
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Overview of QuantitativeOverview of QuantitativeOverview of Quantitative Overview of Quantitative ApproachesApproachespppp
1. Naive approachpp2. Moving averages
time series3. Exponential smoothing
time-series models
g4. Trend projection5. Linear regression associative
model
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Time Series ForecastingTime Series ForecastingTime Series ForecastingTime 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 importantno other variables important Assumes that factors influencing
past and present will continuepast and present will continue influence in future
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Time Series ComponentsTime Series ComponentsTime Series ComponentsTime Series Components
T d C li lTrend Cyclical
S l R dSeasonal Random
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Components of DemandComponents of DemandComponents of DemandComponents of Demand
e
Trend component
or s
ervi
ce Seasonal peaks
prod
uct o
Actual demand line
man
d fo
r
Average demand over 4 years
Dem
| | | |1 2 3 4
Random variation
4 - 35© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time (years)Figure 4.1
Trend ComponentTrend ComponentTrend ComponentTrend Component
Persistent, overall upward or downward patterndownward pattern
Changes due to population, t h l lt ttechnology, age, culture, etc.
Typically several years Typically several years duration
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Seasonal ComponentSeasonal Component Regular pattern of up and
Seasonal ComponentSeasonal Component Regular pattern of up and
down fluctuations Due to weather, customs, etc. Occurs within a single year Occurs within a single year
Number ofPeriod Length SeasonsPeriod Length SeasonsWeek Day 7Month Week 4-4.5M th D 28 31Month Day 28-31Year Quarter 4Year Month 12Year Week 52
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Year Week 52
Cyclical ComponentCyclical ComponentCyclical ComponentCyclical Component
Repeating up and down movements Affected by business cycle Affected by business cycle,
political, and economic factors Multiple years duration Often causal or Often causal or
associative relationshipsrelationships
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0 5 10 15 20
Random ComponentRandom ComponentRandom ComponentRandom Component Erratic, unsystematic, ‘residual’
fluctuationsDue to random variation or unforeseen
eventsevents Short duration
and nonrepeating
4 - 39© 2011 Pearson Education, Inc. publishing as Prentice HallM T W T F
Naive ApproachNaive ApproachNaive ApproachNaive Approach A d d i t Assumes demand in next
period is the same as d d i t t i ddemand in most recent period e.g., If January sales were 68, then e.g., If January sales were 68, then
February sales will be 68 Sometimes cost effective and Sometimes cost effective and
efficient Can be good starting point
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Moving Average MethodMoving Average MethodMoving Average MethodMoving Average Method
MA is a series of arithmetic means Used if little or no trend Used often for smoothing Used often for smoothing
Provides overall impression of data tiover time
Moving average =∑ demand in previous n periods
n
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Moving Average ExampleMoving Average ExampleMoving Average ExampleMoving Average Example
Actual 3-MonthMonth Shed Sales Moving Average
January 10February 12
10101212y
March 13April 16M 19 (12 13 16)/3 13 2/
1313(1010 + 1212 + 1313)/3 = 11 2/3
May 19June 23July 26
(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3July 26 (16 + 19 + 23)/3 = 19 /3
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Graph of Moving AverageGraph of Moving AverageGraph of Moving AverageGraph of Moving AverageM i
30 –28
Moving Average Forecast
es
28 –26 –24 –22
Actual Sales
Shed
Sal 22 –
20 –18 –
S 16 –14 –12 –
| | | | | | | | | | | |J F M A M J J A S O N D
10 –
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W i ht d M i AW i ht d M i A
Weighted Moving AverageWeighted Moving Average Used when some trend might be
