University of Chicago Booth School of Business
Operations Management, Bus 20500
Birge
Midterm Exam, Winter 2021
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Instructions:
1. PRINT your name legibly on first page of any worksheet files that you upload.
2. Be sure to complete Question 1 to confirm the Booth honor code before uploading any files.
3. This is a closed book/closed note exam. By submitting an answer, you are affirming that you have not
consulted any sources or had any discussions related to the exam with anyone. You are allowed only one
sheet of notes.
4. You may use the calculator function in your computer but also affirm that you have not used “search” or
attempted to access outside sources.
5. Total Points = 33. It is YOUR responsibility to ensure that you have 33 points worth of questions in your
exam and the Excel answer sheet.
6. Exam duration = 80 minutes. The total amount of access time on Canvas is 110 minutes; so, you have
an additional 30 minutes to print the exam and to prepare a PDF of your answers before uploading your
submission.
7. You must use the units specified to receive full credit.
8. Points for each question are shown in brackets.
9. You must use the Excel file to record your answers and you must submit your “work” on the
exam pages to receive credit for those answers (and especially to receive any partial credit).
10. Only your final answers recorded on Excel entry sheet will be graded; HOWEVER, for problems 1–4, as
noted above, if a question requires analysis, you must show your work with each question on pages 2–8 in
order to receive credit.
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1. [4] Every night in the city of Audisonville, refuse collects at a rate of 8,000 pounds per hour in
the central district (home to bars, restaurants and night clubs) from 10:00 pm to 5:00 am Central
Standard Time (CST). Crews from Audisonville sanitation start collecting the refuse at a rate of
6,000 pounds per hour from midnight until all the accumulated refuse is collected. Audisonville
health department finds it unsafe to have more than 20,000 pounds of refuse in the central district
at any time due to the plentiful local rodent population. They also have a policy of collecting all of
the refuse from the central district before the start of the following evening. [Hint: You may find it
useful for answering the questions that follow to make a buildup diagram using the axes below. ]
INV(t) (Lbs.*1000)
0
time, t (CST)
10pm
Considering this situation, answer the following questions, using the units in the Excel answer
sheet.
(a) [2] Does the balance in the shell accounts ever exceed the targeted limit of 20,000 pounds?
What is the highest balanced reached each day?
(b) [1] For how many hours a day does the balance exceed its base level of 20,000 pounds?
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(c) [1] For how many hours, if at all, does the balance go above the targeted upper limit of 20,000
pounds?
2. [5] The city of Audisonville has become a destination wedding spot due to its liberal opening policies
in the central district. Couples must complete two steps to be married in the court house. First,
they must obtain a license after completing an application. Second, they are joined together legally
in a ceremony performed by a judge. These tasks must be done in this order. When Alice and Bob
arrived for their ceremony early on Monday morning, there was a single judge, Vera Fast, who was
both issuing licenses and performing ceremonies. Vera takes on average 7 minutes to issue a license
and exactly 5 minutes to ask the necessary questions, receive the replies, and pronounce the union
of the couple.
(a) [1] When only Vera is working, what is the capacity of the Audisonville marriage process (in
couples per hour)?
Suppose that later in the morning a clerk of the court, Tay Kentime, arrives for duty. Tay
can process the licenses, but is not as efficient as Vera at that process. He can only process
licenses in 10 minutes on average. When Tay is processing licenses, he is the only one who can
enter the information due to security regulations. While Tay is working on the licenses, Vera
can then only hold the wedding ceremonies and cannot process licenses during her idle time.
On average, couples arrive at the court house for weddings at a rate of 3 per hour.
(b) [1] What is the capacity of the court house for weddings now that Tay is on duty (in couples
per hour)?
(c) [2] Assuming no variation in any of the processing times, what is the average number of couples
to be wed in the court house at any point in time?
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(d) [1] Suppose now that the process have some variation but the average times all remain the
same. Which of your answers to the previous questions would change and why?
3. [4] After completing their wedding ceremony, many of the newly married couples proceed to Fotomemories, a photographer’s studio conveniently located next door the Audisonville court house.
Information for the first four couples to visit Fotomemories appear in the table below. The time between their successive arrivals to Fotomemories (starting from its opening) and the time for taking
their photos are as follows:
Couple
1
2
3
4
Interarrival time
to Fotomemories (minutes)
1
2
2
1
Service time
at Fotomemories (in minutes)
3
3
2
2
Upon having their photos taken, the couples pay for and receive their photos in a separate process.
Assume that no other couples were present when these couples were photographed and that each
is served in the order of their arrival. There is a single (very efficient!) photographer, so only one
couple can be photographed at a time. Others must wait in a waiting area outside the photographer’s
wedding setup area. Note: Fotomemories’ entire studio includes both the wedding setup and the
waiting area.
(a) [1] Compute the makespan T of the four couples, i.e. the time at which the fourth couple has
completed having their photos taken after the starting from time 0 (in minutes).
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(b) [1] How long (in minutes) did the four couples spend in the Fotomemories studio on average?
(c) [1] On average how many of the four couples were in the Fotomemories studio at any given
time (take the average from time 0 to time T)?
(d) [1] Compute the total time spent by all four couples in the holding area (in minutes).
