Demand forecasting methods2 gp
- 1. Demand Forecasting Methods Professor & Lawyer.Professor & Lawyer. Puttu Guru Prasad,Puttu Guru Prasad, M.Com. M.B.A., L.L.B., M.Phil, PGDFTM, APSET.M.Com. M.B.A., L.L.B., M.Phil, PGDFTM, APSET. ICFAI TMF, (PhD) at JNTUK,ICFAI TMF, (PhD) at JNTUK, Expert Resource person at APHRDI, Bapatla,Expert Resource person at APHRDI, Bapatla, Senior Faculty for Management Studies,Senior Faculty for Management Studies, Certified NSS Program Officer,Certified NSS Program Officer, Coordinator – College BeautificationCoordinator – College Beautification S&HS&H Department,Department, VVIT,VVIT, Nambur,Nambur, 93 94 96 98 98, 807 444 95 39,93 94 96 98 98, 807 444 95 39, My Blog: puttuguru.blogspot.inMy Blog: puttuguru.blogspot.in
- 2. MGMT6020Forecast Learning Objectives When you complete this chapter, you should be able to : Identify or DefineIdentify or Define:: ForecastingForecasting Categories of forecastsCategories of forecasts Time horizonsTime horizons Approaches to measure forecastsApproaches to measure forecasts Explain and Apply:Explain and Apply: Moving averagesMoving averages Exponential smoothingExponential smoothing Trend and seasonal projectionsTrend and seasonal projections Measures of forecast accuracyMeasures of forecast accuracy
- 3. MGMT6020Forecast Why Forecasting? Forecasting lays a ground for reducing the risk inForecasting lays a ground for reducing the risk in all decision making because many of the decisionsall decision making because many of the decisions need to be made under uncertainty.need to be made under uncertainty. In business applications, forecasting serves as aIn business applications, forecasting serves as a starting point of major decisions in finance,starting point of major decisions in finance, marketing, productions, and purchasing.marketing, productions, and purchasing. Under what condition there is no value forUnder what condition there is no value for forecasting?forecasting?
- 4. MGMT6020Forecast Decisions Relevant to Demand Forecasts Select product portfolioSelect product portfolio Predicting new facility locationPredicting new facility location Anticipating capacity needsAnticipating capacity needs Identifying labor requirementsIdentifying labor requirements Projecting material requirementsProjecting material requirements Developing production schedulesDeveloping production schedules Creating maintenance schedulesCreating maintenance schedules
- 5. MGMT6020Forecast Forecasting at Tupperware Via forecasting, managers make importantVia forecasting, managers make important decisionsdecisions Each of 50 profit centers around the world isEach of 50 profit centers around the world is responsible for computerized monthly,responsible for computerized monthly, quarterly, and 12-month sales projectionsquarterly, and 12-month sales projections These projections are aggregated by productThese projections are aggregated by product family and region, then globally, atfamily and region, then globally, at Tupperware’s World HeadquartersTupperware’s World Headquarters Tupperware uses all techniques discussed in textTupperware uses all techniques discussed in text
- 6. MGMT6020Forecast Successful Forecasting = Science + Art "Science" implies that the body of the forecasting"Science" implies that the body of the forecasting knowledge lies on the solid ground of quantitativeknowledge lies on the solid ground of quantitative forecasting methods and their correct utilization forforecasting methods and their correct utilization for various business situations.various business situations. "Art" represents a combination of a decision"Art" represents a combination of a decision maker's experience, logic, and intuition tomaker's experience, logic, and intuition to supplement the forecasting quantitative analysis.supplement the forecasting quantitative analysis. Both the science and art of forecasting are essentialBoth the science and art of forecasting are essential in developing accurate forecasts.in developing accurate forecasts. All managers are forecasters!All managers are forecasters!