present Older data usually less important
W i ht b d i d Weights based on experience and intuition
Weighted∑ (weight for period n)
x (demand in period n)Weightedmoving average =
( )∑ weights
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W i ht d M i AW i ht d M i AWeights Applied Period
Weighted Moving AverageWeighted Moving Average33 Last month22 Two months ago11 Th th11 Three months ago6 Sum of weights
Actual 3-Month WeightedMonth Shed Sales Moving Average
January 10February 12
10101212
March 13April 16May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3
1313[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6
May 19June 23July 26
[(3 x 16) + (2 x 13) + (12)]/6 = 14 /3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2
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Potential Problems WithPotential Problems WithPotential Problems WithPotential Problems WithMoving AverageMoving Average
Increasing n smooths the forecast
g gg g Increasing n smooths the forecast
but makes it less sensitive to changeschanges
Do not forecast trends well Require extensive historical data
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Moving Average AndMoving Average AndMoving Average And Moving Average And Weighted Moving AverageWeighted Moving Average
30 –Weighted moving average
25 –
and
average
20 –
15 –es d
ema Actual
sales
10 –Sale Moving
average
5 –
| | | | | | | | | | | |
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J F M A M J J A S O N DFigure 4.2
Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing
Form of weighted moving average Weights decline exponentially Weights decline exponentially Most recent data weighted most
Requires smoothing constant () Ranges from 0 to 1 Ranges from 0 to 1 Subjectively chosen
Involves little record keeping of past data
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data
Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing
New forecast = Last period’s forecast+ (Last period’s actual demand ( p
– Last period’s forecast)
Ft = Ft – 1 + (At – 1 - Ft – 1)
where Ft = new forecastFt – 1 = previous forecast
= smoothing (or weighting) constant (0 ≤ ≤ 1)
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Exponential SmoothingExponential SmoothingExponential Smoothing Exponential Smoothing ExampleExampleExampleExample
Predicted demand = 142 Ford MustangsPredicted demand 142 Ford MustangsActual demand = 153Smoothing constant = .20Smoothing constant .20
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Exponential SmoothingExponential SmoothingExponential Smoothing Exponential Smoothing ExampleExampleExampleExample
Predicted demand = 142 Ford MustangsPredicted demand 142 Ford MustangsActual demand = 153Smoothing constant = .20Smoothing constant .20
N f t 142 + 2(153 142)New forecast = 142 + .2(153 – 142)
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Exponential SmoothingExponential SmoothingExponential Smoothing Exponential Smoothing ExampleExampleExampleExample
Predicted demand = 142 Ford MustangsPredicted demand 142 Ford MustangsActual demand = 153Smoothing constant = .20Smoothing constant .20
N f t 142 + 2(153 142)New forecast = 142 + .2(153 – 142)= 142 + 2.2= 144.2 ≈ 144 cars
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Effect ofEffect ofEffect ofEffect ofSmoothing ConstantsSmoothing Constantsgg
Weight Assigned toMost 2nd Most 3rd Most 4th Most 5th Most
R t R t R t R t R tRecent Recent Recent Recent RecentSmoothing 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 DifferentImpact of Different Impact of Different Impact of Different
225 –
200 –
nd
Actual demand
= .5
175 –Dem
an
150 | | | | | | | | | = .1
150 – | | | | | | | | |1 2 3 4 5 6 7 8 9
Quarter
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Quarter
Impact of DifferentImpact of Different Impact of Different Impact of Different
225 –
200 –
nd
Actual demand
= .5 Chose high values of when underlying average
175 –Dem
an when underlying average is likely to change
Choose low values of
| | | | | | | | | = .1
Choose low values of when underlying average is stable150 – | | | | | | | | |
