MGB 452Y HW 1
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MBAD-614
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Industrial Engineering
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Jan 9, 2024
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MGB 452Y HW 1
Due Date: 18
th
October 2023 11:59pm
1.
A manufacturing company producing medical devices reported $60,000,000 in sales over the last
year. At the end of the same year, the company had $20,000,000 worth of inventory of ready-to-ship
devices.
a.
If units in inventory with cost of $1,000 per unit are sold for $2,000 per unit, how fast does the
company turn its inventory?
b.
The company uses a 25 percent per year cost of inventory. That is, for the hypothetical case that
one unit of $1,000 would sit exactly one year in inventory, the company charges its operations
division a $250 inventory cost. What---in absolute terms ($) ---is the per unit inventory cost for a
product that costs $1,000?
2.
The following figures are taken from the 2003 financial statements of McDonald’s and Wendy’s.
Figures are in million dollars.
McDonald’s
Wendy’s
Inventory
$129.4
$54.4
Revenue
17,140.5
3,148.9
Cost of goods sold
11,943.7
1634.6
Gross profit
5,196.8
1514.4
a.
In 2003, what were McDonald’s inventory turns? What were Wendy’s inventory turns?
b.
Suppose it costs both McDonald’s and Wendy’s $3 (COGS) per their value meal offerings, each
sold at the same price of $4. Assume that the cost of inventory for both companies is 30 percent
a year. Approximately how much does McDonald’s save in inventory cost per value meal
compared to that of Wendy’s? You may assume that inventory turns are independent of the
price.
3.
A donut store is open 8 hours a day and sells two types of donuts – blueberry cake donut and
chocolate frosted donut. On average the demand is 80 donuts per day for EACH type. The store has only
one machine which makes both types, and once it starts, it produces one donut every 2 minutes for
either type. The production alternates between the two types, i.e., a batch of one type is followed by a
batch of the other. The setup time is 20 minutes per batch for either type.
a.
If the batch size is 10 donuts per batch, what is the capacity per day for each type of donut?
b.
If the batch size is 20 donuts per batch, what is the capacity per day for each type of donut?
c.
What is the minimal batch size in order to satisfy demand for both types?
d.
If the setup time is 8 minutes for either type, and batch size is 20 donuts per batch, what is the
capacity per day for each type of donut?
4.
Furniture Face Lift refinishes old wood furniture. Their process for refinishing chairs has 8 workers and
4 stations. Each chair starts at the Stripping station, then goes to Priming, then to Painting and finally to
Inspection.
Where there are multiple workers within a station, each worker works independently on
his/her own chair.
Assume inventory buffers are allowed between each station and each station has
inventory to work on at the beginning of the day.
Station
Staffing
Processing time
(hours per chair per
worker)
Stripping
3
2.5
Priming
2
1.5
Painting
2
1.75
Inspection
1
0.8
a.
What is the maximum number of chairs per hour that can be produced?
b.
Suppose now that each worker is trained to do all tasks and each worker works on a chair from
start to finish, i.e., each worker does Stripping, Priming, Painting and Inspection. What is the
maximum capacity of the process in chairs per hour?
5.
Consider the following assembly line:
Department
Processing Capacity (units/day)
Yield
A
2200 input, 1760 output
80%
B
1600 input, 1440 output
90%
C
1800 output
100%
D
1000 input, 800 output
80%
E
800 output
100%
Three units of output from Department C and one unit from Department D are used to assemble one unit of
final product in Department E.
Department E can produce at most 800 units of final product per day.
Suppose that all defective units produced at any Department will be detected and removed from further
processing.
a.
What is the system capacity?
b.
Where is the bottleneck?
c.
What is the utilization of each department when the system operates at its full capacity?
B
C
D
E
A
3 parts
1 part
6. (M/M/1 queue)
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank
transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller
window occur at random, with a mean arrival rate of 24 customers per hour or 0.4 customers per
minute. Assume that the service times for the drive-up teller follow an exponential probability
distribution with a mean service rate of 36 customers per hour or 0.6 customers per minute.
a.
The probability that no customers are in the system.
b.
The average number of customers waiting in line.
c.
The average number of customers in the system.
d.
The average time a customer spends waiting in line.
e.
The average time a customer spends in the system.
f.
The probability that arriving customers will have to wait for service (hint: an arriving customer has to
wait except when no customers are in the system upon his arrival).
7. (Multiple-server queue)
Consider a post office with two employees and a single waiting line. On average, the inter-arrival time is
6 minutes. Standard deviation of inter-arrival time is 3.94 minutes. Average service time is 5 minutes.
Standard deviation of service time is 2.83 minutes.
a.
What is the arrival rate?
What is the service rate per employee?
b.
What is the utilization of each employee?
c.
What is the average time a customer waits for service?
d.
What is the average number of customers waiting to be served?
e.
What is the average number of customers being served?
f.
What is the average number of customers in the system?
g.
What is the average time a customer spends in the system?
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