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1、 University of Science and Technology of ChinaChapter 7Demand Forecastingin a Supply ChainSupply Chain Management(3rd Edition)7-1 University of Science and Technology of China OutlineuThe role of forecasting in a supply chainuCharacteristics of forecastsuComponents of forecasts and forecasting metho
2、dsuBasic approach to demand forecastinguTime series forecasting methodsuMeasures of forecast erroruForecasting demand at Tahoe SaltuForecasting in practice2 University of Science and Technology of China Demand ForecastinguHow does BMW know how many Mini Coopers it will sell in North America? uHow ma
3、ny Prius cars should Toyota build to meet demand in the U.S. this year? Worldwide? uWhen is it time to tweak production, upward or downward, to reflect a change in the market?What factors influence customer demand?3 University of Science and Technology of China Role of ForecastingPushPushPushPushPus
4、hPushPullPullPullManufacturerDistributorRetailerCustomerSupplierIs demand forecasting more important for a push or pull system? University of Science and Technology of China Role of Forecasting in a Supply ChainuThe basis for all strategic and planning decisions in a supply chainuUsed for both push
5、and pull processesuExamples:Production: scheduling, inventory, aggregate planningMarketing: sales force allocation, promotions, new production introductionFinance: plant/equipment investment, budgetary planningPersonnel: workforce planning, hiring, layoffsuAll of these decisions are interrelated5 Un
6、iversity of Science and Technology of China Characteristics of ForecastsuForecasts are always wrong. Should include expected value and measure of error.uLong-term forecasts are less accurate than short-term forecasts (forecast horizon is important)uAggregate forecasts are more accurate than disaggre
7、gate forecasts6 University of Science and Technology of China 1) Characteristics of ForecastsuForecasts are always wrong!Forecasts should include an expected value and a measure of error (or demand uncertainty)Forecast 1: sales are expected to range between 100 and 1,900 unitsForecast 2: sales are e
8、xpected to range between 900 and 1,100 units University of Science and Technology of China 2) Characteristics of ForecastsuLong-term forecasts are less accurate than short-term forecastsLess easy to consider other variables Hard to include the effects of weather in a forecastForecast horizon is impo
9、rtant, long-term forecast have larger standard deviation of error relative to the mean University of Science and Technology of China 3) Characteristics of ForecastsuAggregate forecasts are more accurate than disaggregate forecasts University of Science and Technology of China 3) Characteristics of F
10、orecastsuAggregate forecasts are more accurate than disaggregate forecastsThey tend to have a smaller standard deviation of error relative to the meanMonthly sales SKUMonthly sales product line University of Science and Technology of China 4) Characteristics of ForecastsuInformation gets distorted w
11、hen moving away from the customerBullwhip effect University of Science and Technology of China Forecasting MethodsuQualitative: primarily subjective; rely on judgment and opinionuTime Series: use historical demand onlyStatic AdaptiveuCausal: use the relationship between demand and some other factor
12、to develop forecastuSimulationImitate consumer choices that give rise to demandCan combine time series and causal methods12 University of Science and Technology of China Components of an ObservationObserved demand (O) =Systematic component (S) + Random component (R)Level (current deseasonalized dema
13、nd)Trend (growth or decline in demand)Seasonality (predictable seasonal fluctuation) Systematic component: Expected value of demand Random component: The part of the forecast that deviates from the systematic component Forecast error: difference between forecast and actual demand13 University of Sci
14、ence and Technology of China Components of an ObservationuQuarterly demand at Tahoe SaltActual demand (D)14 University of Science and Technology of China Components of an ObservationuQuarterly demand at Tahoe SaltLevel (L) and Trend (T)15 University of Science and Technology of China Components of a
15、n ObservationuQuarterly demand at Tahoe SaltSeasonality (S)16 University of Science and Technology of China Components of an ObservationObserved demand =Systematic component + Random componentLLevel (current deseasonalized demand)TTrend (growth or decline in demand)SSeasonality (predictable seasonal
