Model Answer
0 min readIntroduction
Forecasting is a crucial aspect of inventory management, production planning, and overall business strategy. Accurate forecasts enable organizations to optimize resource allocation and minimize costs. Exponential smoothing is a widely used time series forecasting method that assigns exponentially decreasing weights to past observations. This method is particularly useful when historical data exhibits a trend or seasonality, but in this case, we are dealing with a simple application without considering trend or seasonality. The smoothing constant, denoted by 'alpha', determines the weight given to the most recent observation.
Understanding Exponential Smoothing
Exponential smoothing is a forecasting technique that uses weighted averages of past data. The formula for a single exponential smoothing forecast (Ft+1) is:
Ft+1 = αAt + (1 - α)Ft
Where:
- Ft+1 is the forecast for the next period
- α is the smoothing constant (0 < α < 1)
- At is the actual value for the current period
- Ft is the forecast for the current period
Calculating the Forecast for This Week
Given:
- Forecast for last week (Ft) = ₹ 1,10,000
- Actual sales for last week (At) = ₹ 1,25,000
- Smoothing constant (α) = 0.1
Applying the formula to calculate the forecast for this week (Ft+1):
Ft+1 = 0.1 * 1,25,000 + (1 - 0.1) * 1,10,000
Ft+1 = 12,500 + 0.9 * 1,10,000
Ft+1 = 12,500 + 99,000
Ft+1 = ₹ 1,11,500
Therefore, the forecast for this week is ₹ 1,11,500.
Calculating the Forecast for the Next Week
Now, let's assume the actual sales for this week (At) turn out to be ₹ 1,20,000. We need to calculate the forecast for the next week (Ft+2).
Given:
- Forecast for this week (Ft) = ₹ 1,11,500 (calculated above)
- Actual sales for this week (At) = ₹ 1,20,000
- Smoothing constant (α) = 0.1
Applying the formula to calculate the forecast for the next week (Ft+2):
Ft+2 = 0.1 * 1,20,000 + (1 - 0.1) * 1,11,500
Ft+2 = 12,000 + 0.9 * 1,11,500
Ft+2 = 12,000 + 1,00,350
Ft+2 = ₹ 1,12,350
Therefore, the forecast for the next week is ₹ 1,12,350.
Sensitivity Analysis of Alpha
The value of alpha significantly impacts the forecast. A higher alpha gives more weight to recent observations, making the forecast more responsive to changes in demand. Conversely, a lower alpha gives more weight to past observations, resulting in a smoother forecast. Choosing the optimal alpha value often involves minimizing the Mean Absolute Deviation (MAD) or Mean Squared Error (MSE) using historical data.
Conclusion
In conclusion, using the single exponential smoothing method with a smoothing constant of 0.1, the forecast for this week is ₹ 1,11,500, and the forecast for the next week, given actual sales of ₹ 1,20,000 this week, is ₹ 1,12,350. This demonstrates a simple yet effective technique for short-term forecasting. The accuracy of these forecasts depends heavily on the stability of the underlying demand pattern and the appropriate selection of the smoothing constant.
Answer Length
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