- 7. MGMT6020Forecast Forecast Categories TYPESTYPES QualitativeQualitative Executive opinionsExecutive opinions Sales force surveysSales force surveys Delphi methodDelphi method Consumer surveysConsumer surveys QuantitativeQuantitative Times series methodsTimes series methods Associative (causal)Associative (causal) methodsmethods
- 8. MGMT6020Forecast Forecast Categories TIME HORIZONTIME HORIZON Long-termLong-term For duration of 3-5For duration of 3-5 years or more (onyears or more (on annual basis)annual basis) Medium-termMedium-term For duration of up to threeFor duration of up to three years (usually on quarterlyyears (usually on quarterly or monthly basis)or monthly basis) Short-termShort-term Up to one year, usually lessUp to one year, usually less than three months (onthan three months (on daily, weekly)daily, weekly)
- 9. MGMT6020Forecast Facts in Forecasting Main assumption: Past pattern repeats itself into the future. Forecasts are rarely perfect: Don't expect forecasts to be exactly equal to the actual data. The science and art of forecasting try to minimize, but not to eliminate, forecast errors. Forecast errors mean the difference between actual and forecasted values. Forecasts for a group of products are usually more accurate than these for individual products; a shorter period tend to be more accurate. Computer and IT are critical parts of the modern forecasting in large corporations.
- 10. MGMT6020Forecast Seven Steps in Forecasting (Demands) Determine the use of the forecastDetermine the use of the forecast Select the items to be forecastSelect the items to be forecast Determine the time horizon of the forecastDetermine the time horizon of the forecast 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
- 11. MGMT6020Forecast Quantitative Methods A time series is an uninterrupted set of dataA time series is an uninterrupted set of data observations that have been ordered inobservations that have been ordered in equally spaced intervals (units of time).equally spaced intervals (units of time). Associative (causal) forecasting is based onAssociative (causal) forecasting is based on identification of variables (factors) that canidentification of variables (factors) that can predict values of the variable in question.predict values of the variable in question.
- 12. MGMT6020Forecast Quantitative Forecasting Models ·· Time Series ModelsTime Series Models Naive ForecastNaive Forecast Simple Moving AveragesSimple Moving Averages Weighted Moving AveragesWeighted Moving Averages Simple Exponential SmoothingSimple Exponential Smoothing Exponential Smoothing withExponential Smoothing with TrendTrend Linear Trend ProjectionLinear Trend Projection Time Series DecompositionTime Series Decomposition ·· Associative (Causal)Associative (Causal) ModelsModels Simple Linear RegressionSimple Linear Regression Multiple Linear RegressionMultiple Linear Regression Nonlinear RegressionNonlinear Regression
- 13. MGMT6020Forecast Time Series Pattern: Stationary The result of manyThe result of many influences that actinfluences that act independently so as toindependently so as to yield nonsystematicyield nonsystematic and non-repeatingand non-repeating patterns about somepatterns about some average value.average value. Forecasting methods:Forecasting methods: naive, moving average,naive, moving average, exponential smoothingexponential smoothing
- 14. MGMT6020Forecast Time Series Pattern: Trend It represents a generalIt represents a general increase or decrease inincrease or decrease in a time series overa time series over several consecutiveseveral consecutive periods (some sourcesperiods (some sources present six-seven orpresent six-seven or more periods).more periods). Forecasting methods:Forecasting methods: linear trend projection,linear trend projection, exponential smoothingexponential smoothing with trend, etc.with trend, etc.
- 15. MGMT6020Forecast Time Series Pattern: Seasonal Seasonal PatternsSeasonal Patterns represent patterns thatrepresent patterns that are periodic andare periodic and recurrent (usually on arecurrent (usually on a quarterly, monthly, orquarterly, monthly, or annual basis).annual basis). Forecasting methods:Forecasting methods: exponential smoothingexponential smoothing with trend andwith trend and seasonality, time seriesseasonality, time series decomposition, etc.decomposition, etc.
- 16. MGMT6020Forecast Time Series Pattern: Cyclical The result of economic andThe result of economic and business expansions (increasingbusiness expansions (increasing demand) and contractionsdemand) and contractions (recessions and depressions)(recessions and depressions) and usually repeat every two-and usually repeat every two- five years. Cyclical influencesfive years. Cyclical influences are difficult to forecast becauseare difficult to forecast because cyclical demands are recurrentcyclical demands are recurrent but not periodic (they happen inbut not periodic (they happen in different intervals of time withdifferent intervals of time with great variability of demands).great variability of demands). Forecasting methods: timeForecasting methods: time series decomposition, multipleseries decomposition, multiple regressionregression
- 17. MGMT6020Forecast Product Demand Charted over 4 Years with Trend and Seasonality Year 1 Year 2 Year 3 Year 4 Seasonal peaks Trend component Actual demand line Average demand over four years Demandforproductorservice Random variation
- 18. MGMT6020Forecast Set of evenly spaced numerical dataSet of evenly spaced numerical data Obtained by observing response variable atObtained by observing response variable at regular time periodsregular time periods Forecast based only on past valuesForecast based only on past values Assumes that factors influencing past andAssumes that factors influencing past and present will continue influence in futurepresent will continue influence in future ExampleExample Year:Year: 19931993 19941994 19951995 19961996 19971997 Sales:Sales: 78.778.7 63.563.5 89.789.7 93.293.2 92.192.1 What is a Time Series?