1 2 3 4 5 6 7 8 9
Quarter
is stable
4 - 55© 2011 Pearson Education, Inc. publishing as Prentice Hall
Quarter
ChoosingChoosing Choosing Choosing
The objective is to obtain the most accurate forecast no matter theaccurate 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 forecastmodel that gives us the lowest forecastmodel that gives us the lowest forecast model that gives us the lowest forecast errorerror
Forecast error = Actual demand - Forecast value
= At - Ft
4 - 56© 2011 Pearson Education, Inc. publishing as Prentice Hall
At Ft
C M f EC M f ECommon Measures of ErrorCommon Measures of Error
Mean Absolute Deviation (MAD)
MAD =∑ |Actual - Forecast|
MAD n
Mean Squared Error (MSE)
∑ (F t E )2
MSE =∑ (Forecast Errors)2
n
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C M f EC M f ECommon Measures of ErrorCommon Measures of Error
M Ab l t P t E (MAPE)Mean Absolute Percent Error (MAPE)
MAPE∑100|Actuali - Forecasti|/Actuali
n
i = 1MAPE =n
i = 1
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Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = 10 = 10 = 50 = 50Quarter 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 19.565 190 173.36 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 4 308 182 178.22 3.78 186.30 4.30
82.45 98.62
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Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error
∑ |deviations|Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = 10 = 10 = 50 = 50
MAD =∑ |deviations|
nQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 82.45/8 = 10.31
For = .10
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.56
For = .505 190 173.36 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
= 98.62/8 = 12.33
8 182 178.22 3.78 186.30 4.3082.45 98.62
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Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error
∑ (forecast errors)2Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast DeviationTonnage with for with for
Quarter Unloaded = 10 = 10 = 50 = 50
MSE =∑ (forecast errors)
nQuarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 1,526.54/8 = 190.82
For = .10
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.56
,
For = .505 190 173.36 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
= 1,561.91/8 = 195.24
8 182 178.22 3.78 186.30 4.3082.45 98.62
MAD 10.31 12.33
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Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error ∑100|deviationi|/actuali
n
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = 10 = 10 = 50 = 50
MAPE =∑100|deviationi|/actuali
ni = 1
Quarter Unloaded = .10 = .10 = .50 = .50
1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 44.75/8 = 5.59%
For = .10
3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.56
%
For = .505 190 173.36 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
= 54.05/8 = 6.76%
8 182 178.22 3.78 186.30 4.3082.45 98.62
MAD 10.31 12.33
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MSE 190.82 195.24
Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error
Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation
Tonnage with for with forQuarter Unloaded = 10 = 10 = 50 = 50Quarter 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 19.565 190 173.36 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 4 308 182 178.22 3.78 186.30 4.30
82.45 98.62MAD 10.31 12.33
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MSE 190.82 195.24MAPE 5.59% 6.76%
Exponential Smoothing withExponential Smoothing withExponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustmentjj
When a trend is present, exponentialWhen a trend is present, exponential smoothing must be modified
Forecast including (FITt) =
Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)
trend forecast trend
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Exponential Smoothing withExponential Smoothing withExponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustmentjj
Ft = (At - 1) + (1 - )(Ft - 1 + Tt - 1)
Tt = (Ft - Ft - 1) + (1 - )Tt - 1
Step 1: Compute Ft
St 2 C t TStep 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt
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t t t
Exponential Smoothing withExponential Smoothing withExponential 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 13.002 172 173 204 195 245 246 217 318 288 289 36
10
4 - 66© 2011 Pearson Education, Inc. publishing as Prentice Hall
Table 4.1
Exponential Smoothing withExponential Smoothing withExponential 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 13.002 172 173 204 195 24 Step 1: Forecast for Month 25 246 217 318 28
F2 = A1 + (1 - )(F1 + T1)F ( 2)(12) (1 2)(11 2)
Step 1: Forecast for Month 2
8 289 36
10
F2 = (.2)(12) + (1 - .2)(11 + 2)= 2.4 + 10.4 = 12.8 units
4 - 67© 2011 Pearson Education, Inc. publishing as Prentice Hall
Table 4.1
Exponential Smoothing withExponential Smoothing withExponential 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 12.802 17 12.803 204 195 24 Step 2: Trend for Month 25 246 217 318 28
T2 = (F2 - F1) + (1 - )T1
T ( 4)(12 8 11) (1 4)(2)
Step 2: Trend for Month 2
8 289 36
10
T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 units
4 - 68© 2011 Pearson Education, Inc. publishing as Prentice Hall
Table 4.1
Exponential Smoothing withExponential Smoothing withExponential 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 1.922 17 12.80 1.923 204 195 24 Step 3: Calculate FIT for Month 25 246 217 318 28
FIT2 = F2 + T2
FIT 12 8 1 92
Step 3: Calculate FIT for Month 2
8 289 36
10
FIT2 = 12.8 + 1.92= 14.72 units
4 - 69© 2011 Pearson Education, Inc. publishing as Prentice Hall
Table 4.1
Exponential Smoothing withExponential Smoothing withExponential 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 14.722 17 12.80 1.92 14.723 204 195 24
15.18 2.10 17.2817.82 2.32 20.1419 91 2 23 22 145 24
6 217 318 28
19.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827 14 2 45 29 598 28
9 3610
27.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16
4 - 70© 2011 Pearson Education, Inc. publishing as Prentice Hall
Table 4.1
Exponential Smoothing withExponential Smoothing withExponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
35 –Actual demand (A )
man
d
30 –
25 –
Actual demand (At)
duct
dem 20 –
15 –
Prod
10 –
5
Forecast including trend (FITt)with = .2 and = .4
| | | | | | | | |1 2 3 4 5 6 7 8 9
5 –
0 –
4 - 71© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 4.31 2 3 4 5 6 7 8 9
Time (month)
Trend ProjectionsTrend ProjectionsTrend ProjectionsTrend ProjectionsFitting a trend line to historical data pointsFitting 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)
i i t t
^
a = y-axis interceptb = slope of the regression linex = the independent variable
4 - 72© 2011 Pearson Education, Inc. publishing as Prentice Hall
x the independent variable
L t S M th dL t S M th dLeast Squares MethodLeast Squares Methodia
ble
Deviation7Actual observation (y-value)
ent V
ar
Deviation5 Deviation6
(y-value)
Dep
end
Deviation4
Deviation3
ues
of D
Deviation1(error) Deviation2
4
T d li + b^
Valu 2 Trend line, y = a + bx
4 - 73© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time period Figure 4.4
L t S M th dL t S M th dLeast Squares MethodLeast Squares Method
iabl
e
Deviation7Actual observation (y-value)
ent V
ar
Deviation5 Deviation6
(y-value)
Dep
end
Deviation4
Deviation3Least squares method
minimizes the sum of the squared errors (deviations)
ues
of D
Deviation1(error) Deviation2
4
T d li + b^
squared errors (deviations)
Valu 2 Trend line, y = a + bx
4 - 74© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time period Figure 4.4
L t S M th dL t S M th dLeast Squares MethodLeast Squares MethodEquations to calculate the regression variables
y = a + bx^
b =xy - nxy
b =x2 - nx2
a = y - bx
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Least Squares ExampleLeast Squares ExampleLeast Squares ExampleLeast Squares ExampleTime Electrical Power
Y P i d ( ) D d 2Year Period (x) Demand x2 xy
2003 1 74 1 742004 2 79 4 1582004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252007 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
b = = = 10.54∑xy - nxy∑x2 - nx2
3,063 - (7)(4)(98.86)140 - (7)(42)
4 - 76© 2011 Pearson Education, Inc. publishing as Prentice Hall
