Ft+1 = αdt+ (1 - α)Ft, where, Ft+1= forecast for next period, α = smoothing coefficient, dt = demand from the most recent period, Ft = Forecast for the given period. Identify the equivalent equation to the exponential smoothing model.单项选择题
A
Ft+1 = Ft+ α(Ft- dt)
B
Ft+1 = Ft+ α(dt - Ft)
C
Ft+1 = dt+ (1 - α)Ft
D
Ft = αdt+ (1 - α)Ft

Question

Ft+1 = αdt+ (1 - α)Ft, where, Ft+1= forecast for next period, α = smoothing coefficient, dt = demand from the most recent period, Ft = Forecast for the given period. Identify the equivalent equation to the exponential smoothing model.单项选择题

A

Ft+1 = Ft+ α(Ft- dt)

B

Ft+1 = Ft+ α(dt - Ft)

C

Ft+1 = dt+ (1 - α)Ft

D

Ft = αdt+ (1 - α)Ft

BlackTom AI · Accepted Answer

Rewriting Ft+1 = αdt + (1 - α)Ft gives the equivalent linear update form.

1. Relevant knowledge points and concepts
- Exponential smoothing updates the forecast as a weighted average of the most recent actual demand dt and the previous forecast Ft.
- α is the smoothing constant (0 ≤ α ≤ 1) that determines how much weight the new observation receives.
- The forecast error for period t is et = dt − Ft. The update can be expressed in terms of this error.

2. Complete reasoning process step by step
Start with the given formula:
Ft+1 = α dt + (1 − α) Ft

Distribute and collect terms involving Ft:
Ft+1 = α dt + Ft − α Ft

Factor out α from the terms involving dt and Ft:
Ft+1 = Ft + α dt − α Ft

Factor α from the last two terms:
Ft+1 = Ft + α (dt − Ft)

3. Intermediate calculation steps (explicit)
Given: Ft+1 = α dt + (1 − α) Ft
Expand: Ft+1 = α dt + Ft − α Ft
Reorder: Ft+1 = Ft + (α dt − α Ft)
Factor α: Ft+1 = Ft + α (dt − Ft)

4. Why the correct answer is correct
This form shows the forecast is the previous forecast plus α times the forecast error (dt − Ft). It is equivalent algebraically to the original exponential smoothing expression and clarifies that the update nudges Ft toward dt by a fraction α of the error.

5. Why the other options are incorrect
- Ft+1 = Ft + α(Ft − dt): This reverses the sign of the error term; it would move the forecast away from the actual when dt > Ft, which contradicts smoothing logic.
- Ft+1 = dt + (1 − α)Ft: This gives the dt term full weight (coefficient 1 rather than α), so it is not algebraically equivalent to α dt + (1 − α)Ft unless α = 1.
- Ft = αdt + (1 − α)Ft: This places Ft on both sides and is not an update equation for Ft+1; it is tautological/incorrect as written.

6. Conclusion
Therefore the equivalent equation is Ft+1 = Ft + α(dt − Ft), which matches the provided correct answer.

Ft+1 = αdt+ (1 - α)Ft, where, Ft+1= forecast for next period, α = smoothing coefficient, dt = demand from the most recent period, Ft = Forecast for the given period. Identify the equivalent equation to the exponential smoothing model.单项选择题

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