16、 fluctuation)17 University of Science and Technology of China Time Series ForecastingForecast demand for thenext four quarters.18 University of Science and Technology of China Time Series Forecasting19 University of Science and Technology of China Forecasting MethodsuStatic uAdaptiveMoving averageSi
17、mple exponential smoothingHolts model (with trend)Winters model (with trend and seasonality)20 University of Science and Technology of China Basic Approach toDemand ForecastinguUnderstand the objectives of forecastinguIntegrate demand planning and forecastinguIdentify major factors that influence th
18、e demand forecastuUnderstand and identify customer segmentsuDetermine the appropriate forecasting techniqueuEstablish performance and error measures for the forecast21 University of Science and Technology of China Time Series Forecasting MethodsuGoal is to predict systematic component of demandMulti
19、plicative: (level)(trend)(seasonal factor)Additive: level + trend + seasonal factorMixed: (level + trend)(seasonal factor)uStatic methodsuAdaptive forecasting22 University of Science and Technology of China Static MethodsuAssume a mixed model:Systematic component = (level + trend)(seasonal factor)Ft
20、+l = L + (t + l)TSt+l= forecast in period t for demand in period t + lL = estimate of level for period 0T = estimate of trendSt = estimate of seasonal factor for period tDt = actual demand in period tFt = forecast of demand in period t23 University of Science and Technology of China Static MethodsuE
21、stimating level and trenduEstimating seasonal factors24 University of Science and Technology of China Estimating Level and TrenduBefore estimating level and trend, demand data must be deseasonalizeduDeseasonalized demand = demand that would have been observed in the absence of seasonal fluctuationsu
22、Periodicity (p) the number of periods after which the seasonal cycle repeats itselffor demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 425 University of Science and Technology of China Time Series Forecasting (Table 7.1)Forecast demand for thenext four quarters.26 University of Science and Technolo
23、gy of China Time Series Forecasting(Figure 7.1)27 University of Science and Technology of China Estimating Level and TrenduBefore estimating level and trend, demand data must be deseasonalizeduDeseasonalized demand = demand that would have been observed in the absence of seasonal fluctuationsuPeriod
24、icity (p) the number of periods after which the seasonal cycle repeats itselffor demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 428 University of Science and Technology of China Deseasonalizing Demand Dt-(p/2) + Dt+(p/2) + S 2Di / 2p for p evenDt = (sum is from i = t+1-(p/2) to t+1+(p/2) S Di / p
25、for p odd (sum is from i = t-(p/2) to t+(p/2), p/2 truncated to lower integer29 University of Science and Technology of China Deseasonalize demanduPeriodicity p is odduPeriodicity p is even30 University of Science and Technology of China Deseasonalizing demand around t= (2,4), that is, year 2 and 4t
26、h quarter, when p is oddDeseasonalize demand31 University of Science and Technology of China Deseasonalize demandAssume p = 3, hence a seasonal cycle consists of three periods32 University of Science and Technology of China Deseasonalize demandDeseasonalized demand for t=(2,4)= 18,000 + 23,000 + 38,
27、000 = 26,33333 University of Science and Technology of China Deseasonalize demandDeseasonalizing demand around t= (2,4), that is, year 2 and 4th quarter, when p is even34 University of Science and Technology of China Deseasonalize demandAssume p = 4, hence a seasonal cycle consists of four periods35
28、 University of Science and Technology of China Deseasonalize demandWhat happens if you take the average demand?36 University of Science and Technology of China Deseasonalize demand37 University of Science and Technology of China Deseasonalize demand38 University of Science and Technology of China De
29、seasonalize demanduPeriodicity p is odduPeriodicity p is even39 University of Science and Technology of China Deseasonalizing DemandFor the example, p = 4 is evenFor t = 3:D3 = D1 + D5 + Sum(i=2 to 4) 2Di/8= 8000+10000+(2)(13000)+(2)(23000)+(2)(34000)/8= 19750D4 = D2 + D6 + Sum(i=3 to 5) 2Di/8= 1300
30、0+18000+(2)(23000)+(2)(34000)+(2)(10000)/8= 2062540 University of Science and Technology of China Deseasonalizing DemandThen include trendDt = L + tTwhere Dt = deseasonalized demand in period tL = level (deseasonalized demand at period 0)T = trend (rate of growth of deseasonalized demand)Trend is de
31、termined by linear regression using deseasonalized demand as the dependent variable and period as the independent variable (can be done in Excel)In the example, L = 18,439 and T = 52441 University of Science and Technology of China Time Series of Demand(Figure 7.3)42 University of Science and Techno
