Please answer the question. Thank you The following table contains the demand fr
ID: 329399 • Letter: P
Question
Please answer the question. Thank you The following table contains the demand from the last 10 months 31 35 37 36 38 40 41 10 a. Calculate the single exponential smoothing forecast for these data using an ?of 30 and an initial forecast (F1) of 31. (Round your answers to 2 decimal places.) Exponential onth 2 10 b. Calculate the exponential smoothing with trend forecast for these data using an a of 0.30, a 8 of 0.30, F1) of 30. (Round an initial trend forecast (T1) of 1, and an initial exponentially smoothed forecast( your answers to 2 decimal places.)Explanation / Answer
a. Constant = 0.3
F1 = 31
F2 = Constant * F1 + (1-Constant) * F1
= 0.3 * 31 + 0.7 31
= 31
F3 = 0.3 * 34 + 0.7 * 31
= 31.90
F4 = 0.3 * 33 + 0.7 * 31.90
= 32.23
F5 = 0.3 * 35 + 0.7 * 32.23
= 33.06
F6 = 0.3 * 37 + 0.7 * 33.06
= 34.24
F7 = 0.3 * 36 + 0.7 * 34.24
= 34.77
F8 = 0.3 * 38 + 0.7 * 34.77
= 35.74
F9 = 0.3 * 40 + 0.7 * 35.74
= 37.02
F10 = 0.3 * 40 + 0.7 * 37.02
= 37.91
b. With Ternd adjust ment the formula of Forecast changes and becomes AFt = Ft + Tt
Ft = Constant * F(t-1) + (1-Constant) * F(t-1)
Tt = Constant * {A(t-1) - F(t-1)} + (1-Constant) * T(t-1)
F2 = 0.3 * 30 + 0.7 * 30
= 30
T2 = 0.3 * (31-30) + 0.7 * 1
= 1
AF2 = 30 + 1
= 31
F3 = 0.3 * 34 + 0.7 * 30
= 31.2
T3 = 0.3 * (34-30) + 0.7 * 1
= 1.9
AF3 = 31.2 + 1.9
= 33.10
F4 = 0.3 * 33 + 0.7 * 31.2
= 31.74
T4 = 0.3 * (33-31.2) + 0.7 * 1.9
= 1.87
AF4 = 31.74 + 1.87
= 33.61
F5 = 0.3 * 35 + 0.7 * 31.74
= 32.72
T5 = 0.3 * (35-31.74) + 0.7 * 1.87
= 2.29
AF5 = 35..1
F6 = 0.3 * 37 + 0.7 * 32.72
= 34
T6 = 0.3 (37-32.72) + 0.7 * 2.29
= 2.88
AF6 = 36.88
F7 = 0.3 * 36 + 0.7 * 34
= 34.6
T7 = 0.3 * (36-34) + 0.7 * 2.88
= 2.62
AF7 = 37.22
F8 = 0.3 * 38 + 0.7 * 34.6
= 35.62
T8 = 0.3 (38-34.6) + 0.7 * 2.62
= 2.87
AF8 = 38.49
F9 = 0.3 * 40 + 0.7 * 35.62
= 36.93
T9 = 0.3 (40-35.62) + 0.7 * 2.87
= 3.32
AF9 = 40.25
F10 = 0.3 * (40) + 0.7 * 36.93
= 37.85
T10 = 0.3 * (40-36.93) + 0.7 * 3.32
= 4.17
AF10 = 42.02
c1 Absolute Deviation = |Actual - Forecast|
Mean Absolute Deviation = Absolute Deviation/No of observations
for exponential smoothing
Absolute Deviation = 2 + 1.2 + 2.77 + 1.94 + 1.76 + 3.23 + 4.26 + 2.98 + 3.09
= 23.23
MAD = 23.23/9
= 2.58
for trend adjusted
Absolute Deviation = 3 + 0.1 + 1.39 + 1.9 + .88 + 1.78 + 1.51 + 0.25 + 1.02
= 11.83
MAD = 11.83/9
= 1.31
c2. Exponential Smoothing with Trend forecast is better because the MAD is less