lecture3-SupplyChain-Forecasting

# 33 trend corrected exponential smoothing holts model

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33 Trend-Corrected Exponential Smoothing (Holt’s Model) After observing demand for period t, revise the estimates for level and trend as follows: L t+1 = aD t+1 + (1-a)(L t + T t ) T t+1 = b(L t+1 - L t ) + (1-b)T t a = smoothing constant for level b = smoothing constant for trend Example: Tahoe Salt demand data. Forecast demand for period 1 using Holt’s model (trend corrected exponential smoothing) Using linear regression, L 0 = 12015 (linear intercept) T 0 = 1549 (linear slope)

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34 Holt’s Model Example (continued) Forecast for period 1: F1 = L0 + T0 = 12015 + 1549 = 13564 Observed demand for period 1 = D1 = 8000 E1 = F1 - D1 = 13564 - 8000 = 5564 Assume a = 0.1, b = 0.2 L1 = aD1 + (1-a)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008 T1 = b(L1 - L0) + (1-b)T0 = (0.2)(13008 - 12015) + (0.8)(1549) = 1438 F2 = L1 + T1 = 13008 + 1438 = 14446 F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760
35 Trend- and Seasonality-Corrected Exponential Smoothing Appropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factor Systematic component = (level+trend)(seasonal factor) Assume periodicity p Obtain initial estimates of level (L 0 ), trend (T 0 ), seasonal factors (S 1 ,…,S p ) using procedure for static forecasting In period t, the forecast for future periods is given by: F t+1 = (L t +T t )(S t+1 ) and F t+n = (L t + nT t )S t+n

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36 Trend- and Seasonality-Corrected Exponential Smoothing (continued) After observing demand for period t+1, revise estimates for level, trend, and seasonal factors as follows: L t+1 = a(D t+1 /S t+1 ) + (1-a)(L t +T t ) T t+1 = b(L t+1 - L t ) + (1-b)T t S t+p+1 = g(D t+1 /L t+1 ) + (1-g)S t+1 a = smoothing constant for level b = smoothing constant for trend g = smoothing constant for seasonal factor 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
37 Trend- and Seasonality-Corrected Exponential Smoothing Example (continued) L 0 = 18439 T 0 = 524 S 1 =0.47, S 2 =0.68, S 3 =1.17, S 4 =1.67 F1 = (L0 + T0)S1 = (18439+524)(0.47) = 8913 The observed demand for period 1 = D1 = 8000 Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913 Assume a = 0.1, b=0.2, g=0.1; revise estimates for level and trend for period 1 and for seasonal factor for period 5 L1 = a(D1/S1)+(1-a)(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769 T1 = b(L1-L0)+(1-b)T0 = (0.2)(18769-18439)+(0.8)(524) = 485 S5 = g(D1/L1)+(1-g)S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47 F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093

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38 Measures of Forecast Error Forecast error = E t = F t - D t Mean squared error (MSE) MSE n = (Sum (t=1 to n) [E t 2 ])/n Absolute deviation = A t = |E t | Mean absolute deviation (MAD) MAD n = (Sum (t=1 to n) [A t ])/n s = 1.25MAD
39 Measures of Forecast Error Mean absolute percentage error (MAPE) MAPE n = (Sum (t=1 to n) [|E t / D t |100])/n Bias Shows whether the forecast consistently under- or overestimates demand; should fluctuate around 0 bias n = Sum (t=1 to n) [E t ] Tracking signal Should be within the range of + 6 Otherwise, possibly use a new forecasting method TS t = bias / MAD t

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40 Forecasting Demand at Tahoe Salt Moving average Simple exponential smoothing Trend-corrected exponential smoothing Trend- and seasonality-corrected exponential smoothing
41 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

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42 Summary of Learning Objectives What are the roles of forecasting for an enterprise and a supply chain? What are the components of a demand forecast? How is demand forecast given historical data using time series methodologies? How is a demand forecast analyzed to estimate forecast error?
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• Fall '09
• Guan
• Forecasting, Period, Time series analysis, seasonal factor

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