Question:
The actual demand for castings in a factory is \(500\) units and \(635\) units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is \(250\) units and the smoothing constant is \(0.7\). Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is ________ units (in integer).
The actual demand for castings in a factory is \(500\) units and \(635\) units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is \(250\) units and the smoothing constant is \(0.7\). Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is ________ units (in integer).
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Apply the exponential smoothing formula twice, first to get the February forecast, then to get March.
Updated On: Aug 14, 2026
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Correct Answer: 572
Solution and Explanation
Step 1: Recall the exponential smoothing update rule.
Each new forecast is \(F_{t+1} = F_t + \alpha (A_t - F_t)\), where \(A_t\) is the actual demand and \(\alpha\) is the smoothing constant.
Step 2: Find the forecast for February 2026.
Here \(F_{Jan} = 250\), \(A_{Jan} = 500\), \(\alpha = 0.7\).
\(F_{Feb} = 250 + 0.7(500 - 250) = 250 + 175 = 425\) units.
Step 3: Find the forecast for March 2026.
Now use \(F_{Feb} = 425\) and \(A_{Feb} = 635\).
\(F_{Mar} = 425 + 0.7(635 - 425) = 425 + 147 = 572\) units.
Final Answer:
The forecast demand for March 2026 is exactly 572 units. \[ \boxed{F_{Mar} = 572} \]
Each new forecast is \(F_{t+1} = F_t + \alpha (A_t - F_t)\), where \(A_t\) is the actual demand and \(\alpha\) is the smoothing constant.
Step 2: Find the forecast for February 2026.
Here \(F_{Jan} = 250\), \(A_{Jan} = 500\), \(\alpha = 0.7\).
\(F_{Feb} = 250 + 0.7(500 - 250) = 250 + 175 = 425\) units.
Step 3: Find the forecast for March 2026.
Now use \(F_{Feb} = 425\) and \(A_{Feb} = 635\).
\(F_{Mar} = 425 + 0.7(635 - 425) = 425 + 147 = 572\) units.
Final Answer:
The forecast demand for March 2026 is exactly 572 units. \[ \boxed{F_{Mar} = 572} \]
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