Consider a single machine with a processing time t_e of 1/3 hours with an associated standard deviation of 1/3 hours.

a. (9 points) Suppose the system is to run in a push environment with a release rate of 2.6 parts per hour according to a Poisson process.

1. (3 points) Calculate the average cycle time in hours
2. (3 points) Calculate the number of parts in the system.
3. (3 points) If the arrival distribution stays the same but the process time variability is reduced to zero, what is the cycle time now? What is the WIP?

b. (11 points) Now suppose this machine is operating under CONWIP with a WIP level of 1 job. Assume we are running with the original levels of variability.

1. (3 points) What is the average cycle time now (in hours) ?
2. (2 point) How many parts are in the system?
3. (3 points) What if the process time variability is reduced to zero, what is the cycle time now (in hours) ? What is the WIP?
4. (3 points) How does the impact of reducing variability differ in push and pull systems? Be specific. (this should be about 2 sentences long)