2022-10-08-Final-Exam-EDM
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School
University of Cincinnati, Main Campus *
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Course
7011
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
xlsx
Pages
22
Uploaded by mille2eo
Question Set
I
II
III
IV
V
VI
Attempted 10
20
20
25
25
Max Points
55
20
20
25
25
25
Total
100
170
For this question, I will be giving two examples of operations decisions or actions taken by G
During my undergrad, I was exposed to a Six Sigma course where we learned about GE's imp
Sigma principles and the benefits of them. By identifying problems such as defects and was
the company back, GE was able to utilize Six Sigma to streamline the organization, make it m
productive, eliminate waste, and increase customer satisfaction. Training was incredibly im
thateveryone understood the benefits of data-driven decision making and the principles wo
forseeable future. One more example of GE's actions to improve their operations mangement is operations pe
management (OPM). OPM helps improve performance of plants by analyzing multitudes of
to help drive decision-making when it comes to intraday and day ahead planning. They also offer operations management leadership programs to help early career leaders ga
in supply chain and leadership principles.
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General Electric (GE). plementation of Six ste that were holding more efficient, mportant here so ould be used for the erformance f different types of data ain valuable experience
Product Name
Price ($/unit)
Unit Cost
P
$ 600.00 $ 50.00 4
$ 130.00 Q
$ 600.00 $ 100.00 4
$ 180.00 Work Station (hours)
1
2
3
Profit
Product P
2
2
$ 420.00 Product Q
2.5
1.5
$ 320.00 Cost of Labor/hr
$ 20.00 **fixed and included in unit cost
Days /month
21
Hours per day
16
Hours / month
336
Expenses
$ 100,000.00 Work Station (hours) to Max Demand
1
2
3
**Workstation
280
350
490
**Workstation
Priority
Unit Profit
Product P
$ 420.00 120
3.50
2
Product Q
$ 320.00 90
3.56
1
answer
Raw Material Cost ($/unit)
Total Labor Hours/unit
Work Station 3 (mins)
Bottleneck Ratio ($/min)
Bottleneck Method
Time (minutes)
Product Q
90
124
11160
124
Minutes remaining on Work Station 3
9000
Product P
120
75
9000
75
Minutes remaining on Work Station 3
0
Work Station 2 (minutes)
Demand (units/month)
Production Plan
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Min
Max
75
140
0
140
**Assuming profit is sell price - raw materials - unit cost
n 3 is the bottleneck to make max demand
n 2 is a secondary bottleneck as it also requires more than 336 hours
answer
Monthly Demand
Monthly Demand
Bottlebeck ratio for both Products utilizing Workstation 3 as the bottleneck are very close at $3.5/min for Product P and $3.56/min for Product Q. We want to maximize this bottleneck ratio to maximize profit
. So, we should create as many Product Q as we can prior to switching over to product Product P to meet minimum demand of 75 per month. If we were only considering maximizing profit, we would produce as many product Q as possible.
Product P must have 75*120 = 9,000 minutes available on Machine 3. I used goal seek to change demand for Q until I had at least 9,000 minutes leftover. Ultimatey, we are losing money due to $100,000 per month in expenses.
$ 39,680 $ (28,820)
$ 31,500 Profit per Product
Total Monthly Profit
Processing Time: (min/part)
0.25
0.4
0.15
Setup Time: (mins)
35
40
45
Question 1
Parts
40
Capacity (units/hour)
Step 1
53.33
Step 2
85.71
**2 machines means double the capacity
Question 2
Number of Identical Machines: 1
Number of Identical Machines: 2
Number of Identical Machines: 1
What is the capacity of Step 1 and Step 2 in units per hour
, if the batc
Bottleneck: (*10 points) For what batch sizes is Step Step 2
Step 1
Step 3
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 1= 𝐵/((35+0.25𝐵))
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 2= 2𝐵/((40+0.4𝐵))
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 3= 𝐵/((45+0.15𝐵))
For Step 1 Bott
35+0.2
5𝐵
≥ 40
+0.
4𝐵
Therefore, step
For Step 2 Bott
40
+0.
4𝐵 ≥ 45+0.1
5
Processing tim
and 3, therefo
is bottleneck a
the bottleneck
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B
20
Step 2
48
Step 3
48
ch size is 40 parts
(at each step)?
1 (2, 3) the bottleneck
?
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦= (𝐵𝑎𝑡𝑐ℎ 𝑆𝑖𝑧𝑒)/((𝑆𝑒𝑡𝑢𝑝 𝑇𝑖𝑚𝑒+𝑃𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑇𝑖𝑚𝑒))
ttleneck: 𝐵
p 1 can never be a bottleneck
ttleneck: 5𝐵
me is the same when B = 20 for Step 2 ore, for batches smaller than 20, step 3 and for batches larger than 20, step 2 is k.
m
p
a
σp
σa
CVp
Self Service
4
7.5
15
7.5
30
1.00
Agent
1
7.5
30
7.5
60
1.00
New Arrival Rate 6 per hour
10 per minute
Proposal #2
m
p
a
σp
σa
CVp
1.