32、logy of China Estimating Seasonal FactorsUse the previous equation to calculate deseasonalized demand for each periodSt = Dt / Dt = seasonal factor for period tIn the example, D2 = 18439 + (524)(2) = 19487 D2 = 13000S2 = 13000/19487 = 0.67The seasonal factors for the other periods are calculated in
33、the same manner43 University of Science and Technology of China Estimating Seasonal Factors (Fig. 7.4)44 University of Science and Technology of China Estimating Seasonal FactorsThe overall seasonal factor for a “season” is then obtained by averaging all of the factors for a “season”If there are r s
34、easonal cycles, for all periods of the form pt+i, 1ip, the seasonal factor for season i is Si = Sum(j=0 to r-1) Sjp+i/r In the example, there are 3 seasonal cycles in the data and p=4, soS1 = (0.42+0.47+0.52)/3 = 0.47S2 = (0.67+0.83+0.55)/3 = 0.68S3 = (1.15+1.04+1.32)/3 = 1.17S4 = (1.66+1.68+1.66)/3
35、 = 1.6745 University of Science and Technology of China Estimating the ForecastUsing the original equation, we can forecast the next four periods of demand:F13 = (L+13T)S1 = 18439+(13)(524)(0.47) = 11868F14 = (L+14T)S2 = 18439+(14)(524)(0.68) = 17527F15 = (L+15T)S3 = 18439+(15)(524)(1.17) = 30770F16
36、 = (L+16T)S4 = 18439+(16)(524)(1.67) = 4479446 University of Science and Technology of China Adaptive ForecastinguThe estimates of level, trend, and seasonality are adjusted after each demand observationuGeneral steps in adaptive forecastinguMoving averageuSimple exponential smoothinguTrend-correcte
37、d exponential smoothing (Holts model)uTrend- and seasonality-corrected exponential smoothing (Winters model)47 University of Science and Technology of China Basic Formula forAdaptive ForecastingFt+1 = (Lt + lT)St+1 = forecast for period t+l in period t Lt = Estimate of level at the end of period t T
38、t = 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 period t Et = Forecast error in period t At = Absolute deviation for period t = |Et|MAD = Mean Absolute Deviation
39、 = average value of At 48 University of Science and Technology of China General Steps inAdaptive ForecastinguInitialize: Compute initial estimates of level (L0), trend (T0), and seasonal factors (S1,Sp). This is done as in static forecasting.uForecast: Forecast demand for period t+1 using the genera
40、l equationuEstimate error: Compute error Et+1 = Ft+1- Dt+1 uModify estimates: Modify the estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Et+1 in the forecastuRepeat steps 2, 3, and 4 for each subsequent period49 University of Science and Technology of China Mov
41、ing AverageuUsed when demand has no observable trend or seasonalityuSystematic component of demand = leveluThe level in period t is the average demand over the last N periods (the N-period moving average)uCurrent forecast for all future periods is the same and is based on the current estimate of the
42、 levelLt = (Dt + Dt-1 + + Dt-N+1) / NFt+1 = Lt and Ft+n = Lt After observing the demand for period t+1, revise the estimates as follows:Lt+1 = (Dt+1 + Dt + + Dt-N+2) / N Ft+2 = Lt+1 50 University of Science and Technology of China Moving Average ExampleFrom Tahoe Salt example (Table 7.1)At the end o
43、f period 4, what is the forecast demand for periods 5 through 8 using a 4-period moving average?L4 = (D4+D3+D2+D1)/4 = (34000+23000+13000+8000)/4 = 19500F5 = 19500 = F6 = F7 = F8Observe demand in period 5 to be D5 = 10000Forecast error in period 5, E5 = F5 - D5 = 19500 - 10000 = 9500Revise estimate
44、of level in period 5:L5 = (D5+D4+D3+D2)/4 = (10000+34000+23000+13000)/4 = 20000F6 = L5 = 2000051 University of Science and Technology of China Example: Tahoe SaltuDemand forecasting using Moving Average52 University of Science and Technology of China Components of an ObservationLevel (L)Forecast(F)F
45、t+n = LtThe simple exponential smoothing is used when demand has no observable trend or seasonality53 University of Science and Technology of China Simple Exponential SmoothinguUsed when demand has no observable trend or seasonalityuSystematic component of demand = leveluInitial estimate of level, L
46、0, assumed to be the average of all historical dataL0 = Sum(i=1 to n)Di/nCurrent forecast for all future periods is equal to the current estimate of the level and is given as follows:Ft+1 = Lt and Ft+n = Lt After observing demand Dt+1, revise the estimate of the level:Lt+1 = aDt+1 + (1-a)Lt Lt+1 = S
47、um(n=0 to t+1)a(1-a)nDt+1-n 54 University of Science and Technology of China Simple Exponential Smoothing ExampleFrom Tahoe Salt data, forecast demand for period 1 using exponential smoothingL0 = average of all 12 periods of data= Sum(i=1 to 12)Di/12 = 22083F1 = L0 = 22083Observed demand for period
