Download to read offline
![© 2006 Prentice Hall, Inc. 4 – 45
JanuaryJanuary 1010
FebruaryFebruary 1212
MarchMarch 1313
AprilApril 1616
MayMay 1919
JuneJune 2323
JulyJuly 2626
ActualActual 3-Month Weighted3-Month Weighted
MonthMonth 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
1010
1212
1313
[(3 x[(3 x 1313) + (2 x) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211
//66
Weights Applied Period
3 Last month
2 Two months ago
1 Three months ago
6 Sum of weights](https://image.slidesharecdn.com/ch04-151103102650-lva1-app6892/75/SP-45-2048.jpg)
![© 2006 Prentice Hall, Inc. 4 – 98
Correlation CoefficientCorrelation Coefficient
r =r =
nnΣΣxyxy -- ΣΣxxΣΣyy
[[nnΣΣxx22
- (- (ΣΣxx))22
][][nnΣΣyy22
- (- (ΣΣyy))22
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![© 2006 Prentice Hall, Inc. 4 – 99
Correlation CoefficientCorrelation Coefficient
r =r =
nn∑∑xyxy -- ∑∑xx∑∑yy
[[nn∑∑xx22
- (- (∑∑xx))22
][][nn∑∑yy22
- (- (∑∑yy))22
]]
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](https://image.slidesharecdn.com/ch04-151103102650-lva1-app6892/75/SP-98-2048.jpg)
Uploaded byJosé Luis Rivera Alpaca
SP
The document outlines a chapter on forecasting that discusses key topics like forecasting time horizons, the influence of product life cycles, and types of forecasts. It provides an example of how Tupperware uses forecasting across its global profit centers and aggregates forecasts. The chapter objectives are to define forecasting terms, describe quantitative and qualitative forecasting methods, and explain techniques like moving averages and regression analysis.
SP
- 1. © 2006 PrenticeHall, Inc. 4 – 1 Operations Management Chapter 4 - Forecasting © 2006 Prentice Hall, Inc. PowerPoint presentation to accompanyPowerPoint presentation to accompany Heizer/RenderHeizer/Render Principles of Operations Management, 6ePrinciples of Operations Management, 6e Operations Management, 8eOperations Management, 8e
- 2. © 2006 PrenticeHall, Inc. 4 – 2 OutlineOutline Global Company Profile:Global Company Profile: Tupperware CorporationTupperware Corporation What Is Forecasting?What Is Forecasting? Forecasting Time HorizonsForecasting Time Horizons The Influence of Product Life CycleThe Influence of Product Life Cycle Types Of ForecastsTypes Of Forecasts
- 3. © 2006 PrenticeHall, Inc. 4 – 3 Outline – ContinuedOutline – Continued The Strategic Importance OfThe Strategic Importance Of ForecastingForecasting Human ResourcesHuman Resources CapacityCapacity Supply-Chain ManagementSupply-Chain Management Seven Steps In The ForecastingSeven Steps In The Forecasting SystemSystem
- 4. © 2006 PrenticeHall, Inc. 4 – 4 Outline – ContinuedOutline – Continued Forecasting ApproachesForecasting Approaches Overview of Qualitative MethodsOverview of Qualitative Methods Overview of Quantitative MethodsOverview of Quantitative Methods
- 5. © 2006 PrenticeHall, Inc. 4 – 5 Outline – ContinuedOutline – Continued Time-series ForecastingTime-series Forecasting Decomposition of a Time SeriesDecomposition of a Time Series Naïve ApproachNaïve Approach Moving AveragesMoving Averages Exponential SmoothingExponential Smoothing Exponential Smoothing with TrendExponential Smoothing with Trend AdjustmentAdjustment Trend ProjectionsTrend Projections Seasonal Variations in DataSeasonal Variations in Data Cyclical Variations in DataCyclical Variations in Data
- 6. © 2006 PrenticeHall, Inc. 4 – 6 Outline – ContinuedOutline – Continued Associative Forecasting Methods:Associative Forecasting Methods: Regression And CorrelationRegression And Correlation AnalysisAnalysis Using Regression Analysis toUsing Regression Analysis to ForecastForecast Standard Error of the EstimateStandard Error of the Estimate Correlation Coefficients forCorrelation Coefficients for Regression LinesRegression Lines Multiple-Regression AnalysisMultiple-Regression Analysis
- 7. © 2006 PrenticeHall, Inc. 4 – 7 Outline – ContinuedOutline – Continued Monitoring And ControllingMonitoring And Controlling ForecastsForecasts Adaptive SmoothingAdaptive Smoothing Focus ForecastingFocus Forecasting Forecasting In The Service SectorForecasting In The Service Sector
- 8. © 2006 PrenticeHall, Inc. 4 – 8 Learning ObjectivesLearning Objectives When you complete this chapter, youWhen you complete this chapter, you should be able to :should be able to : Identify or Define:Identify or Define: ForecastingForecasting Types of forecastsTypes of forecasts Time horizonsTime horizons Approaches to forecastsApproaches to forecasts
- 9. © 2006 PrenticeHall, Inc. 4 – 9 Learning ObjectivesLearning Objectives When you complete this chapter, youWhen you complete this chapter, you should be able to :should be able to : Describe or Explain:Describe or Explain: Moving averagesMoving averages Exponential smoothingExponential smoothing Trend projectionsTrend projections Regression and correlation analysisRegression and correlation analysis Measures of forecast accuracyMeasures of forecast accuracy
- 10. © 2006 PrenticeHall, Inc. 4 – 10 Forecasting at TupperwareForecasting at Tupperware Each of 50 profit centers around theEach of 50 profit centers around the world is responsible forworld is responsible for computerized monthly, quarterly,computerized monthly, quarterly, and 12-month sales projectionsand 12-month sales projections These projections are aggregated byThese projections are aggregated by region, then globally, atregion, then globally, at Tupperware’s World HeadquartersTupperware’s World Headquarters Tupperware uses all techniquesTupperware uses all techniques discussed in textdiscussed in text
- 11. © 2006 PrenticeHall, Inc. 4 – 11 Tupperware’sTupperware’s ProcessProcess
- 12. © 2006 PrenticeHall, Inc. 4 – 12 Three Key Factors forThree Key Factors for TupperwareTupperware The number of registeredThe number of registered “consultants” or sales“consultants” or sales representativesrepresentatives The percentage of currently “active”The percentage of currently “active” dealers (this number changes eachdealers (this number changes each week and month)week and month) Sales per active dealer, on a weeklySales per active dealer, on a weekly basisbasis
- 13. © 2006 PrenticeHall, Inc. 4 – 13 Forecast by ConsensusForecast by Consensus Although inputs come from sales,Although inputs come from sales, marketing, finance, and production,marketing, finance, and production, final forecasts are the consensus offinal forecasts are the consensus of all participating managersall participating managers The final step is Tupperware’sThe final step is Tupperware’s version of the “jury of executiveversion of the “jury of executive opinion”opinion”
- 14. © 2006 PrenticeHall, Inc. 4 – 14 What is Forecasting?What is Forecasting? Process ofProcess of predicting a futurepredicting a future eventevent Underlying basis ofUnderlying basis of all businessall business decisionsdecisions ProductionProduction InventoryInventory PersonnelPersonnel FacilitiesFacilities ??
