# solution

Consider a CONWIP flow line
with 3 stations in series (1Ã  2Ã  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, rb, 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 averagesw =
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 wantboth the THand 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
1. (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 THPWC =
0.9 rb?
1. (*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. Answer the following two questions:
(i) How many machines will be needed at stations 1, 2, and 3, to meet
thepeakdemand?
(ii) If WIP is managed so that it averagesw =
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.
2. (*7 points) This question can take some
thought.
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

(ii) Based on the available
information on the flow line, would you expect the actual lineâ€™s
throughputunder peak demand, as in part d, to
be smaller or larger than your Practical Worst Case estimate? (Clearly explain
your reasoning â€“ 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.)

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