2-Forecasting 4auto Modified 11 Mars 2014

Slide 1

Industrial EngineeringForecasting. 1

Objectives

After completing this lecture, students will be able to:Understand and know when to use various families of forecasting models.Compare moving averages, exponential smoothing, and other time-series models.Seasonally adjust data.Understand Delphi and other qualitative decision making approaches.Compute a variety of error measures.

5/27/20142Prof.Dr.Nahid H.AfiaFORECAST:A statement about the future

Used to help managersPlan the systemPlan the use of the system 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingForecasting is the process of projecting the values of one or more variables (demand, price, labor availability) into the future.Poor forecasting can result in poor inventory and staffing decisions, resulting in part shortages, inadequate customer service, and many customer complaints.All forecasts are wrong, to a degree.Good forecasting results in more sales, less safety stock, better customer service, better staffing. Key is to reduce error as much as possible.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning44Types of ForecastsEconomic forecastsAddress business cycle inflation rate, money supply, housing starts, etc.Technological forecastsPredict rate of technological progressImpacts development of new productsDemand forecastsPredict sales of existing productWeather forecast is almost always wrongremember hurricane season 2006 Prentice Hall, Inc.4 #5Strategic Importance of ForecastingHuman Resources Hiring, training, laying off workersCapacity Capacity shortages can result in undependable delivery, loss of customers, loss of market shareSupply-Chain Management Good supplier relations and price advance 2006 Prentice Hall, Inc.4 #Many firms integrate forecasting with their supply chain trading partners and capacity management systems to make better operational decisions, and to reduce the bullwhip effect. Accurate forecasts are needed throughout the supply chain, and are used by accounting, finance, marketing, operations, and distribution.Must also develop contingency plans.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning77Bullwhip EffectThe bullwhip effect occurs when the demand order variability in the supply chain are amplified as they move up the supply chain.The bullwhip effect can be defined as the increase of variability in order quantities along the supply chain.The bullwhip effect has always been considered as one of the critical problems in a supply chain because it negatively influences costs, inventory, reliability and other important business processes.5/27/20148Prof.Dr.Nahid H.AfiaBasic Concepts in ForecastingPlanning horizon -- length of time for a forecast. Spans from short-range forecasts with a planning horizon of under 3 months to long-range forecasts of 1 to 10 years. The longer the planning horizon, the more likely that errors will result (use judgemental forecasts) Examples?Time bucket time period used for the forecast (daily, weekly, monthly, annually)Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning99Forecasting Time HorizonsA forecast is usually classified by the future time horizon that it covers. Time horizons fall into three categories:Long range forecast :Generally 3 years or more in time span, long range forecasts are used in planning for new products, capital expenditures, Facility location or expansion, and Research and Development R&D.Medium range forecast:A medium-range, or intermediate, forecast generally spans from 3 months to 3 years. It is useful in sales planning, production planning and budgeting, cash budgeting, and analyzing various operating plans.Short range forecast: This forecast has a time span of up to one year but is generally less than three months. It is used for Planning, Purchasing, Job scheduling, Job assignments and Production levels.

5/27/201410Prof.Dr.Nahid H.AfiaMedium and long range forecasts are distinguished from short range forecasts by three features:Intermediate and long run forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plant and processes. Implementing some facility decisions such as GMs decision to open a new Brazilian manufacturing plant can take 5 to 8 years from inception to completion.Second, short term forecasting usually employs different methodologies than longer-term forecasting. Mathematical techniques, such as moving average, exponential smoothing, and trend extrapolation are common to short run projections. Broader, less quantitative methods are useful in predicting such issues as whether a new product should be introduced into a companys product line.Finally, as you would expect, short-range forecasts tend to be more accurate than longer range forecasts. Factors that influence demand change every day. Thus, as the time horizon lengthens, it is likely that forecast accuracy will diminish. It almost goes without saying, then, that sales forecasts must be updated regularly to maintain their value and integrity. After each sales period, forecasts should be reviewed and revised.

5/27/201411Prof.Dr.Nahid H.AfiaIntroductionEight steps to forecasting :Determine the use of the forecastwhat objective are we trying to obtain?Select the items or quantities that are to be forecastedDetermine the time horizon of the forecastSelect the forecasting model or modelsGather the data needed to make the forecastValidate the forecasting modelMake the forecastImplement the results 2009 Prentice-Hall, Inc. 5 #IntroductionThese steps are a systematic way of initiating, designing, and implementing a forecasting systemWhen used regularly over time, data is collected routinely and calculations performed automaticallyThere is seldom one superior forecasting systemDifferent organizations may use different techniquesWhatever tool works best for a firm is the one they should use 2009 Prentice-Hall, Inc. 5 #The Realities!Forecasts are seldom perfectMost techniques assume an underlying stability in the systemProduct family and aggregated forecasts are more accurate than individual product forecasts 2006 Prentice Hall, Inc.4 #Types of Forecasting ApproachesStatistical forecasting is based on the assumption that the future will be an extrapolation of the past.Judgmental forecasting relies upon opinions and expertise of people in developing forecasts.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning15Judgmental ForecastingWhen no historical data is available, only judgmental forecasting is possible.The Delphi method consists of forecasting by expert opinion by gathering judgments and opinions of key personnel based on their experience and knowledge of the situation.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning16Judgmental Forecasting (cont.)Another common approach for making a judgemental forecast is to gather data using a consumer survey. Cost of such surveys can be high.The major reasons for using judgmental methods are:Too into future to project current dataAbility to incorporate unusual or one-time eventsThe difficultly of obtaining the data necessary for quantitative techniquesChapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning1717Regression AnalysisMultiple RegressionMovingAverageExponential SmoothingTrend ProjectionsDecomposition

Delphi MethodsJury of Executive OpinionSales ForceCompositeConsumer Market SurveyTime-Series MethodsQualitative ModelsCausal MethodsForecasting ModelsForecasting TechniquesFigure 5.1 2009 Prentice-Hall, Inc. 5 #Time-Series ModelsTime-series models attempt to predict the future based on the pastCommon time-series models areMoving averageExponential smoothingTrend projectionsDecompositionRegression analysis is used in trend projections and one type of decomposition model 2009 Prentice-Hall, Inc. 5 #Causal ModelsCausal models use variables or factors that might influence the quantity being forecastedThe objective is to build a model with the best statistical relationship between the variable being forecast and the independent variablesRegression analysis is the most common technique used in causal modeling 2009 Prentice-Hall, Inc. 5 #Forecasting ApproachesUsed when situation is vague and little data existNew productsNew technologyInvolves intuition, experiencee.g., forecasting sales on Internet Debate if price, e.g. housing prices would go up or down. Qualitative Methods 2006 Prentice Hall, Inc.4 #21Qualitative ModelsQualitative models incorporate judgmental or subjective factorsUseful when subjective factors are thought to be important or when accurate quantitative data is difficult to obtainCommon qualitative techniques areDelphi methodJury of executive opinionSales force compositeConsumer market surveys 2009 Prentice-Hall, Inc. 5 #Qualitative ModelsDelphi Method an iterative group process where (possibly geographically dispersed) respondents provide input to decision makersJury of Executive Opinion collects opinions of a small group of high-level managers, possibly using statistical models for analysisSales Force Composite individual salespersons estimate the sales in their region and the data is compiled at a district or national levelConsumer Market Survey input is solicited from customers or potential customers regarding their purchasing plans

2009 Prentice-Hall, Inc. 5 #Forecasting ApproachesUsed when situation is stable and historical data existExisting productsCurrent technologyInvolves mathematical techniquese.g., forecasting sales of color televisionsQuantitative Methods 2006 Prentice Hall, Inc.4 #24Overview of Quantitative MethodsFive quantitative forecasting methods, all of which use historical data, are described in this chapter. They fall into two categories:1) Time Series Models- Nave approach-Moving averages.- Exponential smoothing-Trend projection2) Associative model-Linear regression5/27/201425Prof.Dr.Nahid H.AfiaThe forecasting technique to be used depend on:variable being forecast.Length of the time horizon over which the forecast to be made.Forecast weekly sales of product.Historical Data.Length of time until a current technology becomes obsolete.Expert Opinion.New technology.Judgment Forecasting.Historical data are available (for long range)Top ManagerTrend Progression and regression models.Seasonal effect (intermediate range)Middle ManagerClassical Decomposition technique.Short range forecasting Operation Manager Exponential Smoothing 5/27/201426Prof.Dr.Nahid H.Afia5/27/201427

Prof.Dr.Nahid H.AfiaForecasting in PracticeManagers use a combination of judgmental and quantitative forecasting techniques.Statistical methods alone cannot account for such factors as sales promotions, competitive strategies, unusual economic disturbances, new products, large one-time orders, natural disasters, or a feel for the data.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning2828Basic Concepts in ForecastingA time series is a set of observations measured at successive points in time or over successive periods of time. A time series pattern may have one or more of the following five characteristics:TrendSeasonal patternsCyclical patternsRandom variation (or noise)Irregular (one time) variationChapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning29Components of DemandDemand for product or service||||1234YearAverage demand over four yearsSeasonal peaksTrend componentActual demandRandom variationFigure 4.1 2006 Prentice Hall, Inc.4 #30Persistent, overall upward or downward patternChanges due to population, technology, age, culture, etc.Typically several years duration Trend Component 2006 Prentice Hall, Inc.4 #31Regular pattern of up and down fluctuationsDue to weather, customs, etc.Occurs within a single year Seasonality in box-office revenuesSeasonal ComponentNumber ofPeriodLengthSeasonsWeekDay7MonthWeek4-4.5MonthDay28-31YearQuarter4YearMonth12YearWeek52 2006 Prentice Hall, Inc.4 #32Exhibit 11.3