a = y - bx = 98.86 - 10.54(4) = 56.70
Least Squares ExampleLeast Squares ExampleTime Electrical Power
Y P i d ( ) D d 2
Least Squares ExampleLeast Squares ExampleYear Period (x) Demand x2 xy
2003 1 74 1 742004 2 79 4 1582004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 525
The trend line is
y = 56 70 + 10 54x^2007 5 105 25 5252008 6 142 36 8522009 7 122 49 854
y = 56.70 + 10.54x
∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86
b = = = 10.54∑xy - nxy∑x2 - nx2
3,063 - (7)(4)(98.86)140 - (7)(42)
4 - 77© 2011 Pearson Education, Inc. publishing as Prentice Hall
a = y - bx = 98.86 - 10.54(4) = 56.70
Least Squares ExampleLeast Squares ExampleLeast Squares ExampleLeast Squares ExampleT d li160 –
150 –140
Trend line,y = 56.70 + 10.54x^
140 –130 –120 –em
and
110 –100 –
90 –Pow
er d
e
80 –70 –60
P
| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011
60 –50 –
4 - 78© 2011 Pearson Education, Inc. publishing as Prentice Hall
2003 2004 2005 2006 2007 2008 2009 2010 2011Year
L S R iL S R iLeast Squares RequirementsLeast Squares Requirements
1. We always plot the data to insure a linear relationship
2 We do not predict time periods far2. We do not predict time periods far beyond the database
3. Deviations around the least squares line are assumed to be random
4 - 79© 2011 Pearson Education, Inc. publishing as Prentice Hall
Seasonal Variations In DataSeasonal Variations In DataSeasonal Variations In DataSeasonal Variations In Data
The multiplicative seasonal modelseasonal model can adjust trend data for seasonaldata for seasonal variations in demanddemand
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Seasonal Variations In DataSeasonal Variations In DataSeasonal Variations In DataSeasonal Variations In Data
1 Find average historical demand for each season
Steps in the process:Steps in the process:
1. Find average historical demand for each season 2. Compute the average demand over all seasons
C f3. Compute a seasonal index for each season 4. Estimate next year’s total demand5. Divide this estimate of total demand by the
number of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season
4 - 81© 2011 Pearson Education, Inc. publishing as Prentice Hall
Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleDemand Average Average Seasonal
Jan 80 85 105 90 94F b 70 85 85 80 94
g gMonth 2007 2008 2009 2007-2009 Monthly Index
Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94pMay 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94
4 - 82© 2011 Pearson Education, Inc. publishing as Prentice Hall
Dec 82 78 80 80 94
Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleDemand Average Average Seasonal
Jan 80 85 105 90 94F b 70 85 85 80 94
g gMonth 2007 2008 2009 2007-2009 Monthly Index
0.957Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94Seasonal index =
Average 2007-2009 monthly demandAverage monthly demandp
May 113 125 131 123 94Jun 110 115 120 115 94
Average monthly demand
= 90/94 = .957
Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94
4 - 83© 2011 Pearson Education, Inc. publishing as Prentice Hall
Dec 82 78 80 80 94
Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleDemand Average Average Seasonal
Jan 80 85 105 90 94 0.957F b 70 85 85 80 94 0 851
g gMonth 2007 2008 2009 2007-2009 Monthly Index
Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064pMay 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 0.957Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851
4 - 84© 2011 Pearson Education, Inc. publishing as Prentice Hall
Dec 82 78 80 80 94 0.851
Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleDemand Average Average Seasonal
Jan 80 85 105 90 94 0.957F b 70 85 85 80 94 0 851
g gMonth 2007 2008 2009 2007-2009 Monthly Index
Forecast for 2010Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064Expected annual demand = 1,200
Forecast for 2010
pMay 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223
p
Jan x 957 = 961,200
Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957
Jan x .957 = 9612
Feb x 851 = 851,200
Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851
