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Chapter 7 Demand Forecasting in a Supply Chain

Forecasting -5 Adaptive Trend and Seasonality Adjusted Exponential Smoothing Ardavan Asef-Vaziri References: Supply Chain Management; Chopra and Meindl USC Marshall School of Business Lecture Notes. Chapter 7 Demand Forecasting in a Supply Chain. Monthly US Electric Power Consumption.

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Chapter 7 Demand Forecasting in a Supply Chain

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  1. Forecasting -5 Adaptive Trend and Seasonality Adjusted Exponential Smoothing ArdavanAsef-Vaziri References: Supply Chain Management; Chopra and Meindl USC Marshall School of Business Lecture Notes Chapter 7Demand Forecastingin a Supply Chain

  2. Monthly US Electric Power Consumption

  3. Trend and Seasonality

  4. Trend & Seasonality-Corrected Exponential Smoothing The estimates of level, trend, and seasonality are adjusted after each demand observation. Assume periodicity p Ft+1 = ( Lt + Tt)St+1 = forecast for period t+1 in period t Ft+l = ( Lt + lTt)St+l = forecast for period t+l in period t Lt= 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 at period t-1 or earlier) Dt = Actual demand observed in period t

  5. General Steps in Adaptive Forecasting 0- Initialize:Compute initial estimates of level,L0, trend ,T0, and seasonal factors, S1,…,Sp. As in static forecasting. 1- Forecast:Forecast demand for period t+1 using the general equation, Ft+1 = (Lt+Tt)×St+1 2- Estimate error:Compute error Et+1 = Ft+1- Dt+1 3- Modify estimates:Modify the estimates of level, Lt+1, trend, Tt+1, and seasonal factor, St+p+1, given the error Et+1 in the forecast Repeat steps 1, 2, and 3 for each subsequent period

  6. Trend & Seasonality-Corrected Exponential Smoothing After observing demand for period t+1, revise estimates for level, trend, and seasonal factors as follows: Lt+1 = a(Dt+1/St+1) + (1-a)(Lt+Tt) Tt+1 = b(Lt+1 - Lt) + (1-b)Tt St+p+1 = g(Dt+1/Lt+1) + (1-g)St+1 a = smoothing constant for level b = smoothing constant for trend g = smoothing constant for seasonal factor

  7. Trend & Seasonality-Corrected Exponential Smoothing Example: Tahoe Salt data. Forecast demand for period 1 using Winter’s model. Initial estimates of level, trend, and seasonal factors are obtained as in the static forecasting case L0 = 18439 T0 = 524 S1=0.47, S2=0.68, S3=1.17, S4=1.66 F1 = (L0 + T0)S1 = (18439+524)(0.47) = 18963(0.47)= 8913 The observed demand for period 1 = D1 = 8000. • Assume a = 0.1, b=0.2, g=0.1

  8. Trend & Seasonality-Corrected Exponential Smoothing L1 = a(Actual Surrogate) + (1-a)(Forecast Surrogate) Forecast Surrogate for L1 = L0+T0 Actual Surrogate for L1 = D1/S1 L1 = a(D1/S1) + (1-a)(L0+T0) L1 = 0.1(D1/S1) + 0.9(L0+T0) L1 =(0.1)(8000/0.47)+(0.9)(18439+524)=18769 T1 = b(Actual Surrogate) + (1-b)(Forecast Surrogate) Forecast Surrogate for T1 = T0 Actual Surrogate for T1 = D1-D0 T1 = 0.2(L2-L1) + 0.8(T0) T1 = (0.2)(18769-18439)+(0.8)(524) = 485

  9. Trend & Seasonality-Corrected Exponential Smoothing S5 = g(Actual Surrogate) + (1-g)(Forecast Surrogate) Forecast Surrogate for S5 = S1 Actual Surrogate for S5 = D1/L1 S5 = g (D1/L1) + (1-g)(S1) S5 = 0.1 (D1/L1) + 0.9(S1) S5 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47 F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093

  10. Trend & Seasonality-Corrected Exponential Smoothing L1 = 18769, T1 = 485, S2 = 0.68, D2 = 13000. L2 = 0.1(D2/S2) + 0.9(L1+T1) D2/S2 = 13000/0.68 = 19118 L1+T1 = 18769+485 = 19254 L2 = 0.1(19118) + 0.9(19254) = 19240 T2 = 0.2(L2-L1) + 0.8(T1) T1 = (0.2)(19240-18769)+(0.8)(485) = 482 S5 = g(Actual Surrogate) + (1-g)(Forecast Surrogate) S6 = 0.1 (D2/L2) + 0.9(S2) S5 = (0.1)(13000/19240)+(0.9)(0.68) = 0.68 F3 = (L2+T2)S3 = (19240 + 482)(0.68) = 13411

  11. Forecasting in Practice • Collaborate in building forecasts • The value of data depends on where you are in the supply chain • Be sure to distinguish between demand and sales

  12. Practice: Given L0 = 11, T0 = 1, S1 to S4 =0.5,1.0,1.5,1.0 Forecast 1 = (11+1)*0.5

  13. L1, T1, F2, S5 New level = 0.25(6/0.5)+0.75(11+1)=12 New trend = 0.25(12-11)+0.75(1)=1 New seasonal = 0.25(6/12)+0.75(0.5)=0.5 New Forecast = (12+1)*1=13

  14. L2, T2, F3, S6 New level = 0.25(14/1)+0.75*(12+1)=13.25 New trend = 0.25(13.25-12)+0.75(1)=1.06 New seasonal = 0.25(14/13.25)+0.75*1=1.014 New Forecast = (13.25+1.06)*1.5=21.45

  15. Practice:α = 0.05, β = 0.1, δ = 0.1

  16. Assignment • Each cycle is 4 periods long. • Periodicity = 4. There are three cycles. • Compute b0, b1, S1, S2, S3, S4 using static method and forecast using trend and seasonality adjusted method for α= β = δ = 0.25

  17. Using Static Model We Can Compute Seasonality • b0 (Level) and b1 (Trend) are computed exactly the same as static method by applying regression on deseasonalized data. • Initial average seasonality indices are also computed in the same way.

  18. Practice; α=β= γ = 0.25

  19. Practice; α=β= γ = 0.25

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