48、1 = D1 = 8000Forecast error for period 1, E1, is as follows:E1 = F1 - D1 = 22083 - 8000 = 14083Assuming a = 0.1, revised estimate of level for period 1:L1 = aD1 + (1-a)L0 = (0.1)(8000) + (0.9)(22083) = 20675F2 = L1 = 20675Note that the estimate of level for period 1 is lower than in period 055 Unive
49、rsity of Science and Technology of China Example: Tahoe SaltuDemand forecasting using simple exponential smoothing56 University of Science and Technology of China Components of an ObservationTrend (T)Forecast(F)Ft+n = Lt + nTtHolts method is appropriate when demand is assumed to have a level and a t
50、rend57 University of Science and Technology of China Trend-Corrected Exponential Smoothing (Holts Model)uAppropriate when the demand is assumed to have a level and trend in the systematic component of demand but no seasonalityuObtain initial estimate of level and trend by running a linear regression
51、 of the following form:Dt = at + bT0 = aL0 = bIn period t, the forecast for future periods is expressed as follows:Ft+1 = Lt + Tt Ft+n = Lt + nTt 58 University of Science and Technology of China Trend-Corrected Exponential Smoothing (Holts Model)After observing demand for period t, revise the estima
52、tes for level and trend as follows:Lt+1 = aDt+1 + (1-a)(Lt + Tt)Tt+1 = b(Lt+1 - Lt) + (1-b)Tt a = smoothing constant for levelb = smoothing constant for trendExample: Tahoe Salt demand data. Forecast demand for period 1 using Holts model (trend corrected exponential smoothing)Using linear regression
53、,L0 = 12015 (linear intercept)T0 = 1549 (linear slope)59 University of Science and Technology of China Holts Model Example (continued)Forecast for period 1:F1 = L0 + T0 = 12015 + 1549 = 13564Observed demand for period 1 = D1 = 8000E1 = F1 - D1 = 13564 - 8000 = 5564Assume a = 0.1, b = 0.2L1 = aD1 + (
54、1-a)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008T1 = b(L1 - L0) + (1-b)T0 = (0.2)(13008 - 12015) + (0.8)(1549) = 1438F2 = L1 + T1 = 13008 + 1438 = 14446F5 = L1 + 4T1 = 13008 + (4)(1438) = 1876060 University of Science and Technology of China Trend- and Seasonality-Corrected Exponential SmoothinguApp
55、ropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factoruSystematic component = (level+trend)(seasonal factor)uAssume periodicity puObtain initial estimates of level (L0), trend (T0), seasonal factors (S1,Sp) using procedure for static forecastinguIn pe
56、riod t, the forecast for future periods is given by:Ft+1 = (Lt+Tt)(St+1) and Ft+n = (Lt + nTt)St+n 61 University of Science and Technology of China Trend- and Seasonality-Corrected Exponential Smoothing (continued)After observing demand for period t+1, revise estimates for level, trend, and seasonal
57、 factors as follows:Lt+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 = smoothing constant for trendg = smoothing constant for seasonal factorExample: Tahoe Salt data. Forecast demand for period 1 using Winters model.In
58、itial estimates of level, trend, and seasonal factors are obtained as in the static forecasting case62 University of Science and Technology of China Trend- and Seasonality-Corrected Exponential Smoothing Example (continued)L0 = 18439 T0 = 524 S1=0.47, S2=0.68, S3=1.17, S4=1.67F1 = (L0 + T0)S1 = (184
59、39+524)(0.47) = 8913The observed demand for period 1 = D1 = 8000Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913Assume 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)(8000/0.47)+(0.9)(18439+52
60、4)=18769T1 = b(L1-L0)+(1-b)T0 = (0.2)(18769-18439)+(0.8)(524) = 485S5 = g(D1/L1)+(1-g)S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 1309363 University of Science and Technology of China Measures of Forecast ErrorMeasureDescriptionErrorAbsolute ErrorForecast Actual D
61、emandAbsolute deviationMean Squared Error (MSE)Squared deviation of forecast from demandMean Absolute Deviation (MAD)Absolute deviation of forecast from demandMean Absolute Percentage Error (MAPE)Absolute deviation of forecast from demand as a percentage of the demandTracking signal (TS)Ratio of bia
62、s and MAD64 University of Science and Technology of China Measures of Forecast ErroruForecast error = Et = Ft - Dt uMean squared error (MSE)MSEn = (Sum(t=1 to n)Et2)/nuAbsolute deviation = At = |Et|uMean absolute deviation (MAD)MADn = (Sum(t=1 to n)At)/ns = 1.25MAD65 University of Science and Techno
63、logy of China Measures of Forecast ErroruMean absolute percentage error (MAPE)MAPEn = (Sum(t=1 to n)|Et/ Dt|100)/nuBiasuShows whether the forecast consistently under- or overestimates demand; should fluctuate around 0biasn = Sum(t=1 to n)EtuTracking signaluShould be within the range of +6uOtherwise,
