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1、第七章Demand Forecastingin a Supply ChainLearning ObjectivesUnderstand the role of forecasting for both an enterprise and a supply chain.Identify the components of a demand forecast.Forecast demand in a supply chain given historical demand data using time-series methodologies.Analyze demand forecasts t

2、o estimate forecast error.Role of Forecasting in a Supply ChainThe basis for all planning decisions in a supply chainUsed for both push and pull processesProduction scheduling, inventory, aggregate planningSales force allocation, promotions, new production introductionPlant/equipment investment, bud

3、getary planningWorkforce planning, hiring, layoffsAll of these decisions are interrelatedCharacteristics of ForecastsForecasts are always inaccurate and should thus include both the expected value of the forecast and a measure of forecast errorLong-term forecasts are usually less accurate than short

4、-term forecastsAggregate forecasts are usually more accurate than disaggregate forecastsIn general, the farther up the supply chain a company is, the greater is the distortion of information it receivesComponents and MethodsCompanies must identify the factors that influence future demand and then as

5、certain the relationship between these factors and future demandPast demandLead time of product replenishmentPlanned advertising or marketing effortsPlanned price discountsState of the economyActions that competitors have takenComponents and MethodsQualitativePrimarily subjectiveRely on judgmentTime

6、 SeriesUse historical demand onlyBest with stable demandCausalRelationship between demand and some other factorSimulationImitate consumer choices that give rise to demandComponents of an ObservationObserved demand (O) =systematic component (S) + random component (R)Systematic component expected valu

7、e of demandLevel (current deseasonalized demand)Trend (growth or decline in demand)Seasonality (predictable seasonal fluctuation)Random component part of forecast that deviates from systematic componentForecast error difference between forecast and actual demandBasic ApproachUnderstand the objective

8、 of forecasting.Integrate demand planning and forecasting throughout the supply chain.Identify the major factors that influence the demand forecast.Forecast at the appropriate level of aggregation.Establish performance and error measures for the forecast.Time-Series Forecasting MethodsThree ways to

9、calculate the systematic componentMultiplicativeS = level x trend x seasonal factorAdditiveS = level + trend + seasonal factorMixedS = (level + trend) x seasonal factorStatic MethodswhereL=estimate of level at t = 0 T=estimate of trendSt=estimate of seasonal factor for Period tDt=actual demand obser

10、ved in Period tFt=forecast of demand for Period tTahoe SaltYearQuarterPeriod, tDemand, Dt1218,00013213,00014323,00021434,00022510,00023618,00024723,00031838,00032912,000331013,000341132,000411241,000Table 7-1Tahoe SaltFigure 7-1Estimate Level and TrendPeriodicity p = 4, t = 3Tahoe SaltFigure 7-2Taho

11、e SaltFigure 7-3A linear relationship exists between the deseasonalized demand and time based on the change in demand over timeEstimating Seasonal FactorsFigure 7-4Estimating Seasonal FactorsAdaptive ForecastingThe estimates of level, trend, and seasonality are adjusted after each demand observation

12、Estimates incorporate all new data that are observedAdaptive ForecastingwhereLt=estimate of level at the end of Period t Tt=estimate of trend at the end of Period t St=estimate of seasonal factor for Period t Ft=forecast of demand for Period t (made Period t 1 or earlier)Dt=actual demand observed in

13、 Period t Et=Ft Dt = forecast error in Period tSteps in Adaptive ForecastingInitializeCompute initial estimates of level (L0), trend (T0), and seasonal factors (S1,Sp)ForecastForecast demand for period t + 1 Estimate errorCompute error Et+1 = Ft+1 Dt+1 Modify estimatesModify the estimates of level (

14、Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Et+1Moving AverageUsed when demand has no observable trend or seasonalitySystematic component of demand = levelThe level in period t is the average demand over the last N periods Lt = (Dt + Dt-1 + + DtN+1) / NFt+1 = Lt and Ft+n = Lt

15、After observing the demand for period t + 1, revise the estimatesLt+1 = (Dt+1 + Dt + + Dt-N+2) / N, Ft+2 = Lt+1Moving Average ExampleA supermarket has experienced weekly demand of milk of D1 = 120, D2 = 127, D3 = 114, and D4 = 122 gallons over the past four weeksForecast demand for Period 5 using a

16、four-period moving averageWhat is the forecast error if demand in Period 5 turns out to be 125 gallons?Moving Average ExampleL4= (D4 + D3 + D2 + D1)/4 = (122 + 114 + 127 + 120)/4 = 120.75Forecast demand for Period 5F5 = L4 = 120.75 gallonsError if demand in Period 5 = 125 gallonsE5 = F5 D5 = 125 120

17、.75 = 4.25Revised demandL5 = (D5 + D4 + D3 + D2)/4= (125 + 122 + 114 + 127)/4 = 122Simple Exponential SmoothingUsed when demand has no observable trend or seasonalitySystematic component of demand = levelInitial estimate of level, L0, assumed to be the average of all historical dataSimple Exponentia

18、l SmoothingRevised forecast using smoothing constant 0 a 1Given data for Periods 1 to nCurrent forecastThusSimple Exponential SmoothingSupermarket dataE1 = F1 D1 = 120.75 120 = 0.75Trend-Corrected Exponential Smoothing (Holts Model)Appropriate when the demand is assumed to have a level and trend in

19、the systematic component of demand but no seasonalitySystematic component of demand = level + trendTrend-Corrected Exponential Smoothing (Holts Model)Obtain initial estimate of level and trend by running a linear regressionDt = at + bT0 = a, L0 = bIn Period t, the forecast for future periods isFt+1

