Question

The Carbondale Hospital is considering 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   3,000   3,950   3,500   3,750   3,750

a) Using a​ 2-year moving​ average, the forecast for year 6​ =     miles ​(round your response to the nearest whole​ number).

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

​c) The forecast for year 6 using a weighted​ 2-year moving average with weights of 0.45 and .55 ​(the weight of 0.55 is for the most recent​ period) = miles ​(round your response to the nearest whole​ number).

The MAD for the forecast developed using a weighted​ 2-year moving average with weights of 0.45 and 0.55 ​= miles ​(round your response to one decimal​ place).  ​(Hint: You will have only 3 years of matched​ data.)

​d) Using exponential smoothing with alphaα ​= 0.40 and the forecast for year 1 being 3,100​, the forecast for year 6​ =    miles ​(round your response to the nearest whole​ number).

Answer 1

a) Using the 2 year moving average method,

F(6) = {Actual(5) + Actual(4)}/2

= (3750+3750)/2

= 3750

b) F(3) = (3000+3950)/2

= 3475

F(4) = (3950+3500)/2

= 3725

F(5) = (3500+3750)/2

= 3625

MAD(Mean Absolute Deviation) = Sum of absolute deviation/Number of periods

= {|3500-3475| + |3750-3725| + |3750-3625|}/3

= (25+25+125)/3

= 58.3

c) using the weighted average method

F(6) = 0.55*Actual(5) + 0.45*Actual(4)

= 0.55*3750 + 0.45*3750

= 3750

F(3) = 0.55*3950 + 0.45*3000

= 3522.5

F(4) = 0.55*3500 + 0.45*3950

= 3702.5

F(5) = 0.55*3750 + 0.45*3500

= 3672.5

MAD = (22.5 + 47.5 + 77.5)/3

= 49.2

d) using the exponential smoothing method

F(2)= 0.4*Actual(1) + (1-0.4)*F(1)

= 0.4*3000 + 0.6*3100

= 3060

F(3) = 0.4*3950 + 0.6*3060

= 3416

F(4)= 0.4*3500 + 0.6*3416

= 3449.6

F(5) = 0.4*3750 + 0.6*3449.6

= 3569.76

F(6) = 0.4*3750 + 0.6*3569.76

= 3642