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Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
Trend Based + Reg And Holtns
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Trend Based + Reg And Holtns

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  • 1. Forecasting Trend Based Methods
  • 2. Regression Analysis
  • 3. Regression line
  • 4. Forecasting
    • Y: demand D
    • x : time period
    • (1, D 1 ), (2, D 2 ), …, (n, D n )
  • 5. Regression Analysis
    • The optimal value of a and b are given by:
  • 6.  
  • 7.  
  • 8.  
  • 9. Trend-Based Methods Double Exponential Smoothing
  • 10. Holt’s method
    • Method requires
      • two smoothing constants α and β
      • Uses two equations
      • Value of the intercept at time t
      • Value of the slope at time t
  • 11. S t : intercept at time t G t : slope at time t First Equation : similar to simple exponential smoothing Average of current demand & prior forecast of the currebt demand 2nd Equation : New intercept  revise estimate of slope to S t – S t-1 This value is averaged with previous value of the slope
  • 12. Double Exponential Smoothing
    • Intercept at time t
    • and slope at time t
  • 13. The τ -step-ahead forecast made in period t
  • 14. S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  • 15. S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  • 16. S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  • 17. S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 190 8 305 7 285 6 225 5 186 4 175 3 250 2 200 1 |error| F t D t
  • 18. MAD=46.4 S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 85.0 275 190 8 44.2 260.8 305 7 37.3 247.7 285 6 15.3 240.3 225 5 50.1 236.1 186 4 175 3 250 2 200 1 |error| F t D t
  • 19. MAD=46.4 3-step-ahead forecast: F 2,5 = S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 85.0 275 190 8 44.2 260.8 305 7 37.3 247.7 285 6 15.3 240.3 225 5 50.1 236.1 186 4 175 3 250 2 200 1 |error| F t D t
  • 20. MAD=46.4 3-step-ahead forecast: F 2,5 = S 2 +(3) G 2 = 222 + (3) 10.2=252.6 S 3 =(0.1)(175)+(.9)(222+ 10.2 )=226.5 G 3 =(0.1)( 226.5-222 )+(.9)( 10.2 )=9.6 S 2 =(0.1)(250)+(.9)(209+ 9.9 )=222.0 G 2 =(0.1)( 222-209 )+(.9)( 9.9 )=10.2 S 1 =(0.1)( 200 )+(.9)(200+ 10 )=209.0 G 1 =(0.1)( 209-200 )+(.9)( 10 )=9.9 85.0 275 190 8 44.2 260.8 305 7 37.3 247.7 285 6 15.3 240.3 225 5 50.1 236.1 186 4 175 3 250 2 200 1 |error| F t D t
  • 21. Trend Based Methods
    • Regression Analysis
    • Double Exponential Smoothing

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