Seasonal patterns are characterized by repeatable periods of ups and downs over short periods of time.Seasonal Pattern of Home Natural Gas Usage5/27/201433Prof.Dr.Nahid H.Afia33Trend is the gradual upward or downward movement of the data overtime. Changes in income, population, age distribution, or cultural views may account for movement in trend.Seasonality is a data pattern that repeats itself after a period of days, weeks, months, or quarters. There are 6 common seasonality patterns:

Period of PatternSeason / LengthNumber of Seasons in patternWeekDay7MonthWeek

4MonthDay

28-31YearQuarter4YearMonth

12YearWeek

52#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage LearningRepeating up and down movementsAffected by business cycle, political, and economic factorsMultiple years durationOften causal or associative relationshipsCyclical Component05101520 2006 Prentice Hall, Inc.4 #35

Cyclical patterns are regular patterns in a data series that take place over long periods of time.Exhibit Extra Trend and Business Cycle Characteristics (each data point is 1 year apart)#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning36Erratic, unsystematic, residual fluctuationsDue to random variation or unforeseen eventsShort duration and nonrepeating Random ComponentMTWTF 2006 Prentice Hall, Inc.4 #37Random variation (sometimes called noise) is the unexplained deviation of a time series from a predictable pattern, such as a trend, seasonal, or cyclical pattern. Because of these random variations, forecasts are never 100 percent accurate.Chapter 11 Forecasting and Demand Planning 2006 Prentice Hall, Inc.4 #38Cycles are patterns in the data that occur every several years. They are usually tied into the business cycle and of major importance in short term business analysis and planning.Predicting business cycles is difficult because they may be affected by political events or by international turmoil.

Random Variation are blips in the data caused by chance and unusual situations. They follow no discernible pattern, so they cannot be predicted#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage LearningBasic Concepts in ForecastingIrregular variation is a one-time variation that is explainable. For example, a hurricane can cause a surge in demand for building materials, food, and water.

Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning40Forecast VariationsTrendIrregularvariationCyclesSeasonal variations908988Figure 3-15/27/201441Prof.Dr.Nahid H.AfiaExhibit 11.2

Example of Linear and Nonlinear Trend Patterns5/27/201442Prof.Dr.Nahid H.Afia42Scatter Diagrams

RadiosTelevisionsCompact DiscsScatter diagrams are helpful when forecasting time-series data because they depict the relationship between variables. 2009 Prentice-Hall, Inc. 5 #43Scatter DiagramsWacker Distributors wants to forecast sales for three different productsYEARTELEVISION SETSRADIOSCOMPACT DISC PLAYERS12503001102250310100325032012042503301405250340170625035015072503601608250370190925038020010250390190Table 5.1 2009 Prentice-Hall, Inc. 5 #Scatter DiagramsFigure 5.2330 250 200 150 100 50 ||||||||||012345678910Time (Years)Annual Sales of Televisions(a)Sales appear to be constant over timeSales = 250A good estimate of sales in year 11 is 250 televisions 2009 Prentice-Hall, Inc. 5 #Scatter DiagramsSales appear to be increasing at a constant rate of 10 radios per yearSales = 290 + 10(Year)A reasonable estimate of sales in year 11 is 400 televisions420 400 380 360 340 320 300 280 ||||||||||012345678910Time (Years)Annual Sales of Radios(b)Figure 5.2 2009 Prentice-Hall, Inc. 5 #Scatter DiagramsThis trend line may not be perfectly accurate because of variation from year to yearSales appear to be increasingA forecast would probably be a larger figure each year200 180 160 140 120 100 ||||||||||012345678910Time (Years)Annual Sales of CD Players(c)Figure 5.2 2009 Prentice-Hall, Inc. 5 #Forecast Errors and AccuracyA major difference between MSE and MAD is that MSE is influenced much more by large forecasts errors than by small errors (because the errors are squared).MAPE is different in that the measurement scale factor is eliminated by dividing the absolute error by the time-series data value. This makes the measure easier to interpret.The selection of the best measure of forecast accuracy is not a simple matter; indeed, forecasting experts often disagree on which measure should be used.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning48Forecasting PerformanceMean Forecast Error (MFE or Bias): Measures average deviation of forecast from actuals. Mean Absolute Deviation (MAD): Measures average absolute deviation of forecast from actuals.Mean Absolute Percentage Error (MAPE): Measures absolute error as a percentage of the forecast.Standard Squared Error (MSE): Measures variance of forecast errorHow good is the forecast? Mean Absolute Deviation (MAD)Measures absolute errorPositive and negative errors thus do not cancel out (as with MFE)Want MAD to be as small as possibleNo way to know if MAD error is large or small in relation to the actual data

