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 comma 000 4 comma 050 3 comma 500 3 comma 800 3 comma 750 ​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​ = 50 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 0.40 and 0.60 ​(the weight of 0.60 is for the most recent​ period) = 553 miles ​(round your response to the nearest whole​ number).

Answer 1

a) Using a two period moving average method the forecast for a period is calculated as the sum of the actual value for the previous two periods / 2

So forecast for year 6 = (3800+3750)/2 = 7550/2 = 3775

b) Using the two year moving average method the forecast for year 3 through 5 are

• For year 3 = (3000+4050)/2 = 7050/2 = 3525
• For year 4 = (4050+3500)/2 = 7550/2 = 3775
• For year 5 = (3500+3800)/2 = 7300/2 = 3650

MAD = Sum of the absolute deviation for all the periods/number of periods

Where,absolute deviation = absolute value of deviation

Deviation = Actual value - forecasted value

So the deviation and absolute deviation for year 3 through 5 are

• For year 3 deviation = 3500-3525 = -25 and absolute deviation = 25
• For year 4 deviation = 3800-3775 = 25 and absolute deviation = 25
• For year 5 deviation = 3750-3650 = 100 and absolute deviation = 100

MAD = (25+25+100) / 3 = 150/3 = 50 miles

C) Using a two period weighted moving average method the forecast for a period is calculated as the sum of the product of the actual value and their respective weight for the previous two periods.

So forecast for year 6 = (0.40x3800) + (0.60x3750)

= 1520 + 2250

= 3770 miles