5. Consider a production line with three single-machine stations in series. Each has processing times with mean 2 hours and standard deviation of 2 hours. (Note that this makes it identical to the line represented in the practical worst case of Chapter 7.)

a. Suppose we run this line as a push system and release jobs into it at a rate of 0.45 per hour with arrival variability given by ca=1. 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. Is the throughput higher or lower than 0.45? Explain your result.

6. Consider the same production line as in the previous problem. Suppose the marginal profit is $50 per piece and the cost of WIP is $0.25 per piece per hour.

a. What is the profit from the push system if we set TH = 0.4?

b. What is the profit from the pull system if we set WIP=12? How does this compare to the answer of a. and what does it imply about the relative profitability of push and pull systems?

c. Increase TH in a. by 20 percent to 0.48, and compute the profit for the push system. Increase WIP in b. by 25 percent to 15, and compute the profit for the pull system. Compare the difference to the difference computed in b. What does it imply about the relative robustness of push and pull systems?