Mean Squared Error (MSE)Measures squared forecast error -- error varianceRecognizes that large errors are disproportionately more expensive than small errorsBut is not as easily interpreted as MAD, MAPE -- not as intuitive

Mean Absolute Percentage Error (MAPE)Same as MAD, except ...Measures deviation as a percentage of actual data

Want MFE to be as close to zero as possible -- minimum biasA large positive (negative) MFE means that the forecast is undershooting (overshooting) the actual observationsNote that zero MFE does not imply that forecasts are perfect (no error) -- only that mean is on targetAlso called forecast BIASMean Forecast Error (MFE or Bias)

Forecasting Performance Measures

Simple to useVirtually no costData analysis is nonexistentEasily understandableCannot provide high accuracyCan be a standard for accuracyNave Forecasts 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingNaive ApproachAssumes demand in next period is the same as demand in most recent periode.g., If May sales were 48, then June sales will be 48 2006 Prentice Hall, Inc.4 #56Measures of Forecast AccuracyUsing a nave forecasting modelYEARACTUAL SALES OF CD PLAYERSFORECAST SALESABSOLUTE VALUE OF ERRORS (DEVIATION), (ACTUAL FORECAST)11102100110|100 110| = 103120100|120 110| = 204140120|140 120| = 205170140|170 140| = 306150170|150 170| = 207160150|160 150| = 108190160|190 160| = 309200190|200 190| = 1010190200|190 200| = 1011190Sum of |errors| = 160MAD = 160/9 = 17.8Table 5.2 2009 Prentice-Hall, Inc. 5 #Measures of Forecast AccuracyUsing a nave forecasting modelYEARACTUAL SALES OF CD PLAYERSFORECAST SALESABSOLUTE VALUE OF ERRORS (DEVIATION), (ACTUAL FORECAST)11102100110|100 110| = 103120100|120 110| = 204140120|140 120| = 205170140|170 140| = 306150170|150 170| = 207160150|160 150| = 108190160|190 160| = 309200190|200 190| = 1010190200|190 200| = 1011190Sum of |errors| = 160MAD = 160/9 = 17.8Table 5.2

2009 Prentice-Hall, Inc. 5 #

#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning













#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage LearningTechniques for AveragingMoving averageWeighted moving averageExponential smoothing 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingMoving AveragesMoving averages can be used when demand is relatively steady over timeThe next forecast is the average of the most recent n data values from the time series The most recent period of data is added and the oldest is droppedThis methods tends to smooth out short-term irregularities in the data series

2009 Prentice-Hall, Inc. 5 #Moving AveragesMathematically

where= forecast for time period t + 1= actual value in time period tn= number of periods to average

2009 Prentice-Hall, Inc. 5 #Single Moving AverageUsed when demand has no observable trend or seasonality

A moving average (MA) forecast is an average of the most recent n observations in a time series.MA methods work best for short planning horizons when there is no major trend, seasonal, or business cycle pattern.As the value of n increases, the forecast reacts slowly to recent changes in the time series data.Chapter 11 Forecasting and Demand Planning#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning76Wallace Garden Supply ExampleWallace Garden Supply wants to forecast demand for its Storage ShedThey have collected data for the past yearThey are using a three-month moving average to forecast demand (n = 3) 2009 Prentice-Hall, Inc. 5 #Wallace Garden Supply ExampleTable 5.3MONTHACTUAL SHED SALESTHREE-MONTH MOVING AVERAGEJanuary10February12March13April16May19June23July26August30September28October18November16December14January(12 + 13 + 16)/3 = 13.67(13 + 16 + 19)/3 = 16.00(16 + 19 + 23)/3 = 19.33(19 + 23 + 26)/3 = 22.67(23 + 26 + 30)/3 = 26.33(26 + 30 + 28)/3 = 28.00(30 + 28 + 18)/3 = 25.33(28 + 18 + 16)/3 = 20.67(18 + 16 + 14)/3 = 16.00(10 + 12 + 13)/3 = 11.67 2009 Prentice-Hall, Inc. 5 #January10February12March13April16May19June23July26Actual3-MonthMonthShed SalesMoving Average(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3Moving Average Example101213(10 + 12 + 13)/3 = 11 2/3 2006 Prentice Hall, Inc.4 #Graph of Moving Average||||||||||||JFMAMJJASONDShed Sales30 28 26 24 22 20 18 16 14 12 10 Actual SalesMoving Average Forecast 2006 Prentice Hall, Inc.4 #80

5/27/201481Prof.Dr.Nahid H.AfiaWeighted Moving AveragesWeighted moving averages use weights to put more emphasis on recent periodsOften used when a trend or other pattern is emerging

Mathematically

wherewi= weight for the ith observation 2009 Prentice-Hall, Inc. 5 #Weighted Moving AveragesBoth simple and weighted averages are effective in smoothing out fluctuations in the demand pattern in order to provide stable estimatesProblemsIncreasing the size of n smoothes out fluctuations better, but makes the method less sensitive to real changes in the dataMoving averages can not pick up trends very well they will always stay within past levels and not predict a change to a higher or lower level 2009 Prentice-Hall, Inc. 5 #Wallace Garden Supply ExampleWallace Garden Supply decides to try a weighted moving average model to forecast demand for its Storage ShedThey decide on the following weighting schemeWEIGHTS APPLIEDPERIOD3Last month2Two months ago1Three months ago6

3 x Sales last month + 2 x Sales two months ago + 1 X Sales three months agoSum of the weights 2009 Prentice-Hall, Inc. 5 #Used when trend is present Older data usually less importantWeights based on experience and intuitionWeighted Moving AverageWeightedmoving average= (weight for period n) x (demand in period n) weights 2006 Prentice Hall, Inc.4 #85January10February12March13April16May19June23July26Actual3-Month WeightedMonthShed SalesMoving Average[(3 x 16) + (2 x 13) + (12)]/6 = 141/3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2Weighted Moving Average101213[(3 x 13) + (2 x 12) + (10)]/6 = 121/6Weights AppliedPeriod3Last month2Two months ago1Three months ago6Sum of weights 2006 Prentice Hall, Inc.4 #Increasing n smooths the forecast but makes it less sensitive to changesDo not forecast trends well why?Require extensive historical dataPotential Problems With Moving Average 2006 Prentice Hall, Inc.4 #87Moving Average And Weighted Moving Average30 25 20 15 10 5 Sales demand||||||||||||JFMAMJJASONDActual salesMoving averageWeighted moving averageFigure 4.2 2006 Prentice Hall, Inc.4 #88Simple Moving Average ForecastingNot Single moving averageA type of statistical forecast (projects past data into future)An average of the most recent n-periodsFt+1 = (Dt + Dt-1 + Dt-2) / 3D is actual or observed dataFor a 3-period moving average forecastBest for short-term, stable dataThe larger the n, the smoother the forecast 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting89

3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting5/27/201491

Prof.Dr.Nahid H.AfiaSimple Moving AverageFigure 3-4MAn = nDii = 1n

ActualMA3MA55/27/201492Prof.Dr.Nahid H.AfiaExhibit 11.7

Summary of 3-Month Moving-Average Forecasts5/27/201493Prof.Dr.Nahid H.Afia93Exhibit 11.8

Milk Sales Forecast Error Analysis5/27/201494Prof.Dr.Nahid H.Afia94Simple Exponential Smoothing Forecast -- a forecasting technique that uses a weighted average of previous period's forecast and demand. Simple not SingleChapter 11 Forecasting and Demand Planningsmoothes out the irregular fluctuations in the time series.Ft+1 = Ft + (A t Ft)Ft+1 = A t + (1- ) Ft = smoothing constant (0 to 1) Must guess for F1 (typically = A1)5/27/201495Prof.Dr.Nahid H.Afia9595For short termForm of weighted moving averageWeights decline exponentiallyMost recent data weighted mostRequires smoothing constant ()Ranges from 0 to 1Subjectively chosenInvolves little record keeping of past dataExponential Smoothing 2006 Prentice Hall, Inc.4 #96Exponential SmoothingNew forecast =last periods forecast+ a (last periods actual demand last periods forecast)Ft = Ft 1 + a(At 1 - Ft 1)whereFt=new forecastFt 1=previous forecasta=smoothing (or weighting) constant (0 a 1) 2006 Prentice Hall, Inc.4 #97

Smoothing Constant

2006 Prentice Hall, Inc.4 #98Exponential Smoothing ExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20 2006 Prentice Hall, Inc.4 #99Exponential Smoothing ExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20New forecast= 142 + .2(153 142) 2006 Prentice Hall, Inc.4 #100Exponential Smoothing ExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20New forecast= 142 + .2(153 142)= 142 + 2.2= 144.2 144 cars 2006 Prentice Hall, Inc.4 #101Single Exponential Smoothing (SES) is a forecasting technique that uses a weighted average of past time-series values to forecast the value of the time series in the next period.Chapter 11 Forecasting and Demand PlanningThe forecast smoothes out the irregular fluctuations in the time series.5/27/2014102Prof.Dr.Nahid H.Afia102Exponential SmoothingPremise--The most recent observations might have the highest predictive value.Therefore, we should give more weight to the more recent time periods when forecasting.Ft = Ft-1 + (At-1 - Ft-1) 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting

3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingExponential Smoothing IInclude all past observationsWeight recent observations much more heavily than very old observations:weighttodayDecreasing weight given to older observationsExponential Smoothing IInclude all past observationsWeight recent observations much more heavily than very old observations:weighttodayDecreasing weight given to older observations

Exponential Smoothing IInclude all past observationsWeight recent observations much more heavily than very old observations:weighttodayDecreasing weight given to older observations

Exponential Smoothing IInclude all past observationsWeight recent observations much more heavily than very old observations:weighttodayDecreasing weight given to older observations

Exponential Smoothing: ConceptInclude all past observationsWeight recent observations much more heavily than very old observations:weighttodayDecreasing weight given to older observations

The smoothing constant is generally in the range from .05 t0 .50 for business applications. It can be changed to give more weight to recent data when is high or more weight to the past data when is low.

When it reaches the extreme of 1 then the equation (3-2a) will be:

Ft = 1.0 (At-1)

All the older values drop out, and the forecast becomes identical to the nave model mentioned earlier.That is, the forecast for the next period is just the same as this periods demand.

5/27/2014110Prof.Dr.Nahid H.Afia

3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingExponential SmoothingNew forecast is weighted sum of old forecast and actual demandNotes:Only 2 values (At and Ft-1 ) are required, compared with n for moving averageParameter a determined empirically (whatever works best)Rule of thumb: < 0.5Typically, = 0.2 or = 0.3 work well

3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting

3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting

Example of Exponential Smoothing5/27/2014115Prof.Dr.Nahid H.AfiaFt = Ft-1 + (Dt-1 - Ft-1)

= 0.1F1 = 42 + 0.1(42 42) = 42F2 = 42 + 0.1 (40 42) = 41.8F3 = 41.8 + 0.1 (43 41.8) = 41.92F4 = 41.92 + 0.1 (40 41.92) = 41.728..F12 = = 41.73

5/27/2014116Prof.Dr.Nahid H.AfiaPicking a Smoothing Constant

.1.4Actual5/27/2014117Prof.Dr.Nahid H.AfiaExhibit 11.9 Summary of Single Exponential Smoothing Milk SalesForecasts with = 0.2

3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting118

Exhibit 11.10 Graph of Single Exponential Smoothing Milk Sales Forecasts with = 0.2 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting119Exhibit 11.6

