Question

During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair. Repair personnel can be hired at the rate of $20 per hour, but they only work as one team. Thus, if one person is hired, he or she works alone; two or three people work together on the same repair.

One repairer can fix cars in an average time of 30 minutes. Two repairers take 20 minutes, and three take 15 minutes. While these cars are down, lost income is $40 per hour. Cars tend to break down at the rate of 1.75 per hour.

Management is trying to decide how many repair persons to hire, and has asked you for cost data.

a.	What is the total hourly cost with one repair person? (Round your intermediate calculations and final answer to 2 decimal places.)

Total cost per hour

$

b.	What is the total hourly cost with two repair persons? (Round your intermediate calculations and final answer to 2 decimal places.)

Total cost per hour

$

c.	What is the total hourly cost with three repair persons? (Round your intermediate calculations and final answer to 2 decimal places.)

Total cost per hour

$

Answer 1

All the repair persons work as one team. So, this is a M/M/1 queue system with following parameters

Cars breakdown rate or arrival rate, = 1.75 cars per hour

Cost of repairperson, Cs = $ 20 per hour

Lost income while the car is down, Cw = $ 40 per hour

a)

With one repair person, s = 1

Repair time = 30 minutes per car

Service rate, = 60 minutes per hour / Repair time = 60/30 = 2 cars per hour

Average number of cars in system (waiting and being repaired), L = /(-)

= 1.75/(2-1.75)

= 7

Total cost per hour = s*Cs+L*Cw   (this includes cost of repair person and lost income)

= 1*20+7*40

= $ 300

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b)

With two repair persons, s = 2

Repair time = 20 minutes per car

Service rate, = 60 minutes per hour / Repair time = 60/20 = 3 cars per hour

Average number of cars in system (waiting and being repaired), L = /(-)

= 1.75/(3-1.75)

= 1.4

Total cost per hour = s*Cs+L*Cw   (this includes cost of repair person and lost income)

= 2*20+1.4*40

= $ 96

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c)

With three repair persons, s = 3

Repair time = 15 minutes per car

Service rate, = 60 minutes per hour / Repair time = 60/15 = 4 cars per hour

Average number of cars in system (waiting and being repaired), L = /(-)

= 1.75/(4-1.75)

= 0.78

Total cost per hour = s*Cs+L*Cw   (this includes cost of repair person and lost income)

= 3*20+0.78*40

= $ 91.2

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d)

Total hourly cost with three repair persons is the lowest.

Therefore, three repair persons should be hired.