(10 points) (i) If Traveling MBA walks to a self-service counter to check in during
(ii) If Traveling MBA goes to an agent, how long must she wait (on average) in line be
(*5 points) Delta Airlines proposes to have all check-ins to be self-service. This would
(*10 points) An alternative proposal to the one in 2 is to keep the four self-service counters an
New arrival time is the sum of the flow rates from (1/a) for both Self-Service and Agent.
𝑁𝑒𝑤 𝐴𝑟𝑟𝑖𝑣𝑎𝑙 𝑅𝑎𝑡𝑒=60∗(1/𝑎_(𝑠𝑒𝑙𝑓 𝑠𝑒𝑟𝑣𝑖𝑐𝑒) +1/𝑎_𝐴𝑔𝑒𝑛
Self Service
5
7.5
10
7.5
30
1.00
Proposal #3
m
p
a
σp
σa
CVp
Self Service
4
4
15
4
30
1.00
Agent
1
2
30
2
60
1.00
Assuming all other values for StDev remain the same for Proposal 2, which
number of self-service counters to 5 and reduced the average arrival time prefer Proposal 2 because the total average time in queue is less than Prop
wait time in queue is still driven by only having 1 agent to process people.
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CVa
p/m
Utilization
Tq (minutes)
2.00
1.875
0.125
0.060
2.00
7.5
0.25
6.25
CVa
p/m
Utilization
Tq (minutes)
g a busy period, how long must she wait (on average) in line before she can use the machine? (Only include the wait
efore being served?
d mean that the previous traffic of agent check-in passengers now flows to the self-service counters. To accommodat
nd one agent but restructure the process and technology so everyone goes to self-service first for initial check-in tak
𝑛𝑡 )
3.00
1.5
0.15
0.082
CVa
p/m
Utilization
Tq (minutes)
1.00
1
0.06666667
0.003
1.00
2
0.06666667
0.143
0.146 Total
h increased the to 10 - we would posal 3. The higher
ting time, not any service time.)
e the new flow rate, Delta Airlines now installs one additional self-service counter (from 4 counters to 5). Wh
king 4 minutes (with a standard deviation of 4 minutes) and then to the agent for 2 minutes (with a standard de
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hat is the new average interarrival time at a self-service counter
?
eviation of 2 minutes). Assuming all unspecified coefficients of variation are 1, would this restructured proces
ss be better than the proposal in 2? Explai
n the reasoning for your answer
Sale Price
$ 28.00 Publisher Cost
$ 20.00 Cu
Underage Cost $ 8.00 Discount Price
$ 7.00 Co
Overage Cost
$ 13.00 Average
150
StDev
40
F(Q)
Critical Ratio
0.380952380952
Q
Quantity
138 Books
Dan's Expected Profit
$ 1,103.05 Publisher Variable Cost
$ 7.50 Publisher Profit Margin
$ 12.50 per book
Publishers Expected Profit
$ 1,723.51 Buyback Price
$ 15.00 Shipping Cost
$ 1.00 New Discount Price
$ 14.00 Sale Price
$ 28.00 Publisher Cost
$ 20.00 Cu
$ 8.00 Co
$ 6.00 Critical Ratio
0.571428571429
Q
157
(15 points) Newsvendor Quantity, Profit:
How many books should Dan order to maximize his expecte
1.
(*10 points) Buyback contract:
The publisher is thinking of offering the followi
𝐶_𝑢=𝑆𝑎𝑙𝑒 𝑃𝑟𝑖𝑐𝑒 −𝑃𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟 𝐶𝑜𝑠𝑡 𝐶_𝑜=𝑃𝑢𝑏𝑙𝑖𝑠ℎ𝑒𝑟 𝑐𝑜𝑠𝑡 −𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑃
Expected profit for Dan is assu
at $8 profit/book.
Expected profit for the publish
books are sold at $12.50 profi
The publisher is offering Dan the buyback dea
because the publisher makes most of it's mon
the original sale of the book to people like Da
the publisher buys the book back from Dan a
$15/book, it's still made $5 on each of those from Dan. The publisher can then turn around and re=s
book in an attempt to recoup any additional g
lost by buying books back from Dan. Assumin
book is still $20 of sales for the publisher (stil
condition), if it can resell all books, they've effectively made $20+$5 = $25 per book inste
$20. They're even making Dan take the brun
shipping cost to maximize their profits.
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ed profit
? For this order quantity, calculate Dan’s expected profit
? If the publisher’s variable cost per book is $
ing deal to Dan. At the end of the season, the publisher will buy back unsold copies at a predetermined price o
𝑃𝑟𝑖𝑐𝑒
uming all 138 books sell her assuming all 138 fit margin.
al ney on an. If at books sell the gap it ng the ll in new ead of nt of the
$7.50, calculate the publisher’s profit
for your order quantity. of $15. However, Dan would have to bear the cost of shipping unsold copies back to the publisher at $1 per co
opy. How many books should Dan order given the buyback offer
? Why do you think the publisher is
consider
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ring offering Dan the buyback deal
?
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