Final answer:
Forecasting demand for period 5 using trend-corrected exponential smoothing involves calculating the level and trend at each period and then using these values to compute the forecast for the next period.
Step-by-step explanation:
To forecast the demand for period 5 using trend-corrected exponential smoothing, we start by calculating the initial level (L1) and initial trend (T1). Since no previous smoothing values are provided, we can use D1 as L1, and the difference between D2 and D1 as T1.
L1 = D1 = 9,213
T1 = D2 - D1 = 9,754 - 9,213 = 541
Now, let's compute the subsequent levels (L2, L3, L4), trends (T2, T3, T4), and forecast for period 5 (F5) using the following formulas:
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- Level (Lt): Lt = α * Dt + (1 - α) * (Lt-1 + Tt-1)
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- Trend (Tt): Tt = β * (Lt - Lt-1) + (1 - β) * Tt-1
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- Forecast (Ft+1): Ft+1 = Lt + Tt
Assuming α (alpha) = 0.15 and β (beta) = 0.25, and using the observed demands (D2, D3, D4), we calculate:
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- L2, T2 based on D2
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- L3, T3 based on D3
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- L4, T4 based on D4
Applying the formulas will yield the following:
L2 = 0.15 * 9,754 + 0.85 * (9,213 + 541) = ...
T2 = 0.25 * (L2 - L1) + 0.75 * T1 = ...
L3 = 0.15 * 10,784 + 0.85 * (L2 + T2) = ...
T3 = 0.25 * (L3 - L2) + 0.75 * T2 = ...
L4 = 0.15 * 11,632 + 0.85 * (L3 + T3) = ...
T4 = 0.25 * (L4 - L3) + 0.75 * T3 = ...
F5 = L4 + T4 = ...
The exact numerical values must be calculated to determine L2, T2, L3, T3, L4, T4, and F5, but it follows the trend-corrected exponential smoothing approach as described.