Jim Wells, vice president for manufacturing of the Northern Airplane Company, is exasperated. His walk through the company's most important plant this morning has left him in a foul mood. However, he now can vent his temper at Jerry Carstairs, the plant's production manager, who has just been summoned to Jim's office. "Jerry, I just got back from walking through the plant, and I am very upset." "What is the problem, Jim?" "Well, you know how much I have been emphasizing the need to cut down on our in-process inventory." "Yes, we've been working hard on that," responds Jerry. "Well, not hard enough!" Jim raises his voice even higher. "Do you know what I found by the presses?" "No." "Five metal sheets still waiting to be formed into wing sections. And then, right next door at the inspection station, 13 wing sections! The inspector was inspecting one of them, but the other 12 were just sitting there. You know we have a couple hundred thousand dollars tied up in each of those wing sections. So between the presses and the inspection station, we have a few million bucks' worth of terribly expensive metal just sitting there. We can't have that!" The chagrined Jerry Carstairs tries to respond. "Yes, Jim, I am well aware that that inspection station is a bottleneck. It usually isn't nearly as bad as you found it this morning, but it is a bottleneck. Much less so for the presses. You really caught us on a bad morning." "I sure hope so," retorts Jim, "but you need to prevent anything nearly this bad happening even occasionally. What do you propose to do about it?" Jerry now brightens noticeably in his response. "Well, actually, I've already been working on this problem. I have a couple proposals on the table and I have asked a management scientist on my staff to analyze these proposals and report back with recommendations." "Great," responds Jim, "glad to see you are on top of the problem. Give this your highest priority and report back to me as soon as possible." "Will do," promises Jerry. Here is the problem that Jerry and his management scientist are addressing. Each of 10 identical presses is being used to form wing sections out of large sheets of specially processed metal. The sheets arrive randomly at a mean rate of seven per hour. The time required by a press to form a wing section out of a sheet has an exponential distribution with a mean of one hour. When finished, the wing sections arrive randomly at an inspection station at the same mean rate as the metal sheets arrived at the presses (seven per hour). A single inspector has the full time job of inspecting these wing sections to make sure they meet specifications. Each inspection takes her 71/2 minutes, so she can inspect eight wing sections per hour. This inspection rate has resulted in a substantial average amount of in-process inventory at the inspection station (i.e., the average number of wing sheets waiting to complete inspection is fairly large), in addition to that already found at the group of machines. The cost of this in-process inventory is estimated to be $16 per hour for each metal sheet at the presses or each wing section at the inspection station. Therefore, Jerry Carstairs has made two alternative proposals to reduce the average level of in-process inventory. Proposal 1 is to use slightly less power for the presses (which would increase their average time to form a wing section to 1.2 hours), so that the inspector can keep up with their output better. This also would reduce the cost for each machine (operating cost plus capital recovery cost) from $14 to $13 per hour. (By contrast, increasing to maximum power would increase this cost to $15 per hour while decreasing the average time to form a wing section to 0.8 hours.) Proposal 2 is to substitute a certain younger inspector for this task. He is somewhat faster (albeit with some variability in his inspection times because of less experience), so he should keep up better. (His inspection time would have a probability distribution with a mean of 7.2 minutes and a standard deviation of 5 minutes.) This inspector is in a job classification that calls for a total compensation (including benefits) of $38 per hour, whereas the current inspector is in a lower job classification where the compensation is $34 per hour. (The inspection times for each of these highly trained and experienced inspectors are typical of those in the same job classi tions.) You are the management scientist on Jerry Carstair's staff who has been asked to analyze this problem. He wants you to "use the latest management science techniques to see how much each proposal would cut down on in-process inventory and then make your recommendations."

a. To provide a basis of comparison, begin by evaluating the status quo. Determine the expected amount of in-process inventory at the presses and at the inspection station. Then calculate the expected total cost per hour of the in-process inventory, the presses, and the inspector.

b. What would be the effect of Proposal 1? Why? Make specific comparisons to the results from part a. Explain this outcome to Jerry Carstairs. c. Determine the effect of Proposal 2. Make specific comparisons to the results from part a. Explain this outcome to Jerry Carstairs. d. Make your recommendations for reducing the average level of in-process inventory at the inspection station and at the group of machines. Be specific in your recommendations, and support them with quantitative analysis like that done in part a. Make specific comparisons to the results from part a, and cite the improvements that your recommendations would yield.