- 15. © 2006 PrenticeHall, Inc. 4 – 15 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, workforcePurchasing, 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++ yearsyears New product planning, facility location,New product planning, facility location, research and developmentresearch and development Forecasting Time HorizonsForecasting Time Horizons
- 16. © 2006 PrenticeHall, Inc. 4 – 16 Distinguishing DifferencesDistinguishing Differences Medium/long rangeMedium/long range forecasts deal withforecasts deal with more comprehensive issues and supportmore comprehensive issues and support management decisions regardingmanagement decisions regarding planning and products, plants andplanning and products, plants and processesprocesses Short-termShort-term forecasting usually employsforecasting usually employs different methodologies than longer-termdifferent methodologies than longer-term forecastingforecasting Short-termShort-term forecasts tend to be moreforecasts tend to be more accurate than longer-term forecastsaccurate than longer-term forecasts
- 17. © 2006 PrenticeHall, Inc. 4 – 17 Influence of Product LifeInfluence of Product Life CycleCycle Introduction and growth require longerIntroduction 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
- 18. © 2006 PrenticeHall, Inc. 4 – 18 Product Life CycleProduct Life Cycle Best period toBest period to increase marketincrease market shareshare R&D engineering isR&D engineering is criticalcritical Practical to changePractical to change price or qualityprice or quality imageimage Strengthen nicheStrengthen niche Poor time toPoor time to change image,change image, price, or qualityprice, or quality Competitive costsCompetitive costs become criticalbecome critical Defend marketDefend market positionposition Cost controlCost control criticalcritical Introduction Growth Maturity Decline CompanyStrategy/IssuesCompanyStrategy/Issues InternetInternet Flat-screenFlat-screen monitorsmonitors SalesSales DVDDVD CD-ROMCD-ROM Drive-throughDrive-through restaurantsrestaurants Fax machinesFax machines 3 1/2”3 1/2” FloppyFloppy disksdisks Color printersColor printers Figure 2.5Figure 2.5
- 19. © 2006 PrenticeHall, Inc. 4 – 19 Product Life CycleProduct Life Cycle Product designProduct design andand developmentdevelopment criticalcritical FrequentFrequent product andproduct and process designprocess design changeschanges Short productionShort production runsruns High productionHigh production costscosts Limited modelsLimited models Attention toAttention to qualityquality Introduction Growth Maturity Decline OMStrategy/IssuesOMStrategy/Issues ForecastingForecasting criticalcritical Product andProduct and processprocess reliabilityreliability CompetitiveCompetitive productproduct improvementsimprovements and optionsand options Increase capacityIncrease capacity Shift towardShift toward product focusproduct focus EnhanceEnhance distributiondistribution StandardizationStandardization Less rapidLess rapid product changesproduct changes – more minor– more minor changeschanges OptimumOptimum capacitycapacity IncreasingIncreasing stability ofstability of processprocess Long productionLong production runsruns ProductProduct improvement andimprovement and cost cuttingcost cutting Little productLittle product differentiationdifferentiation CostCost minimizationminimization OvercapacityOvercapacity in thein the industryindustry Prune line toPrune line to eliminateeliminate items notitems not returningreturning good margingood margin ReduceReduce capacitycapacity Figure 2.5Figure 2.5
- 20. © 2006 PrenticeHall, Inc. 4 – 20 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
- 21. © 2006 PrenticeHall, Inc. 4 – 21 Strategic Importance ofStrategic Importance of ForecastingForecasting Human Resources – Hiring, training,Human Resources – Hiring, training, laying off workerslaying off workers Capacity – Capacity shortages canCapacity – Capacity shortages can result in undependable delivery, lossresult in undependable delivery, loss of customers, loss of market shareof customers, loss of market share Supply-Chain Management – GoodSupply-Chain Management – Good supplier relations and price advancesupplier relations and price advance
- 22. © 2006 PrenticeHall, Inc. 4 – 22 Seven Steps in ForecastingSeven Steps in Forecasting Determine the use of the forecastDetermine the use of the forecast Select the items to be forecastedSelect the items to be forecasted Determine the time horizon of theDetermine the time horizon of the forecastforecast Select the forecasting model(s)Select the forecasting model(s) Gather the dataGather the data Make the forecastMake the forecast Validate and implement resultsValidate and implement results
- 23. © 2006 PrenticeHall, Inc. 4 – 23 The Realities!The Realities! Forecasts are seldom perfectForecasts are seldom perfect Most techniques assume anMost techniques assume an underlying stability in the systemunderlying stability in the system Product family and aggregatedProduct family and aggregated forecasts are more accurate thanforecasts are more accurate than individual product forecastsindividual product forecasts
- 24. © 2006 PrenticeHall, Inc. 4 – 24 Forecasting ApproachesForecasting Approaches Used when situation is vagueUsed 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
- 25. © 2006 PrenticeHall, Inc. 4 – 25 Forecasting ApproachesForecasting Approaches Used when situation is ‘stable’ andUsed 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 colore.g., forecasting sales of color televisionstelevisions Quantitative MethodsQuantitative Methods
- 26. © 2006 PrenticeHall, Inc. 4 – 26 Overview of QualitativeOverview of Qualitative MethodsMethods Jury of executive opinionJury of executive opinion Pool opinions of high-levelPool opinions of high-level executives, sometimes augment byexecutives, sometimes augment by statistical modelsstatistical models Delphi methodDelphi method Panel of experts, queried iterativelyPanel of experts, queried iteratively