Forecast Error of Example Time Series Data#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage Learning120Choosing The objective is to obtain the most accurate forecast no matter the techniqueWe generally do this by selecting the model that gives us the lowest forecast errorForecast error= Actual demand - Forecast value= At - Ft 2006 Prentice Hall, Inc.4 #121Common Measures of ErrorMean Absolute Deviation (MAD)MAD = |actual - forecast|nMean Squared Error (MSE)MSE = (forecast errors)2n 2006 Prentice Hall, Inc.4 #Common Measures of ErrorMean Absolute Percent Error (MAPE)MAPE =100 |actuali - forecasti|/actualinni = 1 2006 Prentice Hall, Inc.4 #Comparison of Forecast Error RoundedAbsoluteRoundedAbsoluteActualForecastDeviationForecastDeviationTonnagewithforwithforQuarterUnloadeda = .10a = .10a = .50a = .501180175517552168176817810315917516173144175173216695190173171702062051753018025718017821931381821784186484100 2006 Prentice Hall, Inc.4 #Comparison of Forecast Error RoundedAbsoluteRoundedAbsoluteActualForecastDeviationForecastDeviationTonnagewithforwithforQuarterUnloadeda = .10a = .10a = .50a = .501180175517552168176817810315917516173144175173216695190173171702062051753018025718017821931381821784186484100MAD10.5012.50MSE194.75201.50MAPE5.70%6.85% 2006 Prentice Hall, Inc.4 #Exponential Smoothing with Trend AdjustmentWhen a trend is present, exponential smoothing must be modifiedForecast including (FITt) = trendexponentiallyexponentiallysmoothed (Ft) +(Tt)smoothedforecasttrend 2006 Prentice Hall, Inc.4 #126Exponential Smoothing with Trend AdjustmentFt = a(At - 1) + (1 - a)(Ft - 1 + Tt - 1)Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1Step 1: Compute FtStep 2: Compute TtStep 3: Calculate the forecast FITt = Ft + Tt 2006 Prentice Hall, Inc.4 #127Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021732041952462173182893610Table 4.1 2006 Prentice Hall, Inc.4 #128Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021732041952462173182893610Table 4.1F2 = aA1 + (1 - a)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)= 2.4 + 10.4 = 12.8 unitsStep 1: Forecast for Month 2 2006 Prentice Hall, Inc.4 #129Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.8032041952462173182893610Table 4.1T2 = b(F2 - F1) + (1 - b)T1T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 unitsStep 2: Trend for Month 2 2006 Prentice Hall, Inc.4 #130Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.801.9232041952462173182893610Table 4.1FIT2 = F2 + T1FIT2 = 12.8 + 1.92= 14.72 unitsStep 3: Calculate FIT for Month 2 2006 Prentice Hall, Inc.4 #131Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.801.9214.7232041952462173182893610Table 4.115.182.1017.2817.822.3220.1419.912.2322.1422.512.3824.8924.112.0726.1827.142.4529.5929.282.3231.6032.482.6835.16 2006 Prentice Hall, Inc.4 #132Trend ProjectionsFitting a trend line to historical data points to project into the medium-to-long-rangeLinear trends can be found using the least squares techniquey = a + bx^where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable^ 2006 Prentice Hall, Inc.4 #133Least Squares MethodTime periodValues of Dependent VariableFigure 4.4Deviation1Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation (y value)Trend line, y = a + bx^ 2006 Prentice Hall, Inc.4 #134Least Squares MethodTime periodValues of Dependent VariableFigure 4.4Deviation1Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation (y value)Trend line, y = a + bx^Least squares method minimizes the sum of the squared errors (deviations) 2006 Prentice Hall, Inc.4 #135Least Squares MethodEquations to calculate the regression variablesb =Sxy - nxySx2 - nx2y = a + bx^a = y - bx 2006 Prentice Hall, Inc.4 #136Least Squares Exampleb = = = 10.54xy - nxyx2 - nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70TimeElectrical Power YearPeriod (x)Demandx2xy19991741742000279415820013809240200249016360200351052552520046142368522005712249854x = 28y = 692x2 = 140xy = 3,063x = 4y = 98.86 2006 Prentice Hall, Inc.4 #137Least Squares Exampleb = = = 10.54Sxy - nxySx2 - nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70TimeElectrical Power YearPeriod (x)Demandx2xy19991741742000279415820013809240200249016360200351052552520046142368522005712249854Sx = 28Sy = 692Sx2 = 140Sxy = 3,063x = 4y = 98.86The trend line isy = 56.70 + 10.54x^ 2006 Prentice Hall, Inc.4 #138Least Squares RequirementsWe always plot the data to insure a linear relationshipWe do not predict time periods far beyond the databaseDeviations around the least squares line are assumed to be random 2006 Prentice Hall, Inc.4 #139Associative ForecastingPredictor variables - used to predict values of variable interestRegression - technique for fitting a line to a set of pointsLeast squares line - minimizes sum of squared deviations around the line 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingRegression analysis is a method for building a statistical model that defines a relationship between a single dependent variable and one or more independent variables, all of which are numerical.Yt = a + bt(11.7)Simple linear regression finds the best values of a and b using the method of least squares.Excel provides a very simple tool to find the best-fitting regression model for a time series by selecting the Add Trendline option from the Chart menu.Chapter 11 Forecasting and Demand Planning 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.Forecasting141Linear Trend Equationb is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope.Yt = a + bt0 1 2 3 4 5 tY 3-#McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.ForecastingCalculating a and bb = n (ty) - tynt2 - (t)2a = y - btn5/27/2014143Prof.Dr.Nahid H.AfiaLinear Trend Equation Example

5/27/2014144Prof.Dr.Nahid H.AfiaLinear Trend Calculationy = 143.5 + 6.3t a = 812 - 6.3(15)5 =b = 5 (2499) - 15(812)5(55) - 225 = 12495-12180275-225 = 6.3143.5 5/27/2014145Prof.Dr.Nahid H.Afia5/27/2014146

Prof.Dr.Nahid H.Afia5/27/2014147






Prof.Dr.Nahid H.AfiaCorrelation0.9 1.00very high correlation0.7 0.9 High correlation0.4 0.7Moderate correlation0.2 0.4Low correlation0 0.2Slight5/27/2014#OM, Ch. 11 Forecasting and Demand Planning2009 South-Western, a part of Cengage LearningStandard Error of the Estimate4.0 3.0 2.0 1.0

