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
using exponential smoothing, calculate the forecast for year 4 (value of R). use alpha = 0.9. let the initial forecast for year 1 be 45, the same as the actual demand.

Answer 1

The forecast for year 4 (value of R) using exponential smoothing with alpha = 0.9 is approximately 55.6, calculated by applying the exponential smoothing formula step by step for each year.

Step-by-step explanation:

To calculate the forecast for year 4 (value of R) using exponential smoothing, we will use the following exponential smoothing formula: ForecastNew = alpha × DemandOld + (1 - alpha) × ForecastOld. Given alpha is 0.9, the initial forecast for year 1 is 45 (same as actual demand), and the subsequent demands for years 2 and 3 are 50 and 52 respectively, we can calculate as follows:

1. Forecast for year 2: (0.9 × 50) + (0.1 × 45) = 45 + 4.5 = 49.5
2. Forecast for year 3: (0.9 × 52) + (0.1 × 49.5) ≈ 46.95 + 4.95 = 51.9
3. Forecast for year 4: (0.9 × 56) + (0.1 × 51.9) ≈ 50.4 + 5.19 = 55.59,

Therefore, the value of R, which is the forecast for year 4, is approximately 55.6.