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

Ardavan Asef-Vaziri Monthly US Electric Power Consumption Trend and Seasonality: Adaptive -2

Ardavan Asef-Vaziri Trend and Seasonality Trend and Seasonality: Adaptive -3

Ardavan Asef-Vaziri Trend & Seasonality-Corrected Exponential Smoothing Trend and Seasonality: Adaptive -4 The estimates of level, trend, and seasonality are adjusted after each demand observation. Assume periodicity p F t+1 = ( L t + T t )S t+1 = forecast for period t+1 in period t F t+l = ( L t + lT t )S t+l = forecast for period t+l in period t L t = Estimate of level at the end of period t T t = Estimate of trend at the end of period t S t = Estimate of seasonal factor for period t F t = Forecast of demand for period t (made at period t-1 or earlier) D t = Actual demand observed in period t

Ardavan Asef-Vaziri General Steps in Adaptive Forecasting 0- Initialize: Compute initial estimates of level, L 0, trend,T 0, and seasonal factors, S 1,…,S p. As in static forecasting. 1- Forecast: Forecast demand for period t+1 using the general equation, F t+1 = (L t +T t )×S t+1 2- Estimate error: Compute error E t+1 = F t+1 - D t+1 3- Modify estimates: Modify the estimates of level, L t+1, trend, T t+1, and seasonal factor, S t+p+1, given the error E t+1 in the forecast Repeat steps 1, 2, and 3 for each subsequent period Trend and Seasonality: Adaptive -5

Ardavan Asef-Vaziri After observing demand for period t+1, revise estimates for level, trend, and seasonal factors as follows: L t+1 =  (D t+1 /S t+1 ) + (1-  )(L t +T t ) T t+1 =  (L t+1 - L t ) + (1-  )T t S t+p+1 =  (D t+1 /L t+1 ) + (1-  )S t+1  = smoothing constant for level  = smoothing constant for trend  = smoothing constant for seasonal factor Trend & Seasonality-Corrected Exponential Smoothing

Ardavan Asef-Vaziri 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 = T0 = 524S1=0.47, S2=0.68, S3=1.17, S4=1.66 F1 = (L0 + T0)S1 = ( )(0.47) = 18963(0.47)= 8913 The observed demand for period 1 = D1 = Assume  = 0.1,  =0.2,  =0.1

Ardavan Asef-Vaziri L1 =  (Actual Surrogate) + (1-  )(Forecast Surrogate) Forecast Surrogate for L1 = L0+T0 Actual Surrogate for L1 = D1/S1 L1 =  (D1/S1) + (1-  )(L0+T0) L1 =  (D1/S1) + 0.9(L0+T0) L1 =(0.1)(8000/0.47)+(0.9)( )=18769 T1 =  (Actual Surrogate) + (1-  )(Forecast Surrogate) Forecast Surrogate for T1 = T0 Actual Surrogate for T1 = D1-D0 T1 =  (L2-L1) + 0.8(T0) T1 = (0.2)( )+(0.8)(524) = 485 Trend & Seasonality-Corrected Exponential Smoothing

Ardavan Asef-Vaziri S5 =  (Actual Surrogate) + (1-  )(Forecast Surrogate) Forecast Surrogate for S5 = S1 Actual Surrogate for S5 = D1/L1 S5 =  (D1/L1) + (1-  )(S1) S5 =  (D1/L1) + 0.9(S1) S5 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47 F2 = (L1+T1)S2 = ( )(0.68) = Trend & Seasonality-Corrected Exponential Smoothing

Ardavan Asef-Vaziri L1 = 18769, T1 = 485, S2 = 0.68, D2 = L2 =  (D2/S2) + 0.9(L1+T1) D2/S2 = 13000/0.68 = L1+T1 = = L2 =  (19118) + 0.9(19254) = T2 =  (L2-L1) + 0.8(T1) T1 = (0.2)( )+(0.8)(485) = 482 S5 =  (Actual Surrogate) + (1-  )(Forecast Surrogate) S6 =  (D2/L2) + 0.9(S2) S5 = (0.1)(13000/19240)+(0.9)(0.68) = 0.68 F3 = (L2+T2)S3 = ( )(0.68) = Trend & Seasonality-Corrected Exponential Smoothing

Ardavan Asef-Vaziri 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

Ardavan Asef-Vaziri Practice: Given L0 = 11, T0 = 1, S1 to S4 =0.5,1.0,1.5,1.0 Trend and Seasonality: Adaptive -12 QuarterDemandForecastLevelTrendSeasonal Forecast 1 = (11+1)*0.5

Ardavan Asef-Vaziri L1, T1, F2, S5 Trend and Seasonality: Adaptive -13 QuarterDemandForecastLevelTrendSeasonal 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

Ardavan Asef-Vaziri L2, T2, F3, S6 Trend and Seasonality: Adaptive -14 QuarterDemandForecastLevelTrendSeasonal New level = 0.25(14/1)+0.75*(12+1)=13.25 New trend = 0.25( )+0.75(1)=1.06 New seasonal = 0.25(14/13.25)+0.75*1=1.014 New Forecast = ( )*1.5=21.45

Ardavan Asef-Vaziri Practice: α = 0.05, β = 0.1, δ = 0.1

Ardavan Asef-Vaziri Assignment Trend and Seasonality: Adaptive -16  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

Ardavan Asef-Vaziri Using Static Model We Can Compute Seasonality Trend and Seasonality: Adaptive -17  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.

Ardavan Asef-Vaziri Practice; α=β= γ = 0.25 Trend and Seasonality: Adaptive -18

Ardavan Asef-Vaziri Practice; α=β= γ = 0.25 Trend and Seasonality: Adaptive -19