- 27. © 2006 PrenticeHall, Inc. 4 – 27 Overview of QualitativeOverview of Qualitative MethodsMethods Sales force compositeSales force composite Estimates from individualEstimates from individual salespersons are reviewed forsalespersons are reviewed for reasonableness, then aggregatedreasonableness, then aggregated Consumer Market SurveyConsumer Market Survey Ask the customerAsk the customer
- 28. © 2006 PrenticeHall, Inc. 4 – 28 Involves small group of high-levelInvolves small group of high-level managersmanagers Group estimates demand by workingGroup estimates demand by working togethertogether Combines managerial experience withCombines managerial experience with statistical modelsstatistical models Relatively quickRelatively quick ‘‘Group-think’Group-think’ disadvantagedisadvantage Jury of Executive OpinionJury of Executive Opinion
- 29. © 2006 PrenticeHall, Inc. 4 – 29 Sales Force CompositeSales Force Composite Each salesperson projects his orEach salesperson projects his or her salesher sales Combined at district and nationalCombined at district and national levelslevels Sales reps know customers’ wantsSales reps know customers’ wants Tends to be overly optimisticTends to be overly optimistic
- 30. © 2006 PrenticeHall, Inc. 4 – 30 Delphi MethodDelphi Method Iterative groupIterative group process,process, continues untilcontinues until consensus isconsensus is reachedreached 3 types of3 types of participantsparticipants Decision makersDecision makers StaffStaff RespondentsRespondents Staff (Administering survey) Decision Makers (Evaluate responses and make decisions) Respondents (People who can make valuable judgments)
- 31. © 2006 PrenticeHall, Inc. 4 – 31 Consumer Market SurveyConsumer Market Survey Ask customers about purchasingAsk customers about purchasing plansplans What consumers say, and whatWhat consumers say, and what they actually do are often differentthey actually do are often different Sometimes difficult to answerSometimes difficult to answer
- 32. © 2006 PrenticeHall, Inc. 4 – 32 Overview of QuantitativeOverview of Quantitative ApproachesApproaches 1.1. Naive approachNaive approach 2.2. Moving averagesMoving averages 3.3. ExponentialExponential smoothingsmoothing 4.4. Trend projectionTrend projection 5.5. Linear regressionLinear regression Time-SeriesTime-Series ModelsModels AssociativeAssociative ModelModel
- 33. © 2006 PrenticeHall, Inc. 4 – 33 Set of evenly spaced numericalSet of evenly spaced numerical datadata Obtained by observing responseObtained by observing response variable at regular time periodsvariable at regular time periods Forecast based only on pastForecast based only on past valuesvalues Assumes that factors influencingAssumes that factors influencing past and present will continuepast and present will continue influence in futureinfluence in future Time Series ForecastingTime Series Forecasting
- 34. © 2006 PrenticeHall, Inc. 4 – 34 Trend Seasonal Cyclical Random Time Series ComponentsTime Series Components
- 35. © 2006 PrenticeHall, Inc. 4 – 35 Components of DemandComponents of DemandDemandforproductorservice | | | | 1 2 3 4 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation Figure 4.1Figure 4.1
- 36. © 2006 PrenticeHall, Inc. 4 – 36 Persistent, overall upward orPersistent, overall upward or downward patterndownward pattern Changes due to population,Changes due to population, technology, age, culture, etc.technology, age, culture, etc. Typically several yearsTypically several years durationduration Trend ComponentTrend Component
- 37. © 2006 PrenticeHall, Inc. 4 – 37 Regular pattern of up andRegular pattern of up and down fluctuationsdown fluctuations Due to weather, customs, etc.Due to weather, customs, etc. Occurs within a single yearOccurs within a single year Seasonal ComponentSeasonal Component Number of Period Length Seasons Week Day 7 Month Week 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52
- 38. © 2006 PrenticeHall, Inc. 4 – 38 Repeating up and down movementsRepeating up and down movements Affected by business cycle,Affected by business cycle, political, and economic factorspolitical, and economic factors Multiple years durationMultiple years duration Often causal orOften causal or associativeassociative relationshipsrelationships Cyclical ComponentCyclical Component 00 55 1010 1515 2020
- 39. © 2006 PrenticeHall, Inc. 4 – 39 Erratic, unsystematic, ‘residual’Erratic, unsystematic, ‘residual’ fluctuationsfluctuations Due to random variation orDue to random variation or unforeseen eventsunforeseen events Short duration andShort duration and nonrepeatingnonrepeating Random ComponentRandom Component MM TT WW TT FF
- 40. © 2006 PrenticeHall, Inc. 4 – 40 Naive ApproachNaive Approach Assumes demand in next period isAssumes demand in next period is the same as demand in mostthe same as demand in most recent periodrecent period e.g., If May sales were 48, then Junee.g., If May sales were 48, then June sales will be 48sales will be 48 Sometimes cost effective andSometimes cost effective and efficientefficient
- 41. © 2006 PrenticeHall, Inc. 4 – 41 MA is a series of arithmetic meansMA is a series of arithmetic means Used if little or no trendUsed if little or no trend Used often for smoothingUsed often for smoothing Provides overall impression of dataProvides 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
- 42. © 2006 PrenticeHall, Inc. 4 – 42 JanuaryJanuary 1010 FebruaryFebruary 1212 MarchMarch 1313 AprilApril 1616 MayMay 1919 JuneJune 2323 JulyJuly 2626 ActualActual 3-Month3-Month MonthMonth 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 1010 1212 1313 ((1010 ++ 1212 ++ 1313)/3 = 11)/3 = 11 22 //33
- 43. © 2006 PrenticeHall, Inc. 4 – 43 Graph of Moving AverageGraph of Moving Average | | | | | | | | | | | | JJ FF MM AA MM JJ JJ AA SS OO NN DD ShedSalesShedSales 3030 – 2828 – 2626 – 2424 – 2222 – 2020 – 1818 – 1616 – 1414 – 1212 – 1010 – ActualActual SalesSales MovingMoving AverageAverage ForecastForecast
