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
6 T
compute the forecast for year 6 using exponential smooting (value T). use alpha = 0.6. let the initial forecast for year 1 equal the actual demand, which is 45.

a. forecast for year 6 can be approximated to the average of forecasts year 2 to year 5
b. it is between 55 and 58
c. forecast for year 6 is over 58 as the patients visiting Hartville Hospital has steadily increased
d. forecast for the year 6 cannot be calculated without having the demand for year 6.

Answer 1

To forecast patient demand for year 6 at Hartville Hospital using exponential smoothing with α = 0.6, we start with the initial forecast equal to the actual demand of year 1 and iteratively apply the smoothing formula. The decision on the forecasting options will depend on the calculation using actual demand from year 5 and the forecast from year 5.

Step-by-step explanation:

To compute the forecast for year 6 using exponential smoothing with a smoothing constant (α) of 0.6, we follow the exponential smoothing formula:

Ft = α * Dt-1 + (1-α) * Ft-1

Where:
Ft is the forecast for the current year,
Dt-1 is the actual demand for the previous year,
Ft-1 is the forecast for the previous year.

Given that the initial forecast for year 1 is the same as the actual demand, which is 45, the subsequent forecasts are calculated as follows:

1. For year 2: F2 = 0.6 * 45 + (1-0.6) * 45 = 45
2. For year 3: F3 = 0.6 * 50 + 0.4 * 45
3. For year 4: F4 is calculated using the demand from year 3 and the forecast from year 3
4. For year 5: F5 is calculated using the demand from year 4 and the forecast from year 4
5. For year 6: F6, which is our forecast for year 6 (T), is calculated using the demand from year 5 and the forecast from year 5

Since the patient numbers are steadily increasing, we can reject options (a) and (d). The choice between options (b) and (c) will depend on the actual computed value of T.