© 2006 Prentice Hall, Inc. 4 – 1
Operations ManagementOperations ManagementChapter 4 - ForecastingChapter 4 - Forecasting
© 2006 Prentice Hall, Inc.
PowerPoint presentation to accompanyPowerPoint presentation to accompany Heizer/Render Heizer/Render Principles of Operations Management, 6ePrinciples of Operations Management, 6eOperations Management, 8e Operations Management, 8e
© 2006 Prentice Hall, Inc. 4 – 2
What is Forecasting?What is Forecasting?
Process of Process of predicting a future predicting a future eventevent
Underlying basis of Underlying basis of all business all business decisionsdecisions ProductionProduction
InventoryInventory
PersonnelPersonnel
FacilitiesFacilities
??
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Short-range forecastShort-range forecast Up to 1 year, generally less than 3 monthsUp to 1 year, generally less than 3 months Purchasing, job scheduling, workforce Purchasing, job scheduling, workforce
levels, job assignments, production levelslevels, job assignments, production levels
Medium-range forecastMedium-range forecast 3 months to 3 years3 months to 3 years Sales and production planning, budgetingSales and production planning, budgeting
Long-range forecastLong-range forecast 33++ years years New product planning, facility location, New product planning, facility location,
research and developmentresearch and development
Forecasting Time HorizonsForecasting Time Horizons
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Influence of Product Life Influence of Product Life CycleCycle
Introduction and growth require longer Introduction and growth require longer forecasts than maturity and declineforecasts than maturity and decline
As product passes through life cycle, As product passes through life cycle, forecasts are useful in projectingforecasts are useful in projecting Staffing levelsStaffing levels
Inventory levelsInventory levels
Factory capacityFactory capacity
Introduction – Growth – Maturity – Decline
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Product Life CycleProduct Life Cycle
Best period to Best period to increase market increase market shareshare
R&D engineering is R&D engineering is criticalcritical
Practical to change Practical to change price or quality price or quality imageimage
Strengthen nicheStrengthen niche
Poor time to Poor time to change image, change image, price, or qualityprice, or quality
Competitive costs Competitive costs become criticalbecome criticalDefend market Defend market positionposition
Cost control Cost control criticalcritical
Introduction Growth Maturity Decline
Co
mp
an
y S
tra
teg
y/Is
sue
sC
om
pa
ny
Str
ate
gy/
Issu
es
InternetInternet
Flat-screen Flat-screen monitorsmonitors
SalesSales
DVDDVD
CD-ROMCD-ROM
Drive-through Drive-through restaurantsrestaurants
Fax machinesFax machines
3 1/2” 3 1/2” Floppy Floppy disksdisks
Color printersColor printers
Figure 2.5Figure 2.5
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Product Life CycleProduct Life Cycle
Product design Product design and and development development criticalcritical
Frequent Frequent product and product and process design process design changeschanges
Short production Short production runsruns
High production High production costscosts
Limited modelsLimited models
Attention to Attention to qualityquality
Introduction Growth Maturity Decline
OM
Str
ate
gy
/Issu
es
OM
Str
ate
gy
/Issu
es
Forecasting Forecasting criticalcritical
Product and Product and process process reliabilityreliability
Competitive Competitive product product improvements improvements and optionsand options
Increase capacityIncrease capacity
Shift toward Shift toward product focusproduct focus
Enhance Enhance distributiondistribution
StandardizationStandardization
Less rapid Less rapid product changes product changes – more minor – more minor changeschanges
Optimum Optimum capacitycapacity
Increasing Increasing stability of stability of processprocess
Long production Long production runsruns
Product Product improvement and improvement and cost cuttingcost cutting
Little product Little product differentiationdifferentiation
Cost Cost minimizationminimization
Overcapacity Overcapacity in the in the industryindustry
Prune line to Prune line to eliminate eliminate items not items not returning returning good margingood margin
Reduce Reduce capacitycapacity
Figure 2.5Figure 2.5
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Types of ForecastsTypes of Forecasts
Economic forecastsEconomic forecasts Address business cycle – inflation rate, Address business cycle – inflation rate,
money supply, housing starts, etc.money supply, housing starts, etc.