- 19. MGMT6020Forecast Naïve Approach Assumes demand in next period is the same asAssumes demand in next period is the same as demand in most recent perioddemand in most recent period e.g., If May sales were 48, then June sales will bee.g., If May sales were 48, then June sales will be around 48around 48 Sometimes it is effective & cost efficientSometimes it is effective & cost efficient e.g. when the demand is steady or changes slowlye.g. when the demand is steady or changes slowly when inventory cost is lowwhen inventory cost is low when unmet demand will not losewhen unmet demand will not lose
- 20. MGMT6020Forecast MA is a series of arithmetic meansMA is a series of arithmetic means Used if little or no trend, seasonal, and cyclicalUsed if little or no trend, seasonal, and cyclical patternspatterns Used oftenUsed often for smoothingfor smoothing Provides overall impression of data over timeProvides overall impression of data over time EquationEquation MAMA nn nn == ∑∑ Demand inDemand in PreviousPrevious PeriodsPeriods Moving Average Method
- 21. MGMT6020Forecast You’re manager of a museum store that sellsYou’re manager of a museum store that sells historical replicas. You want to forecast saleshistorical replicas. You want to forecast sales of item (123) forof item (123) for 20002000 using ausing a 33-period moving-period moving average.average. 19951995 44 19961996 66 19971997 55 19981998 33 19991999 77 © 1995 Corel Corp. Moving Average Example
- 22. MGMT6020Forecast Moving Average Solution Time Response Yi Moving Total (n=3) Moving Average (n=3) 1995 4 NA NA 1996 6 NA NA 1997 5 NA NA 1998 3 4+6+5=15 15/3 = 5 1999 7 2000 NA
- 23. MGMT6020Forecast Moving Average Solution Time Response Yi Moving Total (n=3) Moving Average (n=3) 1995 4 NA NA 1996 6 NA NA 1997 5 NA NA 1998 3 4+6+5=15 15/3 = 5 1999 7 6+5+3=14 14/3=4 2/3 2000 NA
- 24. MGMT6020Forecast Moving Average Solution Time Response Yi Moving Total (n=3) Moving Average (n=3) 1995 4 NA NA 1996 6 NA NA 1997 5 NA NA 1998 3 4+6+5=15 15/3=5.0 1999 7 6+5+3=14 14/3=4.7 2000 NA 5+3+7=15 15/3=5.0
- 25. MGMT6020Forecast 95 96 97 98 99 00 Year Sales 2 4 6 8 Actual Forecast Moving Average Graph
- 26. MGMT6020Forecast Used when trend is presentUsed when trend is present Older data usually less importantOlder data usually less important Weights based on intuitionWeights based on intuition Often lay between 0 & 1, & sum to 1.0Often lay between 0 & 1, & sum to 1.0 EquationEquation WMA =WMA = ΣΣ(Weight for period(Weight for period nn) (Demand in period) (Demand in period nn)) ΣΣWeightsWeights Weighted Moving Average Method
- 27. MGMT6020Forecast Actual Demand, Moving Average, Weighted Moving Average 0 5 10 15 20 25 30 35 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month SalesDemand Actual sales Moving average Weighted moving average
- 28. MGMT6020Forecast IncreasingIncreasing nn makes forecast less sensitivemakes forecast less sensitive to changesto changes Do not forecast trend well due to the delayDo not forecast trend well due to the delay between actual outcome and forecastbetween actual outcome and forecast Difficult to trace seasonal and cyclicalDifficult to trace seasonal and cyclical patternspatterns Require much historical dataRequire much historical data Weighted MA may perform betterWeighted MA may perform better Disadvantages of Moving Average Methods
