ASSIGNMENT QUESTIONS
NEED TO PROVIDE 4 PROGRAMS AND ANSWER QUESTIONS
1a.    A machine processes two different types of parts.
            The time between arrivals of Type 1 parts is triangularly distributed with a mode of 40 minutes, a minimum of 20 minutes, and a maximum of 50 minutes. TRIA(20,40,50)
            The inter-arrival time of Type 2 parts is from a triangular distribution with a mode of 60 minutes, a minimum of 40 minutes, and a maximum of 70 minutes TRIA(40,60,70).
            Processing time for Type 1 parts is exponentially distributed with a mean of 15 minutes. 
            For Type 2 parts processing time is uniformly distributed with a minimum of 15 minutes and a maximum of 20 minutes. 
            Fifteen percent of the parts are rejected and returned to the end of the queue.
            These parts have to be reworked with a rework time equal to 90% of their previous processing time.  Develop a model to estimate the mean time spent in the system by a part and the utilization of the machine.  Simulate this system for 1000 hours.

1b.    Include a downtime of one hour every 8 hours of operations.  Assume that preventive maintenance is performed after the completion of the current job.  Run this model for 1000 hours and collect statistics on the mean time spent in the system by a part.

2a.    A repair shop consists of a work station where incoming units are repaired and an inspection station where the repaired units are either released from the shop or recycled back to work station.  The work station has three servers, and the inspection station has one inspector.  Units entering this system have inter-arrival times which are exponentially distributed with a mean of 10 minutes.  The repair time for each unit is accurately estimated before repair and is lognormal with a mean of 22 minutes and standard deviation of 18 minutes.  The shortest processing time priority dispatching rule is used at the work station, i.e. the unit with the smallest estimated repair time is served first.  Repaired units then queue for inspection on a FIFO basis.  The inspection of a unit requires 6 minutes. A unit is rejected with a probability of 20% and repair time is 80% of the previous repair time.  Rejected units queue up at the work station with the same priority dispatching rule to be repaired again.  Simulate the operation of this shop for 10000 hours.
i.    What is the mean utilization of the inspector?

ii.    What is the mean queue length at the work station?

iii.    What is the mean time spent in the system of each unit?

iv.    What is the average number of units in the system?

2b.    Modify the above model such that there are two queues at the work station. One queue for new jobs and one queue for recycled jobs. Recycled jobs are processed ahead of new jobs. The queue priority of recycled jobs is based on their earliest arrival times at the system.

i.    What is the mean time spent in the system of each unit?

ii.    What is the average number of units in the system?