IndE 311

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IndE 311 Problem Session March 2nd, 2007
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Pr. 17.10-3)
Queuing model M/ M/ s
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Case 17.1
a) Status quo at the presses
Queuing model M/ M/ s
In-process inventory 7.52
Status quo at the inspection station
Queuing model M/ D/ 1
In-process inventory 3.94
Inventory cost (7.52 3.94)(8/hour)
91.68 / hour
Machine cost (10)(7/hour) 70 / hour
Inspector cost 17/hour
Total cost 178.68/ hour
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Case 17.1 (contd)
b) Proposal 1 reduce power at presses
Queuing model for the presses M/ M/ s
In-process inventory at the presses 11.05
In-process inventory at the inspection station
3.94
Inventory cost (11.05 3.94)(8/hour)
119.92 / hour Machine cost (10)(6.50) 65 /
hour Inspector cost 17 / hour Total cost
201.92 / hour
The total cost is higher than for the status quo
(Slowing down the machines wont change
in-process inventory for the inspection station.)
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c) Proposal 2 Substitute a younger inspector,
with original speed
In-process inventory at the presses 7.52
Queuing model for the inspection station M / E2
/ 1
In-process inventory at the inspection station
4.15
Inventory cost (7.52 4.15)(8/hour) 93.36
/ hour Machine cost (10)(7/hour) 70 /
hour Inspector cost 19 / hour Total cost
182.36 / hour
The total cost is higher than for the status quo
due to the increase in the service rate
variability and the resulting increase in the
in-process inventory.
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d)
They should consider increasing power to the
presses (increasing there cost to 7.50 per hour
but reducing their average time to form a wing
section to 0.8 hours).
Queuing model for the presses M / M / s
In-process inventory at the presses 5.69
With original inspector In-process inventory at
the inspection station3.94
Inventory cost (5.69 3.94)(8/hour) 77.04
/ hour Machine cost (10)(7.50/hour) 75 /
hour Inspector cost 17 / hour Total cost
169.04 / hour
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Case 2. The PCB production machine repair shop
a)
Queuing model M / M / s / / / N
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a) (contd)
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Case 2 (contd)
E( of PCB machines available) 10 L 4.782
E revenue E of machines available 50
180 30 1,291,075 per month E cost E
of machines available 30 50 120
90,0003 1,130,717 per month E
profit E revenue - E cost 160,358 per
month
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b) Consider leasing another repair station
Queuing model M / M / s / / / N
L 4.311 E profit 152,010 lt 160,358
No, they should not lease an additional repair
station
c) Consider a new type of repair station
Queuing model M / M / s / / / N
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s3 E cost 1,315,800/month L 4.49 E
profit 171,900 / month