Feb x .851 = 8512
4 - 85© 2011 Pearson Education, Inc. publishing as Prentice Hall
Dec 82 78 80 80 94 0.851
Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index Example2010 Forecast
140 –
130
2010 Forecast2009 Demand 2008 Demand130 –
120 –
110nd
2008 Demand2007 Demand
110 –
100 –
90
Dem
an
90 –
80 –
70 –| | | | | | | | | | | |J F M A M J J A S O N D
4 - 86© 2011 Pearson Education, Inc. publishing as Prentice Hall
Time
San Diego HospitalSan Diego HospitalSan Diego HospitalSan Diego HospitalTrend Data
10,200 –
Trend Data
10,000 –
9,800 –Day
s
9659 9702 9745,
9,600 –
9 400patie
nt D
9530
9551
9573
9594
9616
9637
96599680
9702
9724 9766
9,400 –
9,200 –
| | | | | | | | | | | |
Inp
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
4 - 87© 2011 Pearson Education, Inc. publishing as Prentice Hall
MonthFigure 4.6
San Diego HospitalSan Diego HospitalSan Diego HospitalSan Diego HospitalSeasonal Indices
1.06 –
s 1 04 1 04
Seasonal Indices
1.04 –
1.02 –
ient
Day
s 1.041.02
1.01
1.031.04
1 001.00 –
0.98 –or
Inpa
ti 0.99 1.00
0.980.99
0.96 –
0.94 –| | | | | | | | | | | |
Inde
x fo
0.97 0.970.96
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
4 - 88© 2011 Pearson Education, Inc. publishing as Prentice Hall
MonthFigure 4.7
San Diego HospitalSan Diego HospitalSan Diego HospitalSan Diego HospitalCombined Trend and Seasonal Forecast
10,200 – 10068
Combined Trend and Seasonal Forecast
10,000 –
9,800 –Day
s 99119764
9691
9949
9724,
9,600 –
9 400patie
nt D
9520
9691
9542
9572
9,400 –
9,200 –
| | | | | | | | | | | |
Inp
9265
95209411
9355
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
4 - 89© 2011 Pearson Education, Inc. publishing as Prentice Hall
MonthFigure 4.8
Associative ForecastingAssociative ForecastingAssociative ForecastingAssociative Forecasting
Used when changes in one or more independent variables can be used to predictindependent variables can be used to predict
the changes in the dependent variable
Most common technique is linear regression analysisg y
We apply this technique just as we didWe apply this technique just as we didWe apply this technique just as we did We apply this technique just as we did in the time series examplein the time series example
4 - 90© 2011 Pearson Education, Inc. publishing as Prentice Hall
Associative ForecastingAssociative ForecastingAssociative ForecastingAssociative ForecastingForecasting an outcome based onForecasting an outcome based on predictor variables using the least squares techniquetechnique
y = a + bx^
where y = computed value of the variable to be predicted (dependent variable)
^
be predicted (dependent variable)a = y-axis interceptb = slope of the regression lineb = slope of the regression linex = the independent variable though to
predict the value of the dependent
4 - 91© 2011 Pearson Education, Inc. publishing as Prentice Hall
p pvariable
Associative ForecastingAssociative ForecastingAssociative Forecasting Associative Forecasting ExampleExample
Sales Area Payroll($ millions), y ($ billions), x
2.0 13.0 32.5 4 4 02.0 22.0 13 5 7
4.0 –
3.0 –
es3.5 72.0 –
1 0
Sal
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
4 - 92© 2011 Pearson Education, Inc. publishing as Prentice Hall
0 1 2 3 4 5 6 7Area payroll
Associative ForecastingAssociative ForecastingAssociative Forecasting Associative Forecasting ExampleExample
Sales, y Payroll, x x2 xy2 0 1 1 2 02.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02 0 2 4 4 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
b 2∑xy - nxy 51.5 - (6)(3)(2.5)
x = ∑x/6 = 18/6 = 3
y = ∑y/6 = 15/6 = 2 5
b = = = .25∑ y y∑x2 - nx2
( )( )( )80 - (6)(32)
a = y - bx = 2 5 - ( 25)(3) = 1 75
4 - 93© 2011 Pearson Education, Inc. publishing as Prentice Hall
y = ∑y/6 = 15/6 = 2.5 a = y - bx = 2.5 - (.25)(3) = 1.75
Associative ForecastingAssociative ForecastingAssociative Forecasting Associative Forecasting ExampleExample
y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)
If payroll next year is estimated to be 4.0 –
$6 billion, then: 3.0 –
2 0
sale
s 3.25
Sales = 1.75 + .25(6)Sales = $3,250,000
2.0 –
1.0 –Nod
el’s
| | | | | | |0 1 2 3 4 5 6 7
Area payroll
