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: a) Using a 2-year moving average, the forecast for year 6=3775 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 iround 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 0.55 (the weight of 0.55 is for the most recent period) =3773 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= response to one decimal place). (Hint: You will have only 3 years of matched data.) d) Using exponential smoothing with α=0.40 and the forecast for year 1 being 3,050 , the forecast for year 6= miles (round your driven next year. The miles driven during the past 5 years are as follows: 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 = 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 0.55 (the weight of 0.55 is for the most recent period) =3773 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=144.1 miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) d) Using exponential smoothing with α=0.40 and the forecast for year 1 being 3,050 , the forecast for year 6= miles (round your response to the nearest whole number).

Answer 1

Let's calculate each part step by step:

a) Using a 2-year moving average, the forecast for year 6:

Year 6 forecast = (Miles in Year 5 + Miles in Year 4) / 2

Year 6 forecast = (3,800 + 3,750) / 2

Year 6 forecast = 7,550 / 2

Year 6 forecast = 3,775 miles (rounded to the nearest whole number)

b) To calculate the MAD (Mean Absolute Deviation) for the 2-year moving average forecast, we need to compare it to the actual miles for Year 6:

MAD = |Year 6 forecast - Actual miles in Year 6|

MAD = |3,775 - 3,900|

MAD = 125 miles (rounded to one decimal place)

c) Using a weighted 2-year moving average with weights of 0.45 and 0.55:

Year 6 forecast = (0.45 * Miles in Year 5 + 0.55 * Miles in Year 4)

Year 6 forecast = (0.45 * 3,800 + 0.55 * 3,750)

Year 6 forecast = (1,710 + 2,062.5)

Year 6 forecast = 3,772.5 miles (rounded to the nearest whole number)

To calculate the MAD for the weighted 2-year moving average forecast, compare it to the actual miles for Year 6:

MAD = |Year 6 forecast - Actual miles in Year 6|

MAD = |3,772.5 - 3,900|

MAD = 127.5 miles (rounded to one decimal place)

d) Using exponential smoothing with α = 0.40:

Year 6 forecast = α * Actual miles in Year 5 + (1 - α) * Year 5 forecast

Year 6 forecast = 0.40 * 3,800 + (1 - 0.40) * 3,050

Year 6 forecast = 1,520 + 1,830

Year 6 forecast = 3,350 miles (rounded to the nearest whole number)

Now, you have all the forecasts for Year 6:

2-year moving average: 3,775 miles

Weighted 2-year moving average: 3,772.5 miles

Exponential smoothing: 3,350 miles

You can compare these forecasts with the actual miles for Year 6 to calculate the MAD for each method as needed.

Step-by-step explanation: