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Lecture 3

# Lecture 3 - 540:453 Production Control Lecture 3...

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540:453 Production Control Lecture 3: Forecasting (Ch. 2) Prof. T. Boucher 1 Exponential Smoothing •A t y p e o f w e i g h t e d m o v i n g average that applies declining weights to past data •W e i g h t s m o s t r e c e n t d a t a m o r e s t r o n g l y •R e a c t s m o r e t o r e c e n t c h a n g e s i d e l y u s e d , a c c u r a t e m e t h o d F t +1 = D D t + (1 - D ) F t where: F t +1 =fo re ca s t fo r ne x t pe r iod D t =a c t u a l d e m a n d f o r p r e s e n t p e r i o d F t =p r e v i o u s l y d e t e r m i n e d f o r e c a s t f o r p r e s e n t p e r i o d D =w e i g h t i n g f a c t o r , s m o o t h i n g c o n s t a n t , 0 < D±² 2

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Effect of Smoothing Constant 0.0 d D d 1.0 If D = 0.20, then F t +1 = 0.20 D t + 0.80 F t If D = 0, then F t +1 = 0 D t + 1 F t = F t Forecast does not reflect recent data If D = 1, then F t +1 = 1 D t + 0 F t = D t Forecast based only on most recent data (Naïve Forecast) 3 Exponential Smoothing (cont.) In symbols: F t+1 = D D t + (1- ) F t = D t + (1- ) ( D t-1 + (1- ) F t-1 ) = D t + (1- )( )D t-1 + (1- ² ( )D t-2 + . . . Hence the method applies a set of exponentially declining weights to ALL past data. 4
Weights in Exponential Smoothing D = 0.1 5 Exponential Smoothing ( Į =0.30 ) F 2 = D D 1 + (1 - D ) F 1 = (0.30)(37) + (0.70)(37) = 37 F 3 = D D 2 + (1 - D ) F 2 = (0.30)(40) + (0.70)(37) = 37.9 F 13 = D D 12 + (1 - D ) F 12 = (0.30)(54) + (0.70)(50.84) = 51.79 PERIOD MONTH DEMAND 1J a n 3 7 2F e b 4 0 3M a r 4 1 4A p r 3 7 5M a y 4 5 6J u n 5 0 7J u l 4 3 8A u g 4 7 9S e p 5 6 10 Oct 52 11 Nov 55 12 Dec 54 6

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Exponential Smoothing (cont.) FORECAST, F t + 1 PERIOD MONTH DEMAND ( D = 0.3) ( D = 0.5) 1J a n 3 7 2F e b 4 0 3 7 . 0 0 3 7 . 0 0 3M a r 4 1 3 7 . 9 0 3 8 . 5 0 4A p r 3 7 3 8 . 8 3 3 9 . 7 5 5M a y 4 53 8 . 2 83 8 . 3 7 6J u n 5 0 4 0 . 2 9 4 1 . 6 8 7J u l 4 3 4 3 . 2 0 4 5 . 8 4 8A u g 4 74 3 . 1 44 4 . 4 2 9S e p 5 64 4 . 3 0 4 5 . 7 1 10 Oct 52 47.81 50.85 11 Nov 55 49.06 51.42 12 Dec 54 50.84 53.21 13 Jan 51.79 53.61 7 Exponential Smoothing (cont.) 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – ||||||||||||| 123456789 1 0 1 1 1 2 1 3 Actual Orders Month D = 0.50 D = 0.30 8
Comparison of ES and MA •S im i l a r i t i e s –Bo th me thods a re app rop r iate for stationary series depend on a s ing le pa rame te r lag beh ind a t rend –One can ach ieve the same d is t r ibu t ion o f fo recas

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Lecture 3 - 540:453 Production Control Lecture 3...

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