4 - 94© 2011 Pearson Education, Inc. publishing as Prentice Hall
p y
Standard Error of theStandard Error of theStandard Error of the Standard Error of the EstimateEstimate
A forecast is just a point estimate of a future valuefuture value
This point is actually the
4.0 –actually the mean of a probability
3.0 –
2 0
sale
s 3.25
probability distribution
2.0 –
1.0 –Nod
el’s
Fi 4 9
| | | | | | |0 1 2 3 4 5 6 7
Area payroll
4 - 95© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 4.9 p y
Standard Error of theStandard Error of theStandard Error of the Standard Error of the EstimateEstimate
∑(y y )2Sy,x =
∑(y - yc)2
n - 2
where y = y-value of each data pointyc = computed value of the dependent
variable, from the regression equationequation
n = number of data points
4 - 96© 2011 Pearson Education, Inc. publishing as Prentice Hall
Standard Error of theStandard Error of theStandard Error of the Standard Error of the EstimateEstimate
Computationally, this equation is considerably easier to useconsiderably easier to use
∑y2 a∑y b∑xySy,x =
∑y2 - a∑y - b∑xyn - 2
We use the standard error to set up di i i l d hprediction intervals around the
point estimate
4 - 97© 2011 Pearson Education, Inc. publishing as Prentice Hall
Standard Error of theStandard Error of theStandard Error of the Standard Error of the EstimateEstimate
Sy,x = =∑y2 - a∑y - b∑xyn - 2
39.5 - 1.75(15) - .25(51.5)6 - 2
4.0 –Sy x = .306
3.0 –
sale
s 3.25y,x
The standard error2.0 –
1.0 –Nod
el’s
sThe standard error of the estimate is $306,000 in sales
| | | | | | |0 1 2 3 4 5 6 7
N
A ll
4 - 98© 2011 Pearson Education, Inc. publishing as Prentice Hall
Area payroll
CorrelationCorrelationCorrelationCorrelation
How strong is the linear relationship between the variables?p
Correlation does not necessarily imply causality!imply causality!
Coefficient of correlation, r, , ,measures degree of association Values range from -1 to +1 Values range from -1 to +1
4 - 99© 2011 Pearson Education, Inc. publishing as Prentice Hall
Correlation CoefficientCorrelation CoefficientCorrelation CoefficientCorrelation Coefficient
r = nxy - xy
[ 2 ( )2][ 2 ( )2][nx2 - (x)2][ny2 - (y)2]
4 - 100© 2011 Pearson Education, Inc. publishing as Prentice Hall
Correlation CoefficientCorrelation Coefficienty yCorrelation CoefficientCorrelation Coefficienty y
r = nxy - xy
[ 2 ( )2][ 2 ( )2][nx2 - (x)2][ny2 - (y)2]x(a) Perfect positive correlation: r = +1
x(b) Positive correlation: 0 < r < 10 r 1
y y
x( ) N l ti x(d) Perfect negative
4 - 101© 2011 Pearson Education, Inc. publishing as Prentice Hall
x(c) No correlation: r = 0
x(d) Perfect negative correlation: r = -1
CorrelationCorrelation C ffi i t f D t i ti 2
CorrelationCorrelation Coefficient of Determination, r2,
measures the percent of change in y predicted by the change in x Values range from 0 to 1 Values range from 0 to 1 Easy to interpret
For the Nodel Construction example:r = .901r2 = 81
4 - 102© 2011 Pearson Education, Inc. publishing as Prentice Hall
r2 = .81
M lti l R iM lti l R iMultiple Regression Multiple Regression AnalysisAnalysisAnalysisAnalysis
If more than one independent variable is to be used in the model, linear regression can be
extended to multiple regression to d t l i d d t i blaccommodate several independent variables
y = a + b x + b xy = a + b1x1 + b2x2 …
Computationally this is quiteComputationally this is quiteComputationally, this is quite Computationally, this is quite complex and generally done on the complex and generally done on the
computercomputer4 - 103© 2011 Pearson Education, Inc. publishing as Prentice Hall
computercomputer
M lti l R iM lti l R iMultiple Regression Multiple Regression AnalysisAnalysisAnalysisAnalysis
In the Nodel example, including interest rates in th d l i th ti
y = 1 80 + 30x 5 0x^
the model gives the new equation:
y = 1.80 + .30x1 - 5.0x2
An improved correlation coefficient of r = 96An 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
4 - 104© 2011 Pearson Education, Inc. publishing as Prentice Hall
Sales = $3,000,000
Monitoring and ControllingMonitoring and ControllingMonitoring and Controlling Monitoring and Controlling ForecastsForecastsForecastsForecasts
