spring2022_final_Answer key (All Answers are Correct) University Of Chicago MBA 42201
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Module
MBA 42201
Institution
MBA 42201
University of Chicago Booth School of Business
Operations Management
Spring 2022
Linwei Xin
Final Exam, Spring 2022
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01– Thursday 8:30–11:30am 81– Thursday 6–9pm 85– Saturday 1:30–4:30pm
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1
,1. [4 points] Amber Lime, an aspiring comedian in Chicago, had to look for day jobs when the pandemic
hit the entertainment industry. She was able to find a part time job as an associate at the Hyde Park
office of Parcel Express, a national parcel shipping company.
Like many other shipping companies, Parcel Express su↵ered from disruptions in their shipment net-
works due to several reasons. One reason was the unexpected explosion in the volume of return
shipments due to the boost in online shopping. To partially streamline their local operations, Hyde
Park office of Parcel Express assigned Amber and a coworker to handle all the return shipments from
the customers. They have two tasks.
• Step 1: Amber checks whether the customer has printed the correct return label. If a customer
does not have a correct return label, Amber directs them to a nearby printing facility. The
probability that Amber sees a correct return label upon a customer visit is 70%. Here, each
customer visit is counted separately, so for example, if a customer with an incorrect return label
visits the office, and then comes back to the office after going to the printing facility, two visits
are counted even though the customer is the same on both visits.
• Step 2: If the return label is correct, the package is placed on a conveyor belt which goes to the
temporary storage area. Amber’s coworker then sorts the package and places them in bins to be
loaded onto vehicles.
The inter-arrival times of customer visits for return shipping are distributed exponentially with an
average of 5 minutes. Amber can check return labels at a rate of 30 per hour, and her service times
are exponentially distributed. Amber’s coworker can sort a package in 6 minutes on average, with a
standard deviation of 1 minute.
Hint: Draw a process flow diagram of the return package accepting and sorting process.
Label
Sorting
ta5min Checking
Call Mr301hr 70 ts 6min
CE I 5 1
301
v
2
, (a) [2] Assuming the system is in steady state, how many customers are waiting to be served in Step
1, on average?
MIM I queue
605perhour
fi g 30 perhour 3 0.4
INYg 974 0 2667
(b) [2] Assuming the system is in steady state, how long does a return package spend on average in
the temporary storage area before Amber’s coworker sorts them?
CTg CT ts
CT
CIII ts
If
By Burke's Theorem the interarrival times to sorting stage are exponentially
distributed Cal L
E
where Is 12 0.7 8 H perhour
gs
Is 86 0.84
Ctg I x 6x
9TH 16 1875 minutes
3
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