- 29. MGMT6020Forecast Form of weighted moving averageForm of weighted moving average Weights decline exponentiallyWeights decline exponentially Most recent data weighted mostMost recent data weighted most Requires smoothing constant (Requires smoothing constant (αα)) Ranges from 0 to 1Ranges from 0 to 1 Subjectively chosenSubjectively chosen Involves little record keeping of past dataInvolves little record keeping of past data Exponential Smoothing Method
- 30. MGMT6020Forecast FFtt == FFtt-1-1 ++ αα((AAtt-1-1 -- FFtt-1-1)) == ααAAtt-1-1 + (1 -+ (1 - αα)) FFtt-1-1 FFtt = Forecast value= Forecast value AAtt = Actual value= Actual value αα = Smoothing constant= Smoothing constant FFtt == ααAAtt - 1- 1 ++ αα(1-(1-αα))AAtt - 2- 2 ++ αα(1-(1- αα))22 ·A·Att - 3- 3 ++ αα(1-(1- αα))33 AAtt - 4- 4 + ... ++ ... + αα(1-(1- αα))t-t-11 ·A·A00 Use for computing forecastUse for computing forecast Exponential Smoothing Equations
- 31. MGMT6020Forecast You’re organizing a Kwanza meeting. YouYou’re organizing a Kwanza meeting. You want to forecast attendance forwant to forecast attendance for 20002000 usingusing exponential smoothing (exponential smoothing (αα = .10= .10). The). The 1995 (made in 1994) forecast was1995 (made in 1994) forecast was 175175.. Actual data:Actual data: 19951995 180180 19961996 168168 19971997 159159 19981998 175175 19991999 190190 © 1995 Corel Corp. Exponential Smoothing Example
- 32. MGMT6020Forecast Ft = Ft-1 + α ·(At-1 - Ft-1) TimeTime Actual Forecast, Ft (αα == .10.10)) 19951995 180 175.00 (Given) 19961996 168168 19971997 159159 19981998 175175 19991999 190190 20002000 NANA 175.00 +175.00 + Exponential Smoothing Solution
- 33. MGMT6020Forecast Exponential Smoothing Solution TimeTime Actual Forecast, Ft (αα == .10.10)) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 +175.00 + .10.10(( 19971997 159159 19981998 175175 19991999 190190 20002000 NANA Ft = Ft-1 + α ·(At-1 - Ft-1)
- 34. MGMT6020Forecast Exponential Smoothing Solution TimeTime ActualActual Forecast,Forecast, FFtt ((αα == .10.10)) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 +175.00 + .10.10(180(180 -- 19971997 159159 19981998 175175 19991999 190190 20002000 NANA Ft = Ft-1 + α ·(At-1 - Ft-1)
- 35. MGMT6020Forecast Exponential Smoothing Solution Time Actual Forecast, Ft (αα == .10.10)) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 +175.00 + .10.10(180(180 - 175.00- 175.00)) 19971997 159159 19981998 175175 19991999 190190 20002000 NANA Ft = Ft-1 + α ·(At-1 - Ft-1)
- 36. MGMT6020Forecast Exponential Smoothing Solution TimeTime ActualActual Forecast,Forecast, FFtt ((αα == .10.10)) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 +175.00 + .10.10(180(180 - 175.00- 175.00)) = 175.50= 175.50 19971997 159159 19981998 175175 19991999 190190 20002000 NANA Ft = Ft-1 + α ·(At-1 - Ft-1)
- 37. MGMT6020Forecast Exponential Smoothing Solution Time Actual Forecast, Ft (αα == .10.10)) 1995 180 175.00 (Given) 19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50 19971997 159159 175.50175.50 ++ .10.10(168 -(168 - 175.50175.50)) = 174.75= 174.75 19981998 175175 19991999 190190 20002000 NANA Ft = Ft-1 + α ·(At-1 - Ft-1)