- 44. © 2006 PrenticeHall, Inc. 4 – 44 Used when trend is presentUsed when trend is present Older data usually less importantOlder data usually less important Weights based on experience andWeights based on experience and intuitionintuition Weighted Moving AverageWeighted Moving Average WeightedWeighted moving averagemoving average == ∑∑ ((weight for period nweight for period n)) xx ((demand in period ndemand in period n)) ∑∑ weightsweights
- 45. © 2006 PrenticeHall, Inc. 4 – 45 JanuaryJanuary 1010 FebruaryFebruary 1212 MarchMarch 1313 AprilApril 1616 MayMay 1919 JuneJune 2323 JulyJuly 2626 ActualActual 3-Month Weighted3-Month Weighted MonthMonth 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 1010 1212 1313 [(3 x[(3 x 1313) + (2 x) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211 //66 Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 6 Sum of weights
- 46. © 2006 PrenticeHall, Inc. 4 – 46 Increasing n smooths the forecastIncreasing n smooths the forecast but makes it less sensitive tobut 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 AverageMoving Average
- 47. © 2006 PrenticeHall, Inc. 4 – 47 Moving Average AndMoving Average And Weighted Moving AverageWeighted Moving Average 3030 – 2525 – 2020 – 1515 – 1010 – 55 – SalesdemandSalesdemand | | | | | | | | | | | | JJ FF MM AA MM JJ JJ AA SS OO NN DD ActualActual salessales MovingMoving averageaverage WeightedWeighted movingmoving averageaverage Figure 4.2Figure 4.2
- 48. © 2006 PrenticeHall, Inc. 4 – 48 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 constantRequires smoothing constant ((αα)) Ranges from 0 to 1Ranges from 0 to 1 Subjectively chosenSubjectively chosen Involves little record keeping of pastInvolves little record keeping of past datadata Exponential SmoothingExponential Smoothing
- 49. © 2006 PrenticeHall, Inc. 4 – 49 Exponential SmoothingExponential Smoothing t =t = last period’s forecastlast period’s forecast ++ αα ((last period’s actual demandlast period’s actual demand –– last period’s forecastlast period’s forecast)) FFtt = F= Ftt – 1– 1 ++ αα((AAtt – 1– 1 -- FFtt – 1– 1)) wherewhere FFtt == new forecastnew forecast FFtt – 1– 1 == previous forecastprevious forecast αα == smoothing (or weighting)smoothing (or weighting) constantconstant (0(0 ≤≤ αα ≥≥ 1)1)
- 50. © 2006 PrenticeHall, Inc. 4 – 50 Exponential SmoothingExponential Smoothing ExampleExample Predicted demandPredicted demand = 142= 142 Ford MustangsFord Mustangs Actual demandActual demand = 153= 153 Smoothing constantSmoothing constant αα = .20= .20
- 51. © 2006 PrenticeHall, Inc. 4 – 51 Exponential SmoothingExponential Smoothing ExampleExample Predicted demandPredicted demand = 142= 142 Ford MustangsFord Mustangs Actual demandActual demand = 153= 153 Smoothing constantSmoothing constant αα = .20= .20 New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)
- 52. © 2006 PrenticeHall, Inc. 4 – 52 Exponential SmoothingExponential Smoothing ExampleExample Predicted demandPredicted demand = 142= 142 Ford MustangsFord Mustangs Actual demandActual demand = 153= 153 Smoothing constantSmoothing constant αα = .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
- 53. © 2006 PrenticeHall, Inc. 4 – 53 Effect ofEffect of Smoothing ConstantsSmoothing Constants Weight Assigned toWeight Assigned to MostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th Most RecentRecent RecentRecent RecentRecent RecentRecent RecentRecent SmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod ConstantConstant ((αα)) αα(1 -(1 - αα)) αα(1 -(1 - αα))22 αα(1 -(1 - αα))33 αα(1 -(1 - αα))44 αα = .1= .1 .1.1 .09.09 .081.081 .073.073 .066.066 αα = .5= .5 .5.5 .25.25 .125.125 .063.063 .031.031
- 54. © 2006 PrenticeHall, Inc. 4 – 54 Impact of DifferentImpact of Different αα 225225 – 200200 – 175175 – 150150 – | | | | | | | | | 11 22 33 44 55 66 77 88 99 QuarterQuarter DemandDemand αα = .1= .1 ActualActual demanddemand αα = .5= .5
- 55. © 2006 PrenticeHall, Inc. 4 – 55 ChoosingChoosing αα The objective is to obtain the mostThe objective is to obtain the most accurate forecast no matter theaccurate forecast no matter the techniquetechnique We generally do this by selecting theWe generally do this by selecting the model that gives us the lowest forecastmodel that gives us the lowest forecast errorerror Forecast errorForecast error = Actual demand - Forecast value= Actual demand - Forecast value = A= Att - F- Ftt
- 56. © 2006 PrenticeHall, Inc. 4 – 56 Common Measures of ErrorCommon Measures of Error Mean Absolute DeviationMean Absolute Deviation ((MADMAD)) MAD =MAD = ∑∑ |actual - forecast||actual - forecast| nn Mean Squared ErrorMean Squared Error ((MSEMSE)) MSE =MSE = ∑∑ ((forecast errorsforecast errors))22 nn
- 57. © 2006 PrenticeHall, Inc. 4 – 57 Common Measures of ErrorCommon Measures of Error Mean Absolute Percent ErrorMean Absolute Percent Error ((MAPEMAPE)) MAPE =MAPE = 100100 ∑∑ |actual|actualii - forecast- forecastii|/actual|/actualii nn nn ii = 1= 1
- 58. © 2006 PrenticeHall, Inc. 4 – 58 Comparison of ForecastComparison of Forecast ErrorError RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsolute ActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation TonnageTonnage withwith forfor withwith forfor QuarterQuarter UnloadedUnloaded αα = .10= .10 αα = .10= .10 αα = .50= .50 αα = .50= .50 11 180180 175175 55 175175 55 22 168168 176176 88 178178 1010 33 159159 175175 1616 173173 1414 44 175175 173173 22 166166 99 55 190190 173173 1717 170170 2020 66 205205 175175 3030 180180 2525 77 180180 178178 22 193193 1313 88 182182 178178 44 186186 44 8484 100100
- 59. © 2006 PrenticeHall, Inc. 4 – 59 Comparison of ForecastComparison of Forecast ErrorError RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsolute ActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation TonageTonage withwith forfor withwith forfor QuarterQuarter UnloadedUnloaded αα = .10= .10 αα = .10= .10 αα = .50= .50 αα = .50= .50 11 180180 175175 55 175175 55 22 168168 176176 88 178178 1010 33 159159 175175 1616 173173 1414 44 175175 173173 22 166166 99 55 190190 173173 1717 170170 2020 66 205205 175175 3030 180180 2525 77 180180 178178 22 193193 1313 88 182182 178178 44 186186 44 8484 100100 MAD = ∑ |deviations| n = 84/8 = 10.50 For α = .10 = 100/8 = 12.50 For α = .50
