Consider a production line with three single machine stations in series. Each has processing times (t_e) with mean 3 hours and standard deviation of 3 hours.

a. Suppose we run this as a push system and release jobs into it at a rate of job per hour according to a Poisson process. What is the average WIP in the line?

b. Compute the throughput of this line if it is run as a CONWIP line with a WIP level equal to your answer in a.

c. How does the answer to b compare to throughput in the push system? (show both values plus a sign like greater than or less than or equal)

d. If marginal profit is $50 per piece and the cost of WIP is $0.50 per piece per hour, compute the profit for the push system.

e. Follow the information in part d and compute profit for pull (CONWIP) system.