2. 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 this result.

3. Consider the same production line as in Problem 2. 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?

4.Consider the same production system and profit function as in Problem 3. (a) Compute the optimal throughput level operating as a push system and the optimal WIP level operating as a CONWIP system. What is the difference in the resulting profit levels? (b) Suppose the process times actually have a mean and standard deviation of 2.2 hours, but the throughput used for the push system and the WIP level used for the pull system are computed as if the process times had a mean and standard deviation of 2 hours [i.e., were equal to the levels computed in (a)]. Now what is the profit level in the push and pull systems, and how do they compare? Repeat this calculation for a system in which processing times have a mean and standard deviation of 2.4 hours. What happens to the gap between the profit in the push and pull systems?