4. [7] In addition to wedding photos, Fotomemories has an additional major operation in taking photos
for passports and visas for multiple countries’ consulates also located on the block of the courthouse.
For all photography efforts, their current crew of photographers can provide at most 400 total hours
of labor per month. They have a special printer for passport and visa photos that is limited to 300
hours per month and can process at most 10 photos per hour. Lastly, the dedicated wedding space
is only available 250 hours per month (with other hours dedicated to other events). On average, due
to the efficiency in their wedding setup area, a photographer can photograph 20 wedding couples
per hour. Photographers can only process passport and visa photos can only be processed at a
rate of 10 passport or visa photos per hour due to restrictions on the image size and composition.
Fotomemories earns a net revenue of $5 per wedding photo and each passport or visa photo produced
earns $3 in net revenue.
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(a) [2] Let W indicate the number of wedding photos produced at Fotomemories in one month
and let P indicate the number of passport or visa photos produced in one month. Assuming
that Fotomemories can choose any mix of demand up to their capacities, using these decision
variables, formulate a linear program to optimize net revenue.
(b) [3] You can use the graph below (where the axes are marked in 1000’s) to show the linear
program feasible region and optimal solution. Provide your optimal solution (W ∗ , P ∗ ) in the
spaces on the Excel answer sheet.
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8.0
7.5
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
W (1000s)
3.0
2.5
2.0
1.5
1.0
0.5
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
P (1000s)
4.0
4.5
5.0
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The following is the sensitivity report Excel generated when solving the correct linear program
for parts (a)-(b).
Figure 1: Sensitivity Report.
(c) [1] Are there any bottleneck resources for Fotomemories? If so, which resource(s) are bottleneck(s)?
(d) [1] Which would be better in terms of net revenue for Fotomemories: encourage a photographer
to offer an extra hour of time each month or expand capacity of either the passport/visa
machine or the wedding setup area by an additional hour per month. Justify your answer.
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Multiple Choice Questions
Determine the single best answer for each of the following multiple choice questions and circle your
answer on the Excel answer sheet. No credit will be given if more than one answer is circled.
5. [1] In The Goal, the game of dice and matchsticks illustrates:
(a) the value of small batches.
(b) the impact of statistical fluctuations in a plant.
(c) the value of forecasting.
(d) none of the above.
6. [1] In National Cranberry, we saw that adding a dryer would:
(a) increase overtime.
(b) decrease truck waiting.
(c) increase the daily throughput.
(d) all of the above.
(e) none of the above.
7. [1] The capacity of an operation that consists of multiple steps in series:
(a) depends on the actual total throughput.
(b) follows the exponential distribution.
(c) impacts cycle-time.
(d) can be negative.
8. [1] The average cycle-time of jobs through a business process flow:
(a) increases as capacity increases.
(b) increases as variability increases.
(c) increases as throughput decreases.
9. [1] Little’s Law:
(a) doesn’t hold when there is variability in a process flow.
(b) relates the capacity of a system to its throughput
(c) says the average inventory is proportional to the average cycle-time.
(d) can’t be used for calculating capacity.
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10. [1] We constructed a Gantt chart in class:
(a) to illustrate how resources are allocated through time in the Varsity Subs process.
(b) to model the buildup of wet berries at National Cranberry.
(c) to understand the breakdown of CT in IBM Credit.
(d) to visualize a capacity expansion trajectory.
(e) None of the above.
11. [1] In The Goal, a Herbie is:
(a) an automobile.
(b) a capacity bottleneck.
(c) an inventory buffer with limited storage capacity.
(d) a problematic worker in the production facility.
12. [1] Consider callers waiting on hold at a call center. We plot the number in the queue over time.
That is, the horizontal axis represents time, t, and the vertical axis represents the number of callers
on hold. The area under the curve would indicate:
(a) the total inventory of callers waiting at time t, IN Vq (t).
(b) the total waiting time of all callers.
(c) the maximum time a caller must wait.
(d) the average waiting time of a caller, CTq .
13. [1] The capacity of an operation with unlimited buffer space:
(a) can influence cycle-time.
(b) can be negative.
(c) depends on the variability of the arrival stream.
(d) typically follows an exponential distribution.
14. [1] Shouldice Hospital could increase revenue by decreasing cycle-time because:
(a) their revenues only depend on inventory;
(b) their bed-capacity constrains inventory;
(c) their throughput is constrained;
(d) all of the above.
15. [1] In a linear program for determining an optimal product mix, the contribution-maximizing mix
of products:
(a) cannot violate any of the resource constraints.
(b) includes any product with positive net contributions.
(c) cannot include a product that requires a bottleneck resource.
(d) none of the above.
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16. [1] In the Goal, what did Jonah identify as the key factors to consider to achieve “the goal”?
(a) throughput, inventory, and operational expense.
(b) capacity, revenue, and utilization.
(c) production, cost, and process time.
(d) none of the above.
17. [1] In Sof-Optics, they could ensure close to zero lost calls by:
(a) setting the CSR numbers to achieve 100% utilization at all times.
(b) setting the DEO numbers to achieve 90% utilization at all times.
(c) setting the CSR numbers to achieve 60% utilization at all times.
(d) setting the DEO numbers to achieve 70% utilization at all times.
(e) none of the above.