- 60. © 2006 PrenticeHall, Inc. 4 – 60 Comparison of ForecastComparison of Forecast ErrorError RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsolute ActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation TonageTonage withwith forfor withwith forfor QuarterQuarter UnloadedUnloaded αα = .10= .10 αα = .10= .10 αα = .50= .50 αα = .50= .50 11 180180 175175 55 175175 55 22 168168 176176 88 178178 1010 33 159159 175175 1616 173173 1414 44 175175 173173 22 166166 99 55 190190 173173 1717 170170 2020 66 205205 175175 3030 180180 2525 77 180180 178178 22 193193 1313 88 182182 178178 44 186186 44 8484 100100 MADMAD 10.5010.50 12.5012.50 = 1,558/8 = 194.75 For α = .10 = 1,612/8 = 201.50 For α = .50 MSE = ∑ (forecast errors)2 n
- 61. © 2006 PrenticeHall, Inc. 4 – 61 Comparison of ForecastComparison of Forecast ErrorError RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsolute ActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation TonageTonage withwith forfor withwith forfor QuarterQuarter UnloadedUnloaded αα = .10= .10 αα = .10= .10 αα = .50= .50 αα = .50= .50 11 180180 175175 55 175175 55 22 168168 176176 88 178178 1010 33 159159 175175 1616 173173 1414 44 175175 173173 22 166166 99 55 190190 173173 1717 170170 2020 66 205205 175175 3030 180180 2525 77 180180 178178 22 193193 1313 88 182182 178178 44 186186 44 8484 100100 MADMAD 10.5010.50 12.5012.50 MSEMSE 194.75194.75 201.50201.50 = 45.62/8 = 5.70% For α = .10 = 54.8/8 = 6.85% For α = .50 MAPE = 100 ∑ |deviationi|/actuali n n i = 1
- 62. © 2006 PrenticeHall, Inc. 4 – 62 Comparison of ForecastComparison of Forecast ErrorError RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsolute ActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation TonnageTonnage withwith forfor withwith forfor QuarterQuarter UnloadedUnloaded αα = .10= .10 αα = .10= .10 αα = .50= .50 αα = .50= .50 11 180180 175175 55 175175 55 22 168168 176176 88 178178 1010 33 159159 175175 1616 173173 1414 44 175175 173173 22 166166 99 55 190190 173173 1717 170170 2020 66 205205 175175 3030 180180 2525 77 180180 178178 22 193193 1313 88 182182 178178 44 186186 44 8484 100100 MADMAD 10.5010.50 12.5012.50 MSEMSE 194.75194.75 201.50201.50 MAPEMAPE 5.70%5.70% 6.85%6.85%
- 63. © 2006 PrenticeHall, Inc. 4 – 63 Exponential Smoothing withExponential Smoothing with Trend AdjustmentTrend Adjustment When a trend is present, exponentialWhen a trend is present, exponential smoothing must be modifiedsmoothing must be modified ForecastForecast includingincluding ((FITFITtt)) == trendtrend exponentiallyexponentially exponentiallyexponentially smoothedsmoothed ((FFtt)) ++ ((TTtt)) smoothedsmoothed forecastforecast trendtrend
- 64. © 2006 PrenticeHall, Inc. 4 – 64 Exponential Smoothing withExponential Smoothing with Trend AdjustmentTrend Adjustment FFtt == αα((AAtt - 1- 1) + (1 -) + (1 - αα)()(FFtt - 1- 1 ++ TTtt - 1- 1)) TTtt == ββ((FFtt -- FFtt - 1- 1) + (1 -) + (1 - ββ))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 == FFtt ++ TTtt
- 65. © 2006 PrenticeHall, Inc. 4 – 65 Exponential Smoothing withExponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example ForecastForecast ActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding MonthMonth((tt)) DemandDemand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt 11 1212 1111 22 13.0013.00 22 1717 33 2020 44 1919 55 2424 66 2121 77 3131 88 2828 99 3636 1010 Table 4.1Table 4.1
- 66. © 2006 PrenticeHall, Inc. 4 – 66 Exponential Smoothing withExponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example ForecastForecast ActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding MonthMonth((tt)) DemandDemand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt 11 1212 1111 22 13.0013.00 22 1717 33 2020 44 1919 55 2424 66 2121 77 3131 88 2828 99 3636 1010 Table 4.1Table 4.1 F2 = αA1 + (1 - α)(F1 + T1) F2 = (.2)(12) + (1 - .2)(11 + 2) = 2.4 + 10.4 = 12.8 units Step 1: Forecast for Month 2
- 67. © 2006 PrenticeHall, Inc. 4 – 67 Exponential Smoothing withExponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example ForecastForecast ActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding MonthMonth((tt)) DemandDemand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt 11 1212 1111 22 13.0013.00 22 1717 12.8012.80 33 2020 44 1919 55 2424 66 2121 77 3131 88 2828 99 3636 1010 Table 4.1Table 4.1 T2 = β(F2 - F1) + (1 - β)T1 T2 = (.4)(12.8 - 11) + (1 - .4)(2) = .72 + 1.2 = 1.92 units Step 2: Trend for Month 2
- 68. © 2006 PrenticeHall, Inc. 4 – 68 Exponential Smoothing withExponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example ForecastForecast ActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding MonthMonth((tt)) DemandDemand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt 11 1212 1111 22 13.0013.00 22 1717 12.8012.80 1.921.92 33 2020 44 1919 55 2424 66 2121 77 3131 88 2828 99 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
- 69. © 2006 PrenticeHall, Inc. 4 – 69 Exponential Smoothing withExponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example ForecastForecast ActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding MonthMonth((tt)) DemandDemand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt 11 1212 1111 22 13.0013.00 22 1717 12.8012.80 1.921.92 14.7214.72 33 2020 44 1919 55 2424 66 2121 77 3131 88 2828 99 3636 1010 Table 4.1Table 4.1 15.1815.18 2.102.10 17.2817.28 17.8217.82 2.322.32 20.1420.14 19.9119.91 2.232.23 22.1422.14 22.5122.51 2.382.38 24.8924.89 24.1124.11 2.072.07 26.1826.18 27.1427.14 2.452.45 29.5929.59 29.2829.28 2.322.32 31.6031.60 32.4832.48 2.682.68 35.1635.16
- 70. © 2006 PrenticeHall, Inc. 4 – 70 Exponential Smoothing withExponential 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) ProductdemandProductdemand 3535 – 3030 – 2525 – 2020 – 1515 – 1010 – 55 – 00 – Actual demandActual demand ((AAtt)) Forecast including trendForecast including trend ((FITFITtt))
