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	4,050	3,400	3,750	3,700

​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 0.55 ​(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 α = 0.30 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

Answer a)

Year	Mileage	Forecast
1	3,000
2	4,050
3	3,400
4	3,750
5	3,700
6		3,725

Forecast of year 6 = (Mileage for Year 4 + Mileage for Year 5)/2 = (3750+3700)/2 = 3725 miles

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Answer b)

Year	Mileage	Forecast	Errors	Absolute Errors
T	At	Ft	et = At-Ft	|et|
1	3,000
2	4,050
3	3,400	3,525	-125	125
4	3,750	3,725	25	25
5	3,700	3,575	125	125
6		3,725
			MAD	91.7

MAD = Average of Absolute Errors for Year 3, 4 and 5 = (125+25+125)/3 = 91.7

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Answer c)

Forecast for year 6:

Year	Mileage	Forecast
1	3,000
2	4,050
3	3,400
4	3,750
5	3,700
6		3723

Forecast for year 6 = (3750*0.45) + (3700*0.55) = 3723 miles

MAD calculation:

Year	Mileage	Forecast	Errors	Absolute Errors
t	At	Ft	et = At-Ft	|et|
1	3,000
2	4,050
3	3,400	3578	-178	178
4	3,750	3693	57	57
5	3,700	3593	107	107
6		3723
			MAD	114.0

MAD = Average of Absolute Errors for Year 3, 4 and 5 = (178+57+107)/3 = 114.0

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Answer d)

Exponential smoothing Forecast formula:   

F(t+1)= Ft + α(At-Ft)

Where,

α = Smoothing constant =0.3     

Ft = Forecast for immediate previous period      

At = Actual Demand for immediate previous period        

F(t+1) = Single exponential smoothing forecast for current period           

Based on the formula, following is the calculated forecast:

Year	Mileage (At)	Forecast (Ft)
1	3,000	3050
2	4,050	3035.00
3	3,400	3339.50
4	3,750	3357.65
5	3,700	3475.36
6		3543
Smoothing constant = α =	0.30

Forecast for Year 6 = 3475.36 + 0.30*(3700-3475.36) = 3543 miles

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