Final exam MSQM Spring 2024
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Albany State University *
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Industrial Engineering
Date
Feb 20, 2024
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MSQM: Operations Winter 2024
Prof. Mor Armony
Final exam
I
N
YOUR
SOLUTION
, PLEASE
JUSTIFY
YOUR
STATEMENTS
AND
EXPLICITLY
STATE
ALL
OF
YOUR
ASSUMPTIONS
. Good Luck!!
Total 4 Questions = 100 points
Total time = 120 minutes
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Question 1 (24 points)
True or False (choose one option per question)
a.
(3 points)
According to Little’s Law flow time is equal to throughput multiplied by inventory.
o
True
o
False
b.
(3 points) A process may have multiple bottlenecks.
o
True
o
False
c.
(3 points)
The bottleneck is the resource with the highest capacity.
o
True
o
False
d.
(3 points)
A process flow time always decreases when the batch size increases
o
True
o
False
e.
(3 points)
It is impossible to reduce a process flow time without reducing the duration of its critical path.
o
True
o
False
f.
(3 points)
In the EOQ model, when the cost of capital increases the order quantity increases.
o
True
o
False
g.
(3 points)
In the Newsvendor Model, if the salvage value is zero, it is best not to order items at all.
o
True
o
False
h.
(3 points)
In waiting lines, reducing variability helps reduce delays
o
True
o
False
Question 2 (26 points)
A new do-it-(almost)-yourself tax advisory office has opened last year. This service allows customers to complete their tax return with some minimal help from a tax specialist. Customers arrive into this office by appointment only, and always arrive on time. As soon as a customer arrives they check in with a receptionist who escorts them to a workstation (this step takes 4 minutes
). The customer will occupy the same workstation until their check-out step begins. At the workstation the customer first spends 10 minutes
on their own, filling out paper work, and logging on to the system. At this point a tax specialist approaches the customer and gives them a 15 minute
tutorial. The customer then spends another 80 minutes
completing their tax return information on their own. At this point the same tax specialist approaches the customer and helps
them review their return. This step takes 20 minutes
. During
the last 10 minutes
of this review process the customer and the tax specialist are joined by a supervisor (for the entire 10 minutes) who oversees the end of this process and signs the forms. Finally, the customer walks back to the
same receptionist to check out. This check out step takes 5 minutes
. The office has 6
tax specialists, 2
receptionists and 2
supervisors. Assume that all times are exact.
a.
(
6 points
) Draw a process flow diagram for the process described above. For each
step include the flow time and the resources involved.
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b.
(
6 points
) What is the flow time associated with a typical customer (assuming no wait and an unlimited number of workstations)? c.
(7 points)
What is the capacity of this office (in terms of # of customers per hour)
assuming that there is an unlimited number of workstations? What is (are) the bottleneck(s)?
d.
(7 points)
What is the minimal number of workstations required to ensure that the
capacity of the process remains the same as in c.?
Question 3 (25 points)
You are in charge of the new iPad Pro replenishment at a local Apple store. Demand for the iPad
is incurred at a known and fixed rate during the considered period. Lead time is also known and
does not change over time. Suppose that the ordering cost is $10,000
per order, purchasing cost
is $400
per iPad, annual demand is 1,500,000
iPads, and the annual cost of capital is 20%
.
Assume that opportunity cost is the only factor that is non-negligible for the holding (carrying)
cost. Assume 250
business days per year.
a.
(6 points)
How many iPads should you order every time you place an order? What is the
total annual holding (carrying) + ordering cost (excluding purchasing cost) associated
with this order quantity? b.
(6 points)
Assume that leadtime for iPads is 2 business days. What is your reordering point in this case?
c.
(
6 points
) Under a special promotion the ordering cost goes down to $9500
/order. What
would be the optimal order quantity under this promotion? What is the total annual
holding + ordering cost (excluding purchasing cost) associated with this order quantity? d.
(7 points)
At the end of the promotion period, your supplier has decided to offer you a quantity discount, such that the ordering cost would be $9500/order if the order size is at least 20,000
iPads and $10,000/order otherwise. How many iPads should you purchase under this quantity discount scheme? Justify your answer.
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Question 4 (25 points)
For this question, feel free to utilize the MMS spreadsheet. Lowe’s Cinema is trying to determine
how best to arrange the cashiers at one of its movie theaters. The arrival process of ticket buyers to the movie theater is a Poisson process with arrival rate
of
120
customers per hour. The amount of time it takes to serve a customer at one of the cashiers is exponentially distributed with a mean of 2
minutes. a.
(6 points)
What is the minimal number of cashiers required to keep the system stable?
b.
(6 points)
Using the number of cashiers from a., what is the average time that a customer spends in the system (waiting plus service) assuming a single line and a first-come-first-
serve service discipline? What is the average number of people in the system?
c.
(7 points)
The theater has decided to replace the cashiers with automatic ticket kiosks for
the purpose of purchasing tickets. The time it takes for a customer to purchase a ticket at the kiosk is 1.5
minutes on average. A kiosk can serve up to one customer at a time. The kiosks are physically spread-out throughout the theater lobby, so that each kiosk has its own dedicated line. Customers choose randomly between the lines, and do not switch between lines. How many kiosks will Lowe’s need to guarantee that the average time
in the system
does not exceed the number you got in question b.?
d.
(6 points)
How would your answer to c. change if instead, you wish the average number
of people in the system to be the same as in question b.?