1. (50 points) Factory Dynamics, Chapter 7 of text. FYI, this problem is motivated by a simplified non-reentrant-flow version of the Littlefield game environment with station 1 as board stuffing, station 2 testing, station 3 tuning; the data here can be different from your game. Consider a CONWIP flow line with 3 stations in series (1 2 3); each station consists of one machine and every unit has to flow through all three stations before it is completed. The unit processing times at the three stations are 4.8 hours, 2.1 hours, and 3.6 hours, respectively. (Aside: how would you estimate average processing time at station 1 for your Littlefield game?) There are 24 working hours in a day, and 5 working days per week. Currently there is a single machine at each station and the current demand is 3 units per day. Demand is expected to grow in the future and then stabilize; peak demand is estimated to be 11 units per day. Answer the following questions using the data specified.

1. (8 points) Calculate the bottleneck rate, r_b, the raw process time, T₀, and the critical WIP, W₀, for the current line. [If useful, round the critical WIP up to the closest integer; this is not essential.]
2. (16 points) If WIP is managed so that it averages w = 5 units (this is the CONWIP level), compute the best case, worst case, and Practical Worst Case throughput AND the corresponding cycle times for the line. Note: I want both the TH and the CT values for best, worst, and PWC, so you should be able to fill six values into the following table:

	Best	Worst	PWC
TH
CT

3. (5 points) How much work-in-process inventory, w, is needed to make the practical worst case throughput for this line equal to 90% of the maximum possible throughput, i.e., to make TH_PWC = 0.9 r_b?

4. (*14 points) By definition, station implied utilization = demand rate / station capacity, where station capacity is measured in terms of its production rate. Clearly as demand rate increases, implied utilization increases and can exceed 100% for high enough demand rate. In such cases when implied utilization exceeds 100%, we have insufficient station capacity and one way to rectify this is to increase station capacity by adding machines to a station. Suppose your goal is to keep implied utilization under 100% at all stations[1]. Answer the following two questions: (i) How many machines will be needed at stations 1, 2, and 3, to meet the peak demand? (ii) If WIP is managed so that it averages w = 10 units (this is the CONWIP level), compute the practical worst case cycle time for the line under peak demand, with your chosen of number of machines at stations 1, 2, and 3.
5. (*7 points) This question can take some thought. Answer ANY ONE of the following (i or ii): (i) Can the critical WIP exceed the total number of stations in a line? Can critical WIP exceed the total number of machines in a line? Clearly explain the logic behind your answers. [If your answer is yes, give a supporting example; if your answer is no, explain why not.]

(ii) Based on the available information on the flow line, would you expect the actual lines throughput under peak demand, as in part d, to be smaller or larger than your Practical Worst Case estimate? (Clearly explain your reasoning this question is asking you to examine if the assumptions behind the PWC calculations are satisfied by the line or not and if not what the impact of assumption violation will be.)

[1] This 100% implied utilization may not be an ideal goal because, as we will see in the Variability Basics chapter 8, when there is variability, a 95% utilization can imply long wait times in queue, which may be undesirable. So, a better / pragmatic goal for game play is to keep implied utilization under 85 or 90%, depending on variability and the customer delivery lead time target.