Technological forecastsTechnological forecasts Predict rate of technological progressPredict rate of technological progress
Impacts development of new productsImpacts development of new products
Demand forecastsDemand forecasts Predict sales of existing productPredict sales of existing product
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The Realities!The Realities!
Forecasts are seldom perfectForecasts are seldom perfect
Most techniques assume an Most techniques assume an underlying stability in the systemunderlying stability in the system
Product family and aggregated Product family and aggregated forecasts are more accurate than forecasts are more accurate than individual product forecastsindividual product forecasts
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Forecasting ApproachesForecasting Approaches
Used when situation is vague Used when situation is vague and little data existand little data exist New productsNew products
New technologyNew technology
Involves intuition, experienceInvolves intuition, experience e.g., forecasting sales on Internete.g., forecasting sales on Internet
Qualitative MethodsQualitative Methods
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Forecasting ApproachesForecasting Approaches
Used when situation is ‘stable’ and Used when situation is ‘stable’ and historical data existhistorical data exist Existing productsExisting products
Current technologyCurrent technology
Involves mathematical techniquesInvolves mathematical techniques e.g., forecasting sales of color e.g., forecasting sales of color
televisionstelevisions
Quantitative MethodsQuantitative Methods
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Overview of Qualitative Overview of Qualitative MethodsMethods
Jury of executive opinionJury of executive opinion Pool opinions of high-level Pool opinions of high-level
executives, sometimes augment by executives, sometimes augment by statistical modelsstatistical models
Delphi methodDelphi method Panel of experts, queried iterativelyPanel of experts, queried iteratively
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Overview of Qualitative Overview of Qualitative MethodsMethods
Sales force compositeSales force composite Estimates from individual Estimates from individual
salespersons are reviewed for salespersons are reviewed for reasonableness, then aggregated reasonableness, then aggregated
Consumer Market SurveyConsumer Market Survey Ask the customerAsk the customer
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Overview of Quantitative Overview of Quantitative ApproachesApproaches
1.1. Naive approachNaive approach
2.2. Moving averagesMoving averages
3.3. Exponential Exponential smoothingsmoothing
4.4. Trend projectionTrend projection
5.5. Linear regressionLinear regression
Time-Series Time-Series ModelsModels
Associative Associative ModelModel
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Set of evenly spaced numerical Set of evenly spaced numerical datadata Obtained by observing response Obtained by observing response
variable at regular time periodsvariable at regular time periods
Forecast based only on past Forecast based only on past valuesvalues Assumes that factors influencing Assumes that factors influencing
past and present will continue past and present will continue influence in futureinfluence in future
Time Series ForecastingTime Series Forecasting
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Trend
Seasonal
Cyclical
Random
Time Series ComponentsTime Series Components
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Naive ApproachNaive Approach
Assumes demand in next period is Assumes demand in next period is the same as demand in most the same as demand in most recent periodrecent period e.g., If May sales were 48, then June e.g., If May sales were 48, then June
sales will be 48sales will be 48
Sometimes cost effective and Sometimes cost effective and efficientefficient
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MA is a series of arithmetic means MA is a series of arithmetic means
Used if little or no trendUsed if little or no trend
Used often for smoothingUsed often for smoothingProvides overall impression of data Provides overall impression of data
over timeover time
Moving Average MethodMoving Average Method
Moving average =Moving average =∑∑ demand in previous n periodsdemand in previous n periods
nn
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JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626
