Math Problem Statement
Assume an initial starting Ft of 291 units, a trend ( Tt ) of eight units, an alpha of 0.40, and a delta of 0.40. If actual demand turned out to be 279, calculate the forecast for the next period.
Note: Round your answer to 1 decimal place.
Solution
To calculate the forecast for the next period using a trend-adjusted exponential smoothing model, we use the following formulas:
-
Updated Forecast: Where:
- is the forecast for the current period (291 units)
- is the trend for the current period (8 units)
-
Updated Trend: Where:
- is the smoothing constant for the trend (0.40)
- is the forecast for the current period (291 units)
- is the forecast for the previous period (since we're given the starting forecast for , we assume the previous period's forecast is also 291)
- is the trend for the current period (8 units)
-
Forecast for the next period: Where:
- is the smoothing constant for the level (0.40)
- is the actual demand for the current period (279 units)
- is the forecast for the current period (291 units)
- is the trend for the current period (8 units)
Step-by-step calculation:
-
Update Trend: Using the formula: Since , the term , so:
-
Updated Forecast: Using the formula:
So, the forecast for the next period is 291.0 units.
Would you like more details on any part of this process? Here are some related questions for further exploration:
- How do different values of and affect the forecast?
- What is the difference between simple exponential smoothing and trend-adjusted exponential smoothing?
- How would we adjust this method if we had multiple periods of actual demand data?
- How can we use this model to forecast for multiple periods ahead?
- What other forecasting models can be used for trend and seasonality?
Tip: In trend-adjusted exponential smoothing, the trend component is especially useful when there's consistent movement in the data (either upward or downward), which makes the trend adjustment more accurate.
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Math Problem Analysis
Mathematical Concepts
Exponential Smoothing
Time Series Forecasting
Trend Adjustment
Formulas
F_{t+1} = F_t + T_t
T_{t+1} = \delta \cdot (F_t - F_{t-1}) + (1 - \delta) \cdot T_t
F_{t+1} = \alpha \cdot A_t + (1 - \alpha) \cdot (F_t + T_t)
Theorems
Trend-Adjusted Exponential Smoothing
Suitable Grade Level
Grades 10-12
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