- 38. MGMT6020Forecast Exponential Smoothing Solution Time Actual Forecast, Ft (α = .10) 19951995 180180 175.00 (Given)175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75 19981998 175175 19991999 190190 20002000 NANA 174.75174.75 ++ .10.10(159(159 -- 174.75174.75))= 173.18= 173.18 Ft = Ft-1 + α ·(At-1 - Ft-1)
- 39. MGMT6020Forecast Exponential Smoothing Solution Time Actual Forecast, Ft (α = .10) 1995 180 175.00 (Given) 19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50 19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75 19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18 19991999 190190 173.18 +173.18 + .10.10(175(175 - 173.18- 173.18)) = 173.36= 173.36 20002000 NANA Ft = Ft-1 + α ·(At-1 - Ft-1)
- 40. MGMT6020Forecast Exponential Smoothing Solution Time Actual Forecast, Ft (α = .10) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50 19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75 19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18 19991999 190190 173.18 + .10(175 - 173.18) = 173.36173.18 + .10(175 - 173.18) = 173.36 20002000 NANA 173.36173.36 ++ .10.10(190(190 - 173.36- 173.36) = 175.02) = 175.02 Ft = Ft-1 + α ·(At-1 - Ft-1)
- 41. MGMT6020Forecast Year Sales 140 150 160 170 180 190 93 94 95 96 97 98 Actual Forecast Exponential Smoothing Graph
- 42. MGMT6020Forecast Ft = α At - 1 + α(1- α)At - 2 + α(1- α)2 At - 3 + ... Forecast Effects of Smoothing Constant α Weights Prior Period α 2 periods ago α(1 - α) 3 periods ago α(1 - α)2 α= α= 0.10 α= 0.90 10%
- 43. MGMT6020Forecast Ft = α At - 1 + α(1- α) At - 2 + α(1- α)2 At - 3 + ... Forecast Effects of Smoothing Constant α Weights Prior Period α 2 periods ago α(1 - α) 3 periods ago α(1 - α)2 α= α= 0.10 α= 0.90 10% 9%
- 44. MGMT6020Forecast Ft = α At - 1 + α(1- α)At - 2 + α(1- α)2 At - 3 + ... Forecast Effects of Smoothing Constant α Weights Prior Period α 2 periods ago α(1 - α) 3 periods ago α(1 - α)2 α= α= 0.10 α= 0.90 10% 9% 8.1%
- 45. MGMT6020Forecast Ft = α At - 1 + α(1- α)At - 2 + α(1- α)2 At - 3 + ... Forecast Effects of Smoothing Constant α Weights Prior Period α 2 periods ago α(1 - α) 3 periods ago α(1 - α)2 α= α= 0.10 α= 0.90 10% 9% 8.1% 90%
- 46. MGMT6020Forecast Ft = α At - 1 + α(1- α) At - 2 + α(1- α)2 At - 3 + ... Forecast Effects of Smoothing Constant α Weights Prior Period α 2 periods ago α(1 - α) 3 periods ago α(1 - α)2 α= α= 0.10 α= 0.90 10% 9% 8.1% 90% 9%
- 47. MGMT6020Forecast Ft = α At - 1 + α(1- α) At - 2 + α(1- α)2 At - 3 + ... Forecast Effects of Smoothing Constant α Weights Prior Period α 2 periods ago α(1 - α) 3 periods ago α(1 - α)2 α= α= 0.10 α= 0.90 10% 9% 8.1% 90% 9% 0.9%
- 48. MGMT6020Forecast You want to achieve:You want to achieve: Smallest forecast errorSmallest forecast error Mean square error (MSE)Mean square error (MSE) Mean absolute deviation (MAD)Mean absolute deviation (MAD) No pattern or direction in forecastNo pattern or direction in forecast errorerror Error = (Error = (YYii -- YYii) = (Actual - Forecast)) = (Actual - Forecast) Seen in plots of errors over timeSeen in plots of errors over time Guidelines for Selecting Forecasting Model ^
- 49. MGMT6020Forecast How to Choose α Seek to minimize the Mean Absolute Deviation (MAD) If: Forecast error = demand - forecast Then: n errorsforecast∑ =MAD Note that the sum of all weights in exponential smoothing equals to 1. It is popular because of the simplicity of data keeping.