ActualActual 3-Month3-MonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average
(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33
(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33
Moving Average ExampleMoving Average Example
101012121313
((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33
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Used when trend is present Used when trend is present Older data usually less importantOlder data usually less important
Weights based on experience and Weights based on experience and intuitionintuition
Weighted Moving AverageWeighted Moving Average
WeightedWeightedmoving averagemoving average ==
∑∑ ((weight for period nweight for period n)) x x ((demand in period ndemand in period n))
∑∑ weightsweights
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JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626
ActualActual 3-Month Weighted3-Month WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average
[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33
[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22
Weighted Moving AverageWeighted Moving Average
101012121313
[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66
Weights Applied Period
3 Last month2 Two months ago1 Three months ago6 Sum of weights
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Increasing n smooths the forecast Increasing n smooths the forecast but makes it less sensitive to but makes it less sensitive to changeschanges
Do not forecast trends wellDo not forecast trends well
Require extensive historical dataRequire extensive historical data
Potential Problems WithPotential Problems With Moving Average Moving Average
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Form of weighted moving averageForm of weighted moving average Weights decline exponentiallyWeights decline exponentially
Most recent data weighted mostMost recent data weighted most
Requires smoothing constant Requires smoothing constant (()) Ranges from 0 to 1Ranges from 0 to 1
Subjectively chosenSubjectively chosen
Involves little record keeping of past Involves little record keeping of past datadata
Exponential SmoothingExponential Smoothing
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Exponential SmoothingExponential Smoothing
New forecast =New forecast = last period’s forecastlast period’s forecast+ + ((last period’s actual demand last period’s actual demand
– – last period’s forecastlast period’s forecast))
FFtt = F = Ft t – 1– 1 + + ((AAt t – 1– 1 - - F Ft t – 1– 1))
wherewhere FFtt == new forecastnew forecast
FFt t – 1– 1 == previous forecastprevious forecast
== smoothing (or weighting) smoothing (or weighting) constant constant (0 (0 1) 1)
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Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand Predicted demand = 142= 142 Ford Mustangs Ford MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20 = .20
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Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand Predicted demand = 142= 142 Ford Mustangs Ford MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20 = .20
New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)
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Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand Predicted demand = 142= 142 Ford Mustangs Ford MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20 = .20
New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)
= 142 + 2.2= 142 + 2.2
= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars
© 2006 Prentice Hall, Inc. 4 – 27
Choosing Choosing
The objective is to obtain the most The objective is to obtain the most accurate forecast no matter the accurate forecast no matter the techniquetechnique
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 errorForecast error = Actual demand - Forecast value= Actual demand - Forecast value
= A= Att - F - Ftt
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Common Measure of ErrorCommon Measure of Error
Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))
MAD =MAD =∑∑ |actual - forecast||actual - forecast|
nn
© 2006 Prentice Hall, Inc. 4 – 29
Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment
When a trend is present, exponential When a trend is present, exponential smoothing must be modifiedsmoothing must be modified
Forecast Forecast including including ((FITFITtt)) = = trendtrend