Tracking SignalTracking Signal
Measures how well the forecast is di ti t l l
g gg g
predicting actual values Ratio of cumulative forecast errors to
mean absolute deviation (MAD) Good tracking signal has low valuesg g If forecasts are continually high or low, the
forecast has a bias error
4 - 105© 2011 Pearson Education, Inc. publishing as Prentice Hall
Monitoring and ControllingMonitoring and ControllingMonitoring and Controlling Monitoring and Controlling ForecastsForecastsForecastsForecasts
Tracking signal
Cumulative errorMAD=
∑(Actual demand in i d i
T ki
period i -Forecast demand
in period i)Tracking signal =
in period i)∑|Actual - Forecast|/n)
4 - 106© 2011 Pearson Education, Inc. publishing as Prentice Hall
Tracking SignalTracking SignalTracking SignalTracking Signal
Tracking signal
Signal exceeding limit
Tracking signal
+Upper control limit
0 MADs Acceptable range
–Lower control limito e co t o t
Time
4 - 107© 2011 Pearson Education, Inc. publishing as Prentice Hall
Tracking Signal ExampleTracking Signal ExampleTracking Signal ExampleTracking Signal ExampleCumulative
Absolute AbsoluteActual Forecast Cumm Forecast Forecast
Qtr 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 05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
4 - 108© 2011 Pearson Education, Inc. publishing as Prentice Hall
Tracking Signal ExampleTracking Signal ExampleTracking Signal ExampleTracking Signal ExampleCumulative
Absolute AbsoluteActual Forecast Cumm Forecast Forecast
Qtr Demand Demand Error Error Error Error MAD
TrackingSignal
(Cumm Error/MAD)
1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.5
( )
-10/10 = -1-15/7.5 = -2
3 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11 0
0/10 = 0-10/10 = -1
+5/11 +0 55 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
+5/11 = +0.5+35/14.2 = +2.5
The variation of the tracking signal between -2.0 and +2.5 is within acceptable
4 - 109© 2011 Pearson Education, Inc. publishing as Prentice Hall
plimits
Adaptive ForecastingAdaptive ForecastingAdaptive ForecastingAdaptive Forecasting
It’s possible to use the computer to continually monitor forecast errorcontinually monitor forecast error and adjust the values of the and coefficients used in exponentialcoefficients used in exponential smoothing to continually minimize forecast errorforecast error
This technique is called adaptive smoothing
4 - 110© 2011 Pearson Education, Inc. publishing as Prentice Hall
Focus ForecastingFocus ForecastingFocus ForecastingFocus Forecasting Developed at American Hardware Supply, p pp y,
based on two principles:1. Sophisticated forecasting models are not1. Sophisticated forecasting models are not
always better than simple ones2. There is no single technique that should g q
be used for all products or services This approach uses historical data to test pp
multiple forecasting models for individual items
The forecasting model with the lowest error is then used to forecast the next
4 - 111© 2011 Pearson Education, Inc. publishing as Prentice Hall
demand
Forecasting in the ServiceForecasting in the ServiceForecasting in the Service Forecasting in the Service SectorSector
Presents unusual challengesg Special need for short term records N d diff tl f ti f Needs differ greatly as function of
industry and product Holidays and other calendar events Unusual events Unusual events
4 - 112© 2011 Pearson Education, Inc. publishing as Prentice Hall
Fast Food Restaurant Fast Food Restaurant ForecastForecast
20%20% –
15%
sale
s
15% –
10%ntag
e of
10% –
5%
Perc
en
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)
4 - 113© 2011 Pearson Education, Inc. publishing as Prentice Hall
(Lunchtime) (Dinnertime)Hour of day Figure 4.12
FedEx Call Center ForecastFedEx Call Center ForecastFedEx Call Center ForecastFedEx Call Center Forecast
12% –
10% –10%
8% –
6% –
4% –
2% –
0% –
Hour of dayA.M. P.M.
2 4 6 8 10 12 2 4 6 8 10 12
4 - 114© 2011 Pearson Education, Inc. publishing as Prentice Hall
Figure 4.12Hour of day
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.
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