- 50. MGMT6020Forecast Measuring Forecast Accuracy Mean Squared Error (MSE)Mean Squared Error (MSE) represents the variance of errors in a forecast. This criterionrepresents the variance of errors in a forecast. This criterion is most useful if you want to minimize the occurrence of ais most useful if you want to minimize the occurrence of a major error(s).major error(s). n e = n )2 Ft-At( n 1=t=MSE 2 t n 1=t ∑∑
- 51. MGMT6020Forecast Exponential Smoothing with Trend Adjustment Forecast including trend (FITt) = exponentially smoothed forecast (Ft) + exponentially smoothed trend (Tt)
- 52. MGMT6020Forecast Ft = α(Actual demand this period) + (1- α)(Forecast last period+Trend estimate last period) Ft = α(At-1) + (1- α)Ft-1 + Tt-1 or Tt = β(Forecast this period - Forecast last period) + (1- β)(Trend estimate last period Tt = β(Ft - Ft-1) + (1- β)Tt-1 or Exponential Smoothing with Trend Adjustment - continued
- 53. MGMT6020Forecast FFtt = exponentially smoothed forecast of the= exponentially smoothed forecast of the data series in perioddata series in period tt TTtt = exponentially smoothed trend in period= exponentially smoothed trend in period tt AAtt = actual demand in period= actual demand in period tt αα = smoothing constant for the average= smoothing constant for the average ββ = smoothing constant for the trend= smoothing constant for the trend Exponential Smoothing with Trend Adjustment - continued
- 54. MGMT6020Forecast Comparison of Forecasts 0 5 10 15 20 25 30 35 40 Jan Feb Mar Apr May Jun Jul Aug Sep Month ProductDemand Actual Demand Exponential smoothing Exponential smoothing + Trend
- 55. MGMT6020Forecast Used for forecasting linear trend lineUsed for forecasting linear trend line Assumes relationship between responseAssumes relationship between response variable,variable, Y,Y, and time,and time, X,X, is a linearis a linear functionfunction Estimated by least squares methodEstimated by least squares method Minimizes sum of squared errorsMinimizes sum of squared errors iY a bXi= + Linear Trend Projection
- 56. MGMT6020Forecast Y a bXi i= + b > 0 b < 0 a a Y Time, X Linear Trend Projection Model
- 57. MGMT6020Forecast Slope (Slope (bb)) EstimatedEstimated YY changes bychanges by bb for each 1 unitfor each 1 unit increase inincrease in XX IfIf bb = 2, then sales (= 2, then sales (YY) is expected to increase) is expected to increase by 2 for each 1 unit increase in advertisingby 2 for each 1 unit increase in advertising ((XX)) Y-intercept (Y-intercept (aa)) Average value ofAverage value of YY whenwhen XX = 0= 0 IfIf aa = 4, then average sales (= 4, then average sales (YY) is expected to) is expected to be 4 when advertising (be 4 when advertising (XX) is 0) is 0 Interpretation of Coefficients
- 58. MGMT6020Forecast How to Find a and b: Least Squares Equations Equation: ii bxaYˆ += Slope: 22 1= 1= −∑ −∑ = xnx yxnyx b i n i ii n i Y-Intercept: xbya −= Criteria of finding a and b:
- 59. MGMT6020Forecast Measuring Forecast Accuracy Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD) measures the average absolute error of a forecast. A sign ofmeasures the average absolute error of a forecast. A sign of an error, which represents over- or underestimation, isan error, which represents over- or underestimation, is really not important in most cases; we are rather concernedreally not important in most cases; we are rather concerned with the value of deviation.with the value of deviation. where:where: AAtt = actual value in period t,= actual value in period t, FFtt = forecasted value in period t,= forecasted value in period t, eett = forecast error in period t,= forecast error in period t, n = number of periods.n = number of periods. n |e| = n |F-A| =MAD t n 1=t tt n 1=t ∑∑
- 60. MGMT6020Forecast Measuring Forecast Accuracy Mean Squared Error (MSE)Mean Squared Error (MSE) represents the variance of errors in a forecast. This criterionrepresents the variance of errors in a forecast. This criterion is most useful if you want to minimize the occurrence of ais most useful if you want to minimize the occurrence of a major error(s).major error(s). n e = n )2 Ft-At( n 1=t=MSE 2 t n 1=t ∑∑
- 61. MGMT6020Forecast Include seasonal and cyclical patternsInclude seasonal and cyclical patterns In decomposition, a time series is described as a function ofIn decomposition, a time series is described as a function of four components:four components: Y = T*C*S*IY = T*C*S*I multiplicative model (commonly used)multiplicative model (commonly used) Y = T+C+S+IY = T+C+S+I additive modeladditive model where:where: Y =Y = actual value of time seriesactual value of time series T =T = trend componenttrend component C =C = cyclical componentcyclical component S =S = seasonal componentseasonal component I =I = irregular (random) componentirregular (random) component General Description of TS Models: Time Series Decomposition
- 62. MGMT6020Forecast Multiplicative Seasonal Model FindFind average historical demandaverage historical demand for eachfor each “season”“season” by summing the demand forby summing the demand for that season in each year, and dividing bythat season in each year, and dividing by the number of years for which you havethe number of years for which you have data.data. Compute theCompute the average demand over allaverage demand over all seasonsseasons by dividing the total averageby dividing the total average annual demand by the number of seasons.annual demand by the number of seasons.