20、= Lt + Tt and Ft+n = Lt + nTt Revised estimates for Period tLt+1 = aDt+1 + (1 a)(Lt + Tt)Tt+1 = b(Lt+1 Lt) + (1 b)TtTrend-Corrected Exponential Smoothing (Holts Model)MP3 player demandD1 = 8,415, D2 = 8,732, D3 = 9,014, D4 = 9,808, D5 = 10,413, D6 = 11,961a = 0.1, b = 0.2Using regression analysisL0

21、= 7,367 and T0 = 673Forecast for Period 1F1 = L0 + T0 = 7,367 + 673 = 8,040Trend-Corrected Exponential Smoothing (Holts Model)Revised estimateL1= aD1 + (1 a)(L0 + T0)= 0.1 x 8,415 + 0.9 x 8,040 = 8,078T1= b(L1 L0) + (1 b)T0 = 0.2 x (8,078 7,367) + 0.8 x 673 = 681With new L1F2 = L1 + T1 = 8,078 + 681

22、 = 8,759ContinuingF7 = L6 + T6 = 11,399 + 673 = 12,072Trend- and Seasonality-Corrected Exponential SmoothingAppropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factorSystematic component = (level + trend) x seasonal factorFt+1 = (Lt + Tt)St+1 and Ft+l

23、= (Lt + lTt)St+lTrend- and Seasonality-Corrected Exponential SmoothingAfter observing demand for period t + 1, revise estimates for level, trend, and seasonal factorsLt+1 = a(Dt+1/St+1) + (1 a)(Lt + Tt)Tt+1 = b(Lt+1 Lt) + (1 b)TtSt+p+1 = g(Dt+1/Lt+1) + (1 g)St+1 a = smoothing constant for levelb = s

24、moothing constant for trendg = smoothing constant for seasonal factorWinters ModelL0 = 18,439 T0 = 524S1= 0.47, S2 = 0.68, S3 = 1.17, S4 = 1.67F1 = (L0 + T0)S1 = (18,439 + 524)(0.47) = 8,913The observed demand for Period 1 = D1 = 8,000Forecast error for Period 1 = E1 = F1 D1 = 8,913 8,000 = 913Winte

25、rs ModelAssume a = 0.1, b = 0.2, g = 0.1; revise estimates for level and trend for period 1 and for seasonal factor for Period 5L1= a(D1/S1) + (1 a)(L0 + T0) = 0.1 x (8,000/0.47) + 0.9 x (18,439 + 524) = 18,769T1= b(L1 L0) + (1 b)T0 = 0.2 x (18,769 18,439) + 0.8 x 524 = 485S5= g(D1/L1) + (1 g)S1 = 0

26、.1 x (8,000/18,769) + 0.9 x 0.47 = 0.47F2 = (L1 + T1)S2 = (18,769 + 485)0.68 = 13,093Time Series ModelsForecasting MethodApplicabilityMoving averageNo trend or seasonalitySimple exponential smoothingNo trend or seasonalityHolts modelTrend but no seasonalityWinters modelTrend and seasonalityMeasures

27、of Forecast ErrorDeclining alphaSelecting the Best Smoothing ConstantFigure 7-5Selecting the Best Smoothing ConstantFigure 7-6Forecasting Demand at Tahoe SaltMoving averageSimple exponential smoothingTrend-corrected exponential smoothingTrend- and seasonality-corrected exponential smoothingForecasti

28、ng Demand at Tahoe SaltFigure 7-7Forecasting Demand at Tahoe SaltMoving averageL12 = 24,500F13 = F14 = F15 = F16 = L12 = 24,500s = 1.25 x 9,719 = 12,148Forecasting Demand at Tahoe SaltFigure 7-8Forecasting Demand at Tahoe SaltSingle exponential smoothingL0 = 22,083L12 = 23,490F13 = F14 = F15 = F16 =

29、 L12 = 23,490s = 1.25 x 10,208 = 12,761Forecasting Demand at Tahoe SaltFigure 7-9Forecasting Demand at Tahoe SaltTrend-Corrected Exponential SmoothingL0 = 12,015 and T0 = 1,549L12 = 30,443 and T12 = 1,541F13 = L12 + T12 = 30,443 + 1,541 = 31,984F14 = L12 + 2T12 = 30,443 + 2 x 1,541 = 33,525F15 = L12

30、 + 3T12 = 30,443 + 3 x 1,541 = 35,066F16 = L12 + 4T12 = 30,443 + 4 x 1,541 = 36,607s = 1.25 x 8,836 = 11,045Forecasting Demand at Tahoe SaltFigure 7-10Forecasting Demand at Tahoe SaltTrend- and Seasonality-CorrectedL0 = 18,439 T0 =524S1 = 0.47 S2 = 0.68 S3 = 1.17 S4 = 1.67L12 = 24,791 T12 = 532F13 =

31、 (L12 + T12)S13 = (24,791 + 532)0.47 = 11,940F14 = (L12 + 2T12)S13 = (24,791 + 2 x 532)0.68 = 17,579F15 = (L12 + 3T12)S13 = (24,791 + 3 x 532)1.17 = 30,930F16 = (L12 + 4T12)S13 = (24,791 + 4 x 532)1.67 = 44,928s = 1.25 x 1,469 = 1,836Forecasting Demand at Tahoe SaltForecasting MethodMADMAPE (%)TS Ra

32、ngeFour-period moving average9,719491.52 to 2.21Simple exponential smoothing10,208591.38 to 2.15Holts model8,836522.15 to 2.00Winters model1,46982.74 to 4.00Table 7-2The Role of IT in ForecastingForecasting module is core supply chain softwareCan be used to best determine forecasting methods for the firm and by product categories and marketsReal time updates help