lecture3-SupplyChain-Forecasting

33 trend corrected exponential smoothing holts model

This preview shows page 34 - 43 out of 43 pages.

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)
Image of page 34

Subscribe to view the full document.

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
Image of page 35
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
Image of page 36

Subscribe to view the full document.

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
Image of page 37
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
Image of page 38

Subscribe to view the full document.

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
Image of page 39
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
Image of page 40

Subscribe to view the full document.

40 Forecasting Demand at Tahoe Salt Moving average Simple exponential smoothing Trend-corrected exponential smoothing Trend- and seasonality-corrected exponential smoothing
Image of page 41
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
Image of page 42

Subscribe to view the full document.

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?
Image of page 43
You've reached the end of this preview.
  • Fall '09
  • Guan
  • Forecasting, Period, Time series analysis, seasonal factor

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern