Question

Helpful tip: First, look at the exponential forecasting formula to understand that the forecast for the current period under exponential smoothing never depends on the current period's demand. Second, there are a series of questions using the same data. Therefore, save your calculations somewhere.

over the past several years, the number of patients visiting Hartville Hospital has steadily increased. the hospital administration is seeking the most accurate method for predicting patient demand in the coming years. the data for the previous five years are presented below:
Year demand Forecast
1 45 45
2 50P
3 52Q
4 56R
5 58S
compute the forecast for years 2 to 5 using exponential smooting (values P, Q, R, and S). use alpha = 0.9. let the initial forecast for year 1 equal the actual demand, which is 45. using the calculated forecasts, measure the errors, calculate the mean absolute deviation, and provide the answer for the mean absolute deviation.

Answer 1

To forecast patient demand using exponential smoothing with an alpha value of 0.9, the forecast for each year is calculated based on the previous year's actual demand and forecasted demand. While we can calculate the second-year forecast, there is insufficient data provided to calculate forecasts for years 3 to 5, as well as the errors and the mean absolute deviation.

Step-by-step explanation:

To compute the forecast for years 2 to 5 using exponential smoothing with an alpha value of 0.9, we start with the initial forecast for year 1, which is equal to the actual demand of 45. Exponential smoothing is calculated using the formula: Forecastt+1 = alpha × Actualt + (1 - alpha) × Forecastt, where alpha is the smoothing constant.

For year 2, P is calculated as follows:

Forecast2 = 0.9 × Actual1 + (1 - 0.9) × Forecast1 = 0.9 × 45 + (1 - 0.9) × 45 = 45

Continuing with this method for the subsequent years, using the actual demands of 50, 52, 56, and 58 for years 2, 3, 4, and 5 respectively, we obtain the forecasts Q, R, and S. The errors for each forecast year are calculated as the absolute difference between the actual demand and the forecasted demand. Subsequently, the mean absolute deviation (MAD) is the average of these absolute errors.

Unfortunately, without the specific data for the actual demands in years 3, 4, and 5, we cannot calculate the exact forecasts for Q, R, and S, nor can we determine the errors or the MAD. However, this explanation provides a clear method to follow once the necessary data are available.