- 71. © 2006 PrenticeHall, Inc. 4 – 71 Trend ProjectionsTrend Projections Fitting a trend line to historical data pointsFitting 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 leastLinear trends can be found using the least squares techniquesquares technique yy == aa ++ bxbx^^ where ywhere y = computed value of= computed value of the variable to be predictedthe variable to be predicted (dependent variable)(dependent variable) aa = y-axis intercept= y-axis intercept bb = slope of the regression line= slope of the regression line xx = the independent variable= the independent variable ^^
- 72. © 2006 PrenticeHall, Inc. 4 – 72 Least Squares MethodLeast Squares Method Time periodTime period ValuesofDependentVariable Figure 4.4Figure 4.4 DeviationDeviation11 DeviationDeviation55 DeviationDeviation77 DeviationDeviation22 DeviationDeviation66 DeviationDeviation44 DeviationDeviation33 Actual observationActual observation (y value)(y value) Trend line, y = a + bxTrend line, y = a + bx^^
- 73. © 2006 PrenticeHall, Inc. 4 – 73 Least Squares MethodLeast Squares Method Time periodTime period ValuesofDependentVariable Figure 4.4Figure 4.4 DeviationDeviation11 DeviationDeviation55 DeviationDeviation77 DeviationDeviation22 DeviationDeviation66 DeviationDeviation44 DeviationDeviation33 Actual observationActual 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)
- 74. © 2006 PrenticeHall, Inc. 4 – 74 Least Squares MethodLeast Squares Method Equations to calculate the regression variablesEquations to calculate the regression variables b =b = ΣΣxy - nxyxy - nxy ΣΣxx22 - nx- nx22 yy == aa ++ bxbx^^ a = y - bxa = y - bx
- 75. © 2006 PrenticeHall, Inc. 4 – 75 Least Squares ExampleLeast Squares Example bb = = = 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 PowerElectrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy 19991999 11 7474 11 7474 20002000 22 7979 44 158158 20012001 33 8080 99 240240 20022002 44 9090 1616 360360 20032003 55 105105 2525 525525 20042004 66 142142 3636 852852 20052005 77 122122 4949 854854 ∑∑xx = 28= 28 ∑∑yy = 692= 692 ∑∑xx22 = 140= 140 ∑∑xyxy = 3,063= 3,063 xx = 4= 4 yy = 98.86= 98.86
- 76. © 2006 PrenticeHall, Inc. 4 – 76 Least Squares ExampleLeast Squares Example bb = = = 10.54= = = 10.54 ΣΣxy - nxyxy - nxy ΣΣxx22 - 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 PowerElectrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy 19991999 11 7474 11 7474 20002000 22 7979 44 158158 20012001 33 8080 99 240240 20022002 44 9090 1616 360360 20032003 55 105105 2525 525525 20042004 66 142142 3636 852852 20052005 77 122122 4949 854854 ΣΣxx = 28= 28 ΣΣyy = 692= 692 ΣΣxx22 = 140= 140 ΣΣxyxy = 3,063= 3,063 xx = 4= 4 yy = 98.86= 98.86 The trend line is y = 56.70 + 10.54x^
- 77. © 2006 PrenticeHall, Inc. 4 – 77 Least Squares ExampleLeast Squares Example | | | | | | | | | 19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007 160160 – 150150 – 140140 – 130130 – 120120 – 110110 – 100100 – 9090 – 8080 – 7070 – 6060 – 5050 – YearYear PowerdemandPowerdemand Trend line,Trend line, yy = 56.70 + 10.54x= 56.70 + 10.54x^^
- 78. © 2006 PrenticeHall, Inc. 4 – 79 Seasonal Variations In DataSeasonal Variations In Data The multiplicative seasonal model canThe multiplicative seasonal model can modify trend data to accommodatemodify trend data to accommodate seasonal variations in demandseasonal variations in demand 1.1. Find average historical demand for each seasonFind average historical demand for each season 2.2. Compute the average demand over all seasonsCompute the average demand over all seasons 3.3. Compute a seasonal index for each seasonCompute 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 theDivide this estimate of total demand by the number of seasons, then multiply it by thenumber of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season
- 79. © 2006 PrenticeHall, Inc. 4 – 80 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 SeasonalSeasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex
- 80. © 2006 PrenticeHall, Inc. 4 – 81 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 SeasonalSeasonal 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
- 81. © 2006 PrenticeHall, Inc. 4 – 82 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 SeasonalSeasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex
- 82. © 2006 PrenticeHall, Inc. 4 – 83 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 SeasonalSeasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex Expected annual demand = 1,200 Jan x .957 = 96 1,200 12 Feb x .851 = 85 1,200 12 Forecast for 2006
- 83. © 2006 PrenticeHall, Inc. 4 – 84 Seasonal Index ExampleSeasonal Index Example 140140 – 130130 – 120120 – 110110 – 100100 – 9090 – 8080 – 7070 – | | | | | | | | | | | | JJ FF MM AA MM JJ JJ AA SS OO NN DD TimeTime DemandDemand 2006 Forecast2006 Forecast 2005 Demand2005 Demand 2004 Demand2004 Demand 2003 Demand2003 Demand
- 84. © 2006 PrenticeHall, Inc. 4 – 85 San Diego HospitalSan Diego Hospital 10,20010,200 – 10,00010,000 – 9,8009,800 – 9,6009,600 – 9,4009,400 – 9,2009,200 – 9,0009,000 – | | | | | | | | | | | | JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov DecDec 6767 6868 6969 7070 7171 7272 7373 7474 7575 7676 7777 7878 MonthMonth InpatientDaysInpatientDays 95309530 95519551 95739573 95949594 96169616 96379637 96599659 96809680 97029702 97239723 97459745 97669766 Figure 4.6Figure 4.6 Trend DataTrend Data
- 85. © 2006 PrenticeHall, Inc. 4 – 86 San Diego HospitalSan Diego Hospital 1.061.06 – 1.041.04 – 1.021.02 – 1.001.00 – 0.980.98 – 0.960.96 – 0.940.94 – 0.92 – | | | | | | | | | | | | JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov DecDec 6767 6868 6969 7070 7171 7272 7373 7474 7575 7676 7777 7878 MonthMonth IndexforInpatientDaysIndexforInpatientDays 1.041.04 1.021.02 1.011.01 0.990.99 1.031.03 1.041.04 1.001.00 0.980.98 0.970.97 0.990.99 0.970.97 0.960.96 Figure 4.7Figure 4.7 Seasonal IndicesSeasonal Indices