|||||||01234567SalesArea payroll3.25Sy,x = =y2 - ay - bxyn - 239.5 - 1.75(15) - .25(51.5)6 - 2Sy,x = .306The standard error of the estimate is $30,600 in sales 2006 Prentice Hall, Inc.4 #How strong is the linear relationship between the variables?Correlation does not necessarily imply causality!Coefficient of correlation, r, measures degree of associationValues range from -1 to +1Correlation 2006 Prentice Hall, Inc.4 #155Correlation Coefficientr = nSxy - SxSy [nSx2 - (Sx)2][nSy2 - (Sy)2] 2006 Prentice Hall, Inc.4 #156Correlation Coefficientr = nxy - xy [nx2 - (x)2][ny2 - (y)2]yx(a)Perfect positive correlation: r = +1yx(b)Positive correlation: 0 < r < 1yx(c)No correlation: r = 0yx(d)Perfect negative correlation: r = -1 2006 Prentice Hall, Inc.4 #157Coefficient of Determination, r2, measures the percent of change in y predicted by the change in xValues range from 0 to 1Easy to interpretCorrelationFor the Nodel Construction example:r = .901r2 = .81 2006 Prentice Hall, Inc.4 #158Associative ForecastingUsed when changes in one or more independent variables can be used to predict the changes in the dependent variableMost common technique is linear regression analysisWe apply this technique just as we did in the time series example 2006 Prentice Hall, Inc.4 #Associative ForecastingForecasting an outcome based on predictor variables using the least squares techniquey = a + bx^where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable though to predict the value of the dependent variable^ 2006 Prentice Hall, Inc.4 #160Associative Forecasting ExampleSales, y Payroll, xx2xy2.0112.03.0399.02.541610.02.0244.02.0112.03.574924.5y = 15.0x = 18x2 = 80xy = 51.5x = x/6 = 18/6 = 3y = y/6 = 15/6 = 2.5b = = = .25xy - nxyx2 - nx251.5 - (6)(3)(2.5)80 - (6)(32)a = y - bx = 2.5 - (.25)(3) = 1.75 2006 Prentice Hall, Inc.4 #Associative Forecasting Example4.0 3.0 2.0 1.0

|||||||01234567SalesArea payrolly = 1.75 + .25x^Sales = 1.75 + .25(payroll)If payroll next year is estimated to be $600 million, then:Sales = 1.75 + .25(6)Sales = $325,0003.25 2006 Prentice Hall, Inc.4 #Standard Error of the EstimateA forecast is just a point estimate of a future valueThis point is actually the mean of a probability distributionFigure 4.94.0 3.0 2.0 1.0

|||||||01234567SalesArea payroll3.25 2006 Prentice Hall, Inc.4 #Standard Error of the Estimatewherey=y-value of each data pointyc=computed value of the dependent variable, from the regression equationn=number of data pointsSy,x =(y - yc)2n - 2 2006 Prentice Hall, Inc.4 #Standard Error of the EstimateComputationally, this equation is considerably easier to useWe use the standard error to set up prediction intervals around the point estimateSy,x =y2 - ay - bxyn - 2 2006 Prentice Hall, Inc.4 #Standard Error of the Estimate4.0 3.0 2.0 1.0

|||||||01234567SalesArea payroll3.25Sy,x = =y2 - ay - bxyn - 239.5 - 1.75(15) - .25(51.5)6 - 2Sy,x = .306The standard error of the estimate is $30,600 in sales 2006 Prentice Hall, Inc.4 #5/27/2014167



Prof.Dr.Nahid H.Afia5/27/2014170b = n (x y) - xynx2 - (x)2a = y - bxnCalculating a and bProf.Dr.Nahid H.AfiaDecomposition of a Time-SeriesA time series typically has four componentsTrend (T) is the gradual upward or downward movement of the data over timeSeasonality (S) is a pattern of demand fluctuations above or below trend line that repeats at regular intervalsCycles (C) are patterns in annual data that occur every several yearsRandom variations (R) are blips in the data caused by chance and unusual situations 2009 Prentice-Hall, Inc. 5 #Decomposition of a Time-SeriesAverage Demand over 4 YearsTrend ComponentActual Demand LineTimeDemand for Product or Service||||YearYearYearYear1234Seasonal PeaksFigure 5.3 2009 Prentice-Hall, Inc. 5 #Decomposition of a Time-SeriesThere are two general forms of time-series modelsThe multiplicative modelDemand = T x S x C x RThe additive modelDemand = T + S + C + RModels may be combinations of these two formsForecasters often assume errors are normally distributed with a mean of zero 2009 Prentice-Hall, Inc. 5 #5/27/2014174Prof.Dr.Nahid H.Afia5/27/2014175Prof.Dr.Nahid H.Afia175Chart12502900250300110250310100250320118250330138250340162250350145250360150250370184250380190250390188

Time (Years)Annual Sales

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Time (Years)Annual Sales

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Chart1424042424341.841.24041.9241.924141.72841.1523941.655241.09124641.3896840.254724441.85071242.5528324542.065640843.13169923842.3590767243.879019524041.92316904841.52741171241.730852143240.9164470272



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tyWeekt2Salesty111501502415731439162486416166664525177885S t = 15S t2 = 55S y = 812S ty = 2499(S t)2 = 225

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2-Forecasting 4auto Modified 11 Mars 2014