64、 possibly use a new forecasting methodTSt = bias / MADt66 University of Science and Technology of China Forecast ErroruError (E)uMeasures the difference between the forecast and the actual demand in period tuWant error to be relatively smallEt = Ft Dt67 University of Science and Technology of China
65、Forecast Error68 University of Science and Technology of China Forecast ErroruBiasuMeasures the bias in the forecast erroruWant bias to be as close to zero as possible A large positive (negative) bias means that the forecast is overshooting (undershooting) the actual observationsZero bias does not i
66、mply that the forecast is perfect (no error) - only that the mean of the forecast is “on target”biast = nt=1Et69 University of Science and Technology of China Forecast ErrorUndershootingForecast mean “on target” but not perfect70 University of Science and Technology of China Forecast ErroruAbsolute
67、deviation (A)uMeasures the absolute value of error in period tuWant absolute deviation to be relatively smallAt = |Et|71 University of Science and Technology of China Forecast ErroruMean absolute deviation (MAD)uMeasures absolute erroruPositive and negative errors do not cancel out (as with bias)uWa
68、nt MAD to be as small as possibleNo way to know if MAD error is large or small in relation to the actual data = 1.25*MAD72 University of Science and Technology of China Forecast ErrorNot all that large relative to data73 University of Science and Technology of China Forecast ErroruTracking signal (T
69、S)uWant tracking signal to stay within (6, +6)If at any period the tracking signal is outside the range (6, 6) then the forecast is biasedTSt = biast / MADt74 University of Science and Technology of China Forecast ErrorBiased (underforecasting)75 University of Science and Technology of China Forecas
70、t ErroruMean absolute percentage error (MAPE)uSame as MAD, except .uMeasures absolute deviation as a percentage of actual demanduWant MAPE to be less than 10 (though values under 30 are common)76 University of Science and Technology of China Forecast ErrorSmallest absolute deviation relative to dema
71、ndMAPE 10 is considered very good77 University of Science and Technology of China Forecast ErroruMean squared error (MSE) uMeasures squared forecast error uRecognizes that large errors are disproportionately more “expensive” than small errorsuNot as easily interpreted as MAD, MAPE - not as intuitive
72、VAR = MSE78 University of Science and Technology of China Measures of Forecast ErrorMeasureDescriptionErrorAbsolute ErrorEt = Ft DtAt = |Et|Mean Squared Error (MSE)MSEn = Mean Absolute Deviation (MAD)MADn =Mean Absolute Percentage Error (MAPE)MAPEn = Tracking signal (TS)TSt = biast / MADt79 Universi
73、ty of Science and Technology of China Forecast Error in ExceluCalculate absolute error At=ABS(Et)uCalculate mean absolute deviation MADn=SUM(A1:An)/n=AVERAGE(A1:An)uCalculate mean absolute percentage error MAPEn=AVERAGE()uCalculate tracking signal TSt=biast / MADtuCalculate mean squared error MSEn=S
74、UMSQ(E1:En)/n80 University of Science and Technology of China Forecast Error in ExcelEt = Ft DtForecast Error81 University of Science and Technology of China Forecast Error in ExcelBiasbiasn = nt=1Et82 University of Science and Technology of China Forecast Error in ExcelAbsolute ErrorAt = |Et|83 Uni
75、versity of Science and Technology of China Forecast Error in ExcelMean Absolute Deviationn1nMADn = t=1 At84 University of Science and Technology of China Forecast Error in ExcelTracking SignalTSt = biast / MADt85 University of Science and Technology of China Forecast Error in Excel|%Error|%Error|t =
76、EtDt10086 University of Science and Technology of China Forecast Error in ExcelMean Absolute Percentage Error|%Error|tnMAPEn = nt=187 University of Science and Technology of China Forecast Error in ExcelMean Squared ErrornEt2MSEn = t=11n88 University of Science and Technology of China Forecasting De
77、mand at Tahoe SaltuMoving averageuSimple exponential smoothinguTrend-corrected exponential smoothinguTrend- and seasonality-corrected exponential smoothing89 University of Science and Technology of China Forecasting in PracticeuCollaborate in building forecastsuThe value of data depends on where you
78、 are in the supply chainuBe sure to distinguish between demand and sales90 University of Science and Technology of China Summary of Learning ObjectivesuWhat are the roles of forecasting for an enterprise and a supply chain?uWhat are the components of a demand forecast?uHow is demand forecast given historical data using time series methodologies?uHow is a demand forecast analyzed to estimate forecast error?91