exponentiallyexponentially exponentiallyexponentiallysmoothed smoothed ((FFtt)) + + ((TTtt)) smoothedsmoothedforecastforecast trendtrend
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Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment
FFtt = = ((AAtt - 1 - 1) + (1 - ) + (1 - )()(FFtt - 1 - 1 + + TTtt - 1 - 1))
TTtt = = ((FFtt - - FFtt - 1 - 1) + (1 - ) + (1 - ))TTtt - 1 - 1
Step 1: Compute FStep 1: Compute Ftt
Step 2: Compute TStep 2: Compute Ttt
Step 3: Calculate the forecast FITStep 3: Calculate the forecast FITtt == F Ftt + + TTtt
© 2006 Prentice Hall, Inc. 4 – 31
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636
1010
Table 4.1Table 4.1
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636
1010
Table 4.1Table 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
© 2006 Prentice Hall, Inc. 4 – 33
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 1717 12.8012.8033 202044 191955 242466 212177 313188 282899 3636
1010
Table 4.1Table 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
© 2006 Prentice Hall, Inc. 4 – 34
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.9233 202044 191955 242466 212177 313188 282899 3636
1010
Table 4.1Table 4.1
FIT2 = F2 + T1
FIT2 = 12.8 + 1.92
= 14.72 units
Step 3: Calculate FIT for Month 2
© 2006 Prentice Hall, Inc. 4 – 35
Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding
MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt
11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.92 14.7214.7233 202044 191955 242466 212177 313188 282899 3636
1010
Table 4.1Table 4.1
15.1815.18 2.102.10 17.2817.2817.8217.82 2.322.32 20.1420.1419.9119.91 2.232.23 22.1422.1422.5122.51 2.382.38 24.8924.8924.1124.11 2.072.07 26.1826.1827.1427.14 2.452.45 29.5929.5929.2829.28 2.322.32 31.6031.6032.4832.48 2.682.68 35.1635.16
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Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example
Figure 4.3Figure 4.3
| | | | | | | | |
11 22 33 44 55 66 77 88 99
Time (month)Time (month)
Pro
du
ct d
eman
dP
rod
uct
dem
and
35 35 –
30 30 –
25 25 –
20 20 –
15 15 –
10 10 –
5 5 –
0 0 –
Actual demand Actual demand ((AAtt))
Forecast including trend Forecast including trend ((FITFITtt))
© 2006 Prentice Hall, Inc. 4 – 37
Trend ProjectionsTrend Projections
Fitting a trend line to historical data points Fitting a trend line to historical data points to project into the medium-to-long-rangeto project into the medium-to-long-range
Linear trends can be found using the least Linear trends can be found using the least squares techniquesquares technique
y y = = a a + + bxbx^̂
where ywhere y= computed value of the = computed value of the variable to be predicted (dependent variable to be predicted (dependent variable)variable)aa= y-axis intercept= y-axis interceptbb= slope of the regression line= slope of the regression linexx= the independent variable= the independent variable
^̂
© 2006 Prentice Hall, Inc. 4 – 38
Least Squares MethodLeast Squares Method
Time periodTime period
Va
lue
s o
f D
ep
end
en
t V
ari
able
Figure 4.4Figure 4.4
DeviationDeviation11
DeviationDeviation55
DeviationDeviation77
DeviationDeviation22
DeviationDeviation66
DeviationDeviation44
DeviationDeviation33
Actual observation Actual observation (y value)(y value)
Trend line, y = a + bxTrend line, y = a + bx^̂
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Least Squares MethodLeast Squares Method
Time periodTime period
Va
lue
s o
f D
ep
end
en
t V
ari
able
Figure 4.4Figure 4.4
DeviationDeviation11
DeviationDeviation55
DeviationDeviation77
DeviationDeviation22
DeviationDeviation66
DeviationDeviation44
DeviationDeviation33
Actual observation Actual observation (y value)(y value)
Trend line, y = a + bxTrend line, y = a + bx^̂
Least squares method minimizes the sum of the
squared errors (deviations)
© 2006 Prentice Hall, Inc. 4 – 40
Least Squares MethodLeast Squares Method
Equations to calculate the regression variablesEquations to calculate the regression variables
b =b =xy - nxyxy - nxy
xx22 - nx - nx22
y y = = a a + + bxbx^̂
a = y - bxa = y - bx
© 2006 Prentice Hall, Inc. 4 – 41
Least Squares ExampleLeast Squares Example
b b = = = 10.54= = = 10.54∑∑xy - nxyxy - nxy
∑∑xx22 - nx - nx22
3,063 - (7)(4)(98.86)3,063 - (7)(4)(98.86)
140 - (7)(4140 - (7)(422))
aa = = yy - - bxbx = 98.86 - 10.54(4) = 56.70 = 98.86 - 10.54(4) = 56.70
TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy
19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854