- 86. © 2006 PrenticeHall, Inc. 4 – 87 San Diego HospitalSan Diego Hospital 10,20010,200 – 10,00010,000 – 9,8009,800 – 9,6009,600 – 9,4009,400 – 9,2009,200 – 9,0009,000 – | | | | | | | | | | | | JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov DecDec 6767 6868 6969 7070 7171 7272 7373 7474 7575 7676 7777 7878 MonthMonth InpatientDaysInpatientDays Figure 4.8Figure 4.8 99119911 92659265 97649764 95209520 96919691 94119411 99499949 97249724 95429542 93559355 1006810068 95729572 Combined Trend and Seasonal ForecastCombined Trend and Seasonal Forecast
- 87. © 2006 PrenticeHall, Inc. 4 – 88 Associative ForecastingAssociative Forecasting Used when changes in one or moreUsed when changes in one or more independent variables can be used to predictindependent variables can be used to predict the changes in the dependent variablethe changes in the dependent variable Most common technique is linearMost common technique is linear regression analysisregression analysis We apply this technique just as we didWe apply this technique just as we did in the time series examplein the time series example
- 88. © 2006 PrenticeHall, Inc. 4 – 89 Associative ForecastingAssociative Forecasting Forecasting an outcome based on predictorForecasting an outcome based on predictor variables using the least squares techniquevariables using the least squares technique yy == aa ++ bxbx^^ where ywhere y = computed value of= computed value of the variable to be predictedthe variable to be predicted (dependent variable)(dependent variable) aa = y-axis intercept= y-axis intercept bb = slope of the regression line= slope of the regression line xx = the independent variable= the independent variable though to predict the value of thethough to predict the value of the dependent variabledependent variable ^^
- 89. © 2006 PrenticeHall, Inc. 4 – 90 Associative ForecastingAssociative Forecasting ExampleExample SalesSales Local PayrollLocal Payroll ($000,000), y($000,000), y ($000,000,000), x($000,000,000), x 2.02.0 11 3.03.0 33 2.52.5 44 2.02.0 22 2.02.0 11 3.53.5 77 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Sales Area payroll
- 90. © 2006 PrenticeHall, Inc. 4 – 91 Associative ForecastingAssociative Forecasting ExampleExample Sales, y Payroll, x x2 xy 2.0 1 1 2.0 3.0 3 9 9.0 2.5 4 16 10.0 2.0 2 4 4.0 2.0 1 1 2.0 3.5 7 49 24.5 ∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5 xx == ∑∑xx/6 = 18/6 = 3/6 = 18/6 = 3 yy == ∑∑yy/6 = 15/6 = 2.5/6 = 15/6 = 2.5 bb = = = .25= = = .25 ∑∑xy - nxyxy - nxy ∑∑xx22 - nx- nx22 51.5 - (6)(3)(2.5)51.5 - (6)(3)(2.5) 80 - (6)(380 - (6)(322 )) aa == yy -- bbx = 2.5 - (.25)(3) = 1.75x = 2.5 - (.25)(3) = 1.75
- 91. © 2006 PrenticeHall, Inc. 4 – 92 Associative ForecastingAssociative Forecasting ExampleExample 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Sales Area payroll yy = 1.75 + .25= 1.75 + .25xx^^ SalesSales = 1.75 + .25(= 1.75 + .25(payrollpayroll)) If payroll next yearIf payroll next year is estimated to beis estimated to be $600$600 million, then:million, then: SalesSales = 1.75 + .25(6)= 1.75 + .25(6) SalesSales = $325,000= $325,000 3.25
- 92. © 2006 PrenticeHall, Inc. 4 – 93 Standard Error of theStandard Error of the EstimateEstimate A forecast is just a point estimate of aA forecast is just a point estimate of a future valuefuture value This point isThis point is actually theactually the mean of amean of a probabilityprobability distributiondistribution Figure 4.9Figure 4.9 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Sales Area payroll 3.25
- 93. © 2006 PrenticeHall, Inc. 4 – 94 Standard Error of theStandard Error of the EstimateEstimate wherewhere yy == y-value of each datay-value of each data pointpoint yycc == computed value ofcomputed value of the dependent variable, from thethe dependent variable, from the regression equationregression equation nn == number of datanumber of data pointspoints SSy,xy,x == ∑∑((y - yy - ycc))22 nn - 2- 2
- 94. © 2006 PrenticeHall, Inc. 4 – 95 Standard Error of theStandard Error of the EstimateEstimate Computationally, this equation isComputationally, this equation is considerably easier to useconsiderably easier to use We use the standard error to set upWe use the standard error to set up prediction intervals around theprediction intervals around the point estimatepoint estimate SSy,xy,x == ∑∑yy22 - a- a∑∑y - by - b∑∑xyxy nn - 2- 2
- 95. © 2006 PrenticeHall, Inc. 4 – 96 Standard Error of theStandard Error of the EstimateEstimate 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | 0 1 2 3 4 5 6 7 Sales Area payroll 3.25 SSy,xy,x = == =∑∑yy22 - a- a∑∑y - by - b∑∑xyxy nn - 2- 2 39.5 - 1.75(15) - .25(51.5)39.5 - 1.75(15) - .25(51.5) 6 - 26 - 2 SSy,xy,x == .306.306 The standard errorThe standard error of the estimate isof the estimate is $30,600$30,600 in salesin sales
- 96. © 2006 PrenticeHall, Inc. 4 – 97 How strong is the linearHow strong is the linear relationship between therelationship between the variables?variables? Correlation does not necessarilyCorrelation does not necessarily imply causality!imply causality! Coefficient of correlation, r,Coefficient of correlation, r, measures degree of associationmeasures degree of association Values range fromValues range from -1-1 toto +1+1 CorrelationCorrelation
- 97. © 2006 PrenticeHall, Inc. 4 – 98 Correlation CoefficientCorrelation Coefficient r =r = nnΣΣxyxy -- ΣΣxxΣΣyy [[nnΣΣxx22 - (- (ΣΣxx))22 ][][nnΣΣyy22 - (- (ΣΣyy))22 ]]
- 98. © 2006 PrenticeHall, Inc. 4 – 99 Correlation CoefficientCorrelation Coefficient r =r = nn∑∑xyxy -- ∑∑xx∑∑yy [[nn∑∑xx22 - (- (∑∑xx))22 ][][nn∑∑yy22 - (- (∑∑yy))22 ]] 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
- 99. © 2006 PrenticeHall, Inc. 4 – 100 Coefficient of Determination, rCoefficient of Determination, r22 ,, measures the percent of change inmeasures the percent of change in y predicted by the change in xy predicted by the change in x Values range fromValues range from 00 toto 11 Easy to interpretEasy to interpret CorrelationCorrelation For the Nodel Construction example:For the Nodel Construction example: rr = .901= .901 rr22 = .81= .81