- 63. MGMT6020Forecast Multiplicative Seasonal Model Compute aCompute a seasonal indexseasonal index by dividingby dividing that season’s historical demand (fromthat season’s historical demand (from step 1) by the average demand over allstep 1) by the average demand over all seasons.seasons. Estimate next year’s total demand byEstimate next year’s total demand by using smoothed linear trend projectionusing smoothed linear trend projection modelmodel Divide this estimate of total demand byDivide this estimate of total demand by the number of seasons, then multiply itthe number of seasons, then multiply it by the seasonal index for that season.by the seasonal index for that season. This provides theThis provides the seasonal forecastseasonal forecast..
- 64. MGMT6020Forecast Example of Multiplicative Seasonal Model The following trend projection is used to predict quarterly demand: Y = 350 - 2.5t, where t = 1 in the first quarter of 1998. Seasonal (quarterly) relatives are Quarter 1 = 1.5; Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is the seasonally adjusted forecast for the four quarters of 2000? (10%) Period Projection Adjusted 9 327.5 491.25 10 325 260 11 322.5 354.75 12 320 192
- 65. MGMT6020Forecast Seven Steps in Forecasting (Demands) Determine the use of the forecastDetermine the use of the forecast Select the items to be forecastSelect the items to be forecast Determine the time horizon of the forecastDetermine the time horizon of the forecast 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
- 66. MGMT6020Forecast Past Data of Nurse Demand: What patterns can be observed? 0 5 10 15 20 1 3 5 7 9 11 Time Period NumberofNurses Number of Nurses
- 67. MGMT6020Forecast Forecasting Issues During a Product’s Life Introduction Growth Maturity Decline Standardization Less rapid product changes - more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focused Enhance distribution Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Best period to increase market share R&D product engineering critical Practical to change price or quality image Strengthen niche Cost control critical Poor time to change image, price, or quality Competitive costs become critical Defend market position OMStrategy/IssuesCompanyStrategy/Issues HDTV CD-ROM Color copiers Drive-thru restaurants Fax machines Station wagons Sales 3 1/2” Floppy disks Internet
- 68. MGMT6020Forecast Measures how well the forecast is predictingMeasures how well the forecast is predicting actual valuesactual 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 Should be within upper and lower controlShould be within upper and lower control limitslimits Tracking Signal ( ) MAD errorforecast ˆ 1 ∑∑ = − == = MAD yy MAD RSFE TS n i ii
- 69. MGMT6020Forecast Plot of a Tracking Signal Time Lower control limit Upper control limit Signal exceeded limit Tracking signal Acceptable range MAD + 0 -
- 70. MGMT6020Forecast Time (Years) Error 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast Error: Identified Only by Observation
- 71. MGMT6020Forecast Predicting Cyclical Factors Leading indicatorsLeading indicators Investment (public/private)Investment (public/private) ExportExport Business purchasingBusiness purchasing Consumer confidenceConsumer confidence Government expendingGovernment expending
- 72. Advanced Forecasting Methods To improve the accuracy, more complicatedTo improve the accuracy, more complicated models might be required. For example,models might be required. For example, Adaptive smoothingAdaptive smoothing Focus forecastingFocus forecasting
Editor's Notes
- #4: e.g. weather forecast, predict traffic jam, election result, or stock price.
- #5: Almost all OM decisions requires forecast as the input.
- #6: The emphasis in this chapter will be on demand forecasting. Recently, Boeing’s stock drop, and airline laying off.
- #8: Bottom-up forecasting for quarterly demands.
- #11: This definition is varied among different industries
- #12: Pooling effect is to eliminate pure randomness.
- #15: In this class, associative models will focus on computer-aided application but time-series model will require hand-on exercise. In practice, associated model usually for larger scale and centralized decision making such as economic trends or air travel demand.
- #19: Fortunately, cyclical pattern often is important for strategic decisions in longer term and is responsibility for executives. For most manager, even things went very wrong, you are not along.
- #22: Time series indicates the type of data required for forecasting. Assume the patterns will exist in the future
- #23: Inventory cost includes holding and parish cost
- #53: It is popular because of the simplicity of data keeping.