A city owns and operates a garage in which maintenance and repair work is performed on city-owned vehicles. Included among these vehicles are motor-pool cars, heavy-duty trucks, and so on. City officials are receiving pressure from the police force to keep the police cars operational and they are considering extending the 8 hour work day of the garage by hiring a part time mechanic to work on the vehicles after the regular mechanic has finished his work day.
Determine the effect of extending the work day by 2, 4, 8, and 10 hours to see the effect on keeping the police cars available.
To measure the performance of the garage, output of interest includes
• the average number of police cars serviced in a day and
• the average time a police car resides in the garage from arrival to completion of the servicing.
The city is not large; as a result, the garage is equipped with only one service bay, and employs only one mechanic. This means that service can be performed on only one vehicle at a time. All of the city-owned vehicles are regularly scheduled to come in to the garage for maintenance work. Vehicles scheduled to come in on a given day are all left at the garage at the end of the preceding day. They are therefore already waiting at the garage when each work day begins. A work day itself consists of 8 hours.
Under certain conditions, regularly scheduled maintenance work which is in-progress can be interrupted, so that the service bay can be used for a more important purpose. In particular, the city attempts to keep a full fleet of police cars operating at all times. The police cars are in use 24 hours per day, under demanding conditions. Whenever there is a problem with one of these cars, the car is brought immediately to the garage for unscheduled service. If another vehicle is undergoing scheduled maintenance at the time, the just-arrived police car is permitted to preempt the service bay, so that its repair can begin without delay. However, a police car in need of unscheduled repair is not permitted to preempt another police car on which unscheduled repair is in progress. Of course, if the garage is not open when they arrive, they must wait until 8 am before servicing can begin.