A certain service station uses a team of 3 mechanics in one repair station to work on each car that needs repair. This team can repair cars at a rate of 9 per day. Cars arrive for repairs at the station at the rate of 4.5 per day. The service station owner has decided that this team is not very efficient in terms of labor usage. To remedy the problem, the owner is going to reduce the number of people on the team from 3 to 2 and expects that team of 2 will be able to repair vehicles at the rate of 6 per day. The reduction will reduce the service station expenses by $100 per day. On the other hand, the owner believes that the cost to the service station customers of not having their cars is $20 per day. (Assume that repair times are exponentially distributed and that arrivals are random, that is inter-arrival times are distributed exponentially).
a) What are the percentages of unused available labor (on average) for the two cases?
b) Should the owner implement the new policy?
c) How long will the average "line" be for the 2-person setup?
A queuing problem involving labor usage, percentage unused available labor, exponential distribution is investigated and discussed. The solution is detailed and well presented.