Model of a City’s Vehicle Maintenance Garage

 

A city owns and operates a garage in which maintenance and repair work is performed.  The garage has one repair bay and one mechanic; therefore service can be performed on only one vehicle at a time.

 

·        Number of scheduled arrivals for service per day is uniformly distributed between 2 to 4 vehicles, within 8 hours.

·        The time required to service these vehicles varies uniformly from 1.5 hours to 2.5 hours.

·        A work day, for the garage and the scheduled arrivals, consists of 8 hours; a week consists of 7 work days.

·        A work day, for the police cars, consists of 24 hours; a week consists of 7 work days.

·        Vehicles scheduled to come in on a given day are left at the garage at the end of the preceding day.

·        Scheduled maintenance jobs are interrupted for unscheduled police car arrivals.

·        Unscheduled police cars, however, cannot interrupt another unscheduled police car’s service.

·        Interrupted jobs will be serviced after all unscheduled jobs leave, for the remainder of their service time.

·        Unscheduled police cars arriving while the garage is closed wait until the next day.

·        Police cars arrive for unscheduled service in a Poisson stream with a mean of 48 hours.

·        Service time for unscheduled police cars is exponentially distributed averaging 2.5 hours.

 

Simulate the model to estimate the following:

1.      Distribution of “number of police cars out of service for unscheduled repair”.

2.      95 % confidence interval for the utilization of the mechanic.

3.      Create the following table using a 25-hour run.  Preferably, you do not retype the numbers or do copy-paste but create the table directly.

 

	Minimum	Maximum	Average
# of scheduled cars waiting for service
# of unscheduled cars waiting for service
Time scheduled cars spent with the mechanic
Time scheduled cars spent in service, including interrupted time
Service time for unscheduled cars

 

4.      Create a timeseries showing number of scheduled, unscheduled, and total cars serviced every day for 25 days.   An example of such a timeseries is shown below.