∑∑xx = 28 = 28 ∑∑yy = 692 = 692 ∑∑xx22 = 140 = 140 ∑∑xyxy = 3,063 = 3,063xx = 4 = 4 yy = 98.86 = 98.86
© 2006 Prentice Hall, Inc. 4 – 42
Least Squares ExampleLeast Squares Example
b b = = = 10.54= = = 10.54xy - nxyxy - nxy
xx22 - nx - nx22
3,063 - (7)(4)(98.86)3,063 - (7)(4)(98.86)
140 - (7)(4140 - (7)(422))
aa = = yy - - bxbx = 98.86 - 10.54(4) = 56.70 = 98.86 - 10.54(4) = 56.70
TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy
19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854
xx = 28 = 28 yy = 692 = 692 xx22 = 140 = 140 xyxy = 3,063 = 3,063xx = 4 = 4 yy = 98.86 = 98.86
The trend line is
y = 56.70 + 10.54x^
© 2006 Prentice Hall, Inc. 4 – 43
Least Squares ExampleLeast Squares Example
| | | | | | | | |19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007
160 160 –
150 150 –
140 140 –
130 130 –
120 120 –
110 110 –
100 100 –
90 90 –
80 80 –
70 70 –
60 60 –
50 50 –
YearYear
Po
wer
dem
and
Po
wer
dem
and
Trend line,Trend line,y y = 56.70 + 10.54x= 56.70 + 10.54x^̂
© 2006 Prentice Hall, Inc. 4 – 45
Seasonal Variations In DataSeasonal Variations In Data
The multiplicative seasonal model can The multiplicative seasonal model can modify trend data to accommodate modify trend data to accommodate seasonal variations in demandseasonal variations in demand
1.1. Find average historical demand for each season Find average historical demand for each season
2.2. Compute the average demand over all seasons Compute the average demand over all seasons
3.3. Compute a seasonal index for each season Compute a seasonal index for each season
4.4. Estimate next year’s total demandEstimate next year’s total demand
5.5. Divide this estimate of total demand by the Divide this estimate of total demand by the number of seasons, then multiply it by the number of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season
© 2006 Prentice Hall, Inc. 4 – 46
Seasonal Index ExampleSeasonal Index Example
JanJan 8080 8585 105105 9090 9494
FebFeb 7070 8585 8585 8080 9494
MarMar 8080 9393 8282 8585 9494
AprApr 9090 9595 115115 100100 9494
MayMay 113113 125125 131131 123123 9494
JunJun 110110 115115 120120 115115 9494
JulJul 100100 102102 113113 105105 9494
AugAug 8888 102102 110110 100100 9494
SeptSept 8585 9090 9595 9090 9494
OctOct 7777 7878 8585 8080 9494
NovNov 7575 7272 8383 8080 9494
DecDec 8282 7878 8080 8080 9494
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex
© 2006 Prentice Hall, Inc. 4 – 47
Seasonal Index ExampleSeasonal Index Example
JanJan 8080 8585 105105 9090 9494
FebFeb 7070 8585 8585 8080 9494
MarMar 8080 9393 8282 8585 9494
AprApr 9090 9595 115115 100100 9494
MayMay 113113 125125 131131 123123 9494
JunJun 110110 115115 120120 115115 9494
JulJul 100100 102102 113113 105105 9494
AugAug 8888 102102 110110 100100 9494
SeptSept 8585 9090 9595 9090 9494
OctOct 7777 7878 8585 8080 9494
NovNov 7575 7272 8383 8080 9494
DecDec 8282 7878 8080 8080 9494
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex
0.9570.957
Seasonal index = average 2003-2005 monthly demand
average monthly demand
= 90/94 = .957
© 2006 Prentice Hall, Inc. 4 – 48
Seasonal Index ExampleSeasonal Index Example
JanJan 8080 8585 105105 9090 9494 0.9570.957
FebFeb 7070 8585 8585 8080 9494 0.8510.851
MarMar 8080 9393 8282 8585 9494 0.9040.904
AprApr 9090 9595 115115 100100 9494 1.0641.064
MayMay 113113 125125 131131 123123 9494 1.3091.309
JunJun 110110 115115 120120 115115 9494 1.2231.223
JulJul 100100 102102 113113 105105 9494 1.1171.117
AugAug 8888 102102 110110 100100 9494 1.0641.064
SeptSept 8585 9090 9595 9090 9494 0.9570.957
OctOct 7777 7878 8585 8080 9494 0.8510.851
NovNov 7575 7272 8383 8080 9494 0.8510.851
DecDec 8282 7878 8080 8080 9494 0.8510.851
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex
© 2006 Prentice Hall, Inc. 4 – 49
Seasonal Index ExampleSeasonal Index Example
JanJan 8080 8585 105105 9090 9494 0.9570.957
FebFeb 7070 8585 8585 8080 9494 0.8510.851
MarMar 8080 9393 8282 8585 9494 0.9040.904
AprApr 9090 9595 115115 100100 9494 1.0641.064
MayMay 113113 125125 131131 123123 9494 1.3091.309
JunJun 110110 115115 120120 115115 9494 1.2231.223
JulJul 100100 102102 113113 105105 9494 1.1171.117
AugAug 8888 102102 110110 100100 9494 1.0641.064
SeptSept 8585 9090 9595 9090 9494 0.9570.957
OctOct 7777 7878 8585 8080 9494 0.8510.851
NovNov 7575 7272 8383 8080 9494 0.8510.851
DecDec 8282 7878 8080 8080 9494 0.8510.851
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex
Expected annual demand = 1,200
Jan x .957 = 961,200
12
Feb x .851 = 851,200
12
Forecast for 2006