- 100. © 2006 PrenticeHall, Inc. 4 – 101 Multiple RegressionMultiple Regression AnalysisAnalysis If more than one independent variable is to beIf more than one independent variable is to be used in the model, linear regression can beused in the model, linear regression can be extended to multiple regression toextended to multiple regression to accommodate several independent variablesaccommodate several independent variables yy == aa ++ bb11xx11 + b+ b22xx22 ……^^ Computationally, this is quiteComputationally, this is quite complex and generally done on thecomplex and generally done on the computercomputer
- 101. © 2006 PrenticeHall, Inc. 4 – 102 Multiple RegressionMultiple Regression AnalysisAnalysis yy = 1.80 + .30= 1.80 + .30xx11 - 5.0- 5.0xx22 ^^ In the Nodel example, including interest rates inIn the Nodel example, including interest rates in the model gives the new equation:the model gives the new equation: An improved correlation coefficient of rAn improved correlation coefficient of r = .96= .96 means this model does a better job of predictingmeans this model does a better job of predicting the change in construction salesthe change in construction sales SalesSales = 1.80 + .30(6) - 5.0(.12) = 3.00= 1.80 + .30(6) - 5.0(.12) = 3.00 SalesSales = $300,000= $300,000
- 102. © 2006 PrenticeHall, Inc. 4 – 103 Measures how well the forecast isMeasures how well the forecast is predicting actual valuespredicting actual values Ratio of running sum of forecast errorsRatio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)(RSFE) to mean absolute deviation (MAD) Good tracking signal has low valuesGood tracking signal has low values If forecasts are continually high or low, theIf forecasts are continually high or low, the forecast has a bias errorforecast has a bias error Monitoring and ControllingMonitoring and Controlling ForecastsForecasts Tracking SignalTracking Signal
- 103. © 2006 PrenticeHall, Inc. 4 – 104 Monitoring and ControllingMonitoring and Controlling ForecastsForecasts TrackingTracking signalsignal RSFERSFE MADMAD == TrackingTracking signalsignal == ∑∑(actual demand in(actual demand in period i -period i - forecast demandforecast demand in period i)in period i) ((∑∑|actual - forecast|/n|actual - forecast|/n))
- 104. © 2006 PrenticeHall, Inc. 4 – 105 Tracking SignalTracking Signal Tracking signalTracking signal ++ 00 MADsMADs –– Upper control limitUpper control limit Lower control limitLower control limit TimeTime Signal exceeding limitSignal exceeding limit AcceptableAcceptable rangerange
- 105. © 2006 PrenticeHall, Inc. 4 – 106 Tracking Signal ExampleTracking Signal Example CumulativeCumulative AbsoluteAbsolute AbsoluteAbsolute ActualActual ForecastForecast ForecastForecast ForecastForecast QtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD 11 9090 100100 -10-10 -10-10 1010 1010 10.010.0 22 9595 100100 -5-5 -15-15 55 1515 7.57.5 33 115115 100100 +15+15 00 1515 3030 10.010.0 44 100100 110110 -10-10 -10-10 1010 4040 10.010.0 55 125125 110110 +15+15 +5+5 1515 5555 11.011.0 66 140140 110110 +30+30 +35+35 3030 8585 14.214.2
- 106. © 2006 PrenticeHall, Inc. 4 – 107 CumulativeCumulative AbsoluteAbsolute AbsoluteAbsolute ActualActual ForecastForecast ForecastForecast ForecastForecast QtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD 11 9090 100100 -10-10 -10-10 1010 1010 10.010.0 22 9595 100100 -5-5 -15-15 55 1515 7.57.5 33 115115 100100 +15+15 00 1515 3030 10.010.0 44 100100 110110 -10-10 -10-10 1010 4040 10.010.0 55 125125 110110 +15+15 +5+5 1515 5555 11.011.0 66 140140 110110 +30+30 +35+35 3030 8585 14.214.2 Tracking Signal ExampleTracking Signal Example Tracking Signal (RSFE/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 signalThe variation of the tracking signal betweenbetween -2.0-2.0 andand +2.5+2.5 is within acceptableis within acceptable limitslimits
- 107. © 2006 PrenticeHall, Inc. 4 – 108 Adaptive ForecastingAdaptive Forecasting It’s possible to use the computer toIt’s possible to use the computer to continually monitor forecast error andcontinually monitor forecast error and adjust the values of theadjust the values of the αα andand ββ coefficients used in exponentialcoefficients used in exponential smoothing to continually minimizesmoothing to continually minimize forecast errorforecast error This technique is called adaptiveThis technique is called adaptive smoothingsmoothing
- 108. © 2006 PrenticeHall, Inc. 4 – 109 Focus ForecastingFocus Forecasting Developed at American Hardware Supply,Developed at American Hardware Supply, focus forecasting is based on two principles:focus forecasting is based on two principles: 1.1. Sophisticated forecasting models are notSophisticated forecasting models are not always better than simple modelsalways better than simple models 2.2. There is no single techniques that shouldThere is no single techniques that should be used for all products or servicesbe used for all products or services This approach uses historical data to testThis approach uses historical data to test multiple forecasting models for individual itemsmultiple forecasting models for individual items The forecasting model with the lowest error isThe forecasting model with the lowest error is then used to forecast the next demandthen used to forecast the next demand
- 109. © 2006 PrenticeHall, Inc. 4 – 110 Forecasting in the ServiceForecasting in the Service SectorSector Presents unusual challengesPresents unusual challenges Special need for short term recordsSpecial need for short term records Needs differ greatly as function ofNeeds differ greatly as function of industry and productindustry and product Holidays and other calendar eventsHolidays and other calendar events Unusual eventsUnusual events
- 110. © 2006 PrenticeHall, Inc. 4 – 111 Fast Food RestaurantFast Food Restaurant ForecastForecast 20%20% – 15%15% – 10%10% – 5%5% – 11-1211-12 1-21-2 3-43-4 5-65-6 7-87-8 9-109-10 12-112-1 2-32-3 4-54-5 6-76-7 8-98-9 10-1110-11 (Lunchtime)(Lunchtime) (Dinnertime)(Dinnertime) Hour of dayHour of day PercentageofsalesPercentageofsales Figure 4.12Figure 4.12
Editor's Notes
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