Question

The Carbondale Hospital is considered the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows:     

Year	1	2	3	4	5
Mileage	3100	4050	3450	3850	3700

a. Using a 2-year moving average, the forecast for year 6 = 3775 miles

b. If a 2-year moving average is used to make the forecast, the MAD based on this = Miles (round response to one decimal). (Hint: you will have only 3 years of matched data)

c. Use a weighted 2-year moving average with weights of .40 and .60 to forecast next year’s mileage (the weight of .60 is for the most recent year)

d. Compute the forecast for year 6 using exponential smoothing, an initial forecast for year 1 of 3,000 miles, and alpha = .20

Answer 1

Solution:

(a) 2-year moving average:

Forecast for year 6 = (Year 5 mileage + Year 4 mileage) / 2

Forecast for year 6 = (3,700 + 3,850) / 2

Forecast for year 6 = 3,775 miles

(b) Mean Absolute Deviation (MAD):

Forecast for year 3 = (4,050 + 3,100) / 2 = 3,575

Forecast for year 4 = (3,450 + 4,050) / 2 = 3,750

Forecast for year 5 = (3,850 + 3,450) / 2 = 3,650

MAD = Sum of absolute values of (Actual mileage - Forecast mileage) / Number of periods

MAD = Absolute values of [(3,450 - 3,575) + (3,850 - 3,750) + (3,700 - 3,650)] / 3

MAD = (125 + 100 + 50) / 3

MAD = 91.7 miles

(c) Weighted 2-year moving average:

Forecast for year 6 = [(0.60 x 3,700) + (0.40 x 3,850)]

Forecast for year 6 = 3,760 miles

(d) Exponential smoothing:

In exponential smoothing,

F(t+1) = alpha A(t) + (1 - alpha) F(t)

where,

F(t+1) = Forecast for the next period

A(t) = Actual demand for the current period

F(t) = Forecast for the current period

Alpha = Smoothing constant

Alpha = 0.20

(1 - alpha) = 0.80

Using exponential smoothing, forecasts for years 2 to 6 are calculated as below:

Forecast for year 2 = [(0.20 x 3100) + (0.80 x 3000) = 3020

Forecast for year 3 = [(0.20 x 4050) + (0.80 x 3020) = 3226

Forecast for year 4 = [(0.20 x 3450) + (0.80 x 3226) = 3270.8

Forecast for year 5 = [(0.20 x 3850) + (0.80 x 3270.8) = 3386.64

Forecast for year 6 = [(0.20 x 3700) + (0.80 x 3386.64) = 3449.31

Forecast for year 6 = 3,449.31 miles