Real Options

Part 1 – Real Options (20 points)

Think of an example of a real option for managing information risk that you observed in practice or your own life. Remember that real options are designed to protect against the negative impacts of some information risk. Please answer the questions below.

1. Please describe what the option is, what information risk it is mitigating, who can use the option, and who offers it. For example, Essmart customers have the option to return products they dislike. This option is offered by Essmart and mitigates the risk customers have regarding product quality and usefulness.
2. How does this option address the information risk you mentioned above? Is the risk shifted to someone else, or does it simply disappear? For example, when Essmart offers customers a return option, the quality and fit-risk are transferred from the customer to Essmart. Conversely, the option to put the Circored plant on “standby” eliminates the downside of price risk.
3. What are the operating expenses and assets associated with this option? For example, in Essmart’s case, offering customers a return option has costs and assets associated with reversing logistics and refurbishing the returned product.

Part 2 –Covid and Queues (30 points)

Question 1 (10 points)

In the Atlanta Metropolitan Area (which, for this question, we assume has 5 million people), 0.5% of the population are tested every day for Covid-19.

• For 80% of patients, the test is negative (i.e., they do not have the virus).
• For the remaining 20% of patients who do have the virus:
  • 60% do not need to be hospitalized and recover from their symptoms at home.
  • 40% of patients are admitted to the hospital.
• Of the 40% of patients who are hospitalized:
  • 90% do not need to be admitted to intensive care (ICU) and recover in a regular hospital bed.
  • 10% of patients will require ICU admission after first spending 4 days, on average, in a regular hospital bed.

• If a patient is admitted to the hospital but not to the ICU, they spend 14 days in the hospital on average.
• If a patient is admitted to the ICU, they then spend 7 days there on average. 50% of patients recover in the ICU, while another 50% do not survive.
• Those who survive then return to a hospital bed to recover, where they spend a further 5 days on average.

On average, how many Covid-19 patients will be occupying (i) hospital beds and (ii) ICU beds in Atlanta?

Question 2 (5 points)

Assume that those hospitalized above arrive randomly to one of 20 hospitals in the Atlanta Metropolitan Area (i.e., the allocation decision is not made based on how busy each hospital is, but instead it is the result of a “flip of the coin”).

The ICUs at each hospital are all equally sized and have 56 beds each. Assume that the ICUs are only treating Covid-19 patients. The coefficient of variation of arrival times and service times (i.e., CVa and CVs) are both equal to 1.

On average, how long will a patient have to wait before they are admitted to the ICU?

Question 3 (15 points)

The government is very unhappy with the answer to Question 2. It takes two immediate measures. The first measure is expanding ICU capacity. The government works with hospitals to increase the number of ICU beds from 56 to 75 beds in each hospital.

The second measure is to ensure that patients should not have to wait more than 6 hours before being admitted to an ICU bed in a regular hospital if they need to be. To achieve this, the government has mandated a policy under which patients can be transferred between hospitals whenever the next available bed becomes available. This is a “first-in-first-out” policy: whichever patient has been waiting in the queue, the longer will be moved to the next available ICU bed, regardless of which hospital this is in.

To simplify this process and reduce the need to transfer patients across large distances over the city, the government is looking to separate the hospitals into groups (of 2, 3, 4, or 5 hospitals), so that patient transfers only occur within that group. For example, suppose there were only 4 hospitals, Hospitals A, B, C, and D, and these were formed into 2 groups of 2 such that Hospitals A and B are in one group, and Hospitals C and D in the other group. A patient requiring an ICU bed at Hospital A could be transferred to Hospital B, but not to Hospital C or D.

a) What is the smallest number of hospitals in each group that will ensure that, on average, patients should not have to wait more than 6 hours before being admitted to an ICU bed at a regular hospital if they need to?

b) On average, how many patients will be either waiting for or occupying an ICU bed at each regular hospital under this system?

Part 3 – Uncle George’s Parka Company (20 points)

After you graduated from Georgia Tech, your uncle George P. Burdell hired you to help him with his company that makes Parkas in China. Competition in this market is growing, and to maintain the current market position, your company must be able to reduce its lead-time as much as possible (lead-time is the time it takes between placing an order to a supplier and the order being delivered to you). After looking at a few numbers, you discover that the biggest contributor to your goods’ lead-time is the customs department at the ports in China. You carry out some analysis and narrow down your choice of the port to either Ningbo Port or Shanghai Port. You find that the costs of using either of the ports are similar, and so is the delivery time of getting your shipment to the two ports. Further, you also find that once your shipment clears customs, the cost and time to deliver to the USA are the same from the two ports. Therefore, the only criterion of selection is how fast your shipment can pass through customs at the two ports. Here are some useful data:

All the containers have to pass through customs. At customs, the only time-consuming process is passing each container through an x-ray machine. According to the available data, both ports have one x-ray machine each. The Shanghai port can process about 2 million containers per month, whereas the Ningbo port can process 1 million containers per month. However, the x-ray machines’ utilization at both of the ports is 0.66 (the two ports use different types of x-ray machines). Further, you have credible information that the average number of containers waiting in the container yard to be x-rayed is the same in both ports.

Question 1 (10 points)

Given this information, your uncle George says that since both the ports have the same average queue size, it would not matter which port you choose. Do you agree with your uncle? Use the data provided above and justify your answer. Additionally, you may assume that the coefficient of variation of the time between arrivals for containers (CVa) and the coefficient of variation of the service time of the x-ray machine (CVS) are both equal to 1.

Question 2 (10 points)

The export business in China is growing. Uncle George, who has just returned from a trade expo in Shanghai, has informed you that the port authority of Ningbo expects the demand to reach the same level as Shanghai. The port authority of Ningbo is now deciding how to change its system to accommodate this surge in demand. They have two options, (a) to retire their existing x-ray machine and buy an x-ray machine similar to the one used by the Shanghai port, or (b) to buy another x-ray machine similar to the one they already own and therefore operate the system with two similar machines. Both the options will cost the port authority of Ningbo the same.

Purely from the perspective of reducing lead-time, is (a) or (b) better for you? Please show your detailed analysis.

Part 4 – BlaBlaCar (30 points + 10 bonus points)

Scratching your post-pandemic itch to travel, you decide to accept an internship offer at the Paris headquarters of BlaBlaCar (https://en.wikipedia.org/wiki/BlaBlaCar (Links to an external site.) and https://www.blablacar.com/) (Links to an external site.), an online marketplace for carpooling with 70 million active users. BlaBlaCar matches people that want to go from (near) A to (near) B at a given time (for example, from The Hague to Rotterdam between 7 am and 8 am on some Friday) with drivers that are driving from A to B around that day and time.

Unlike other ridesharing platforms, most BlaBlaCar drivers use the platform to cover travel expenses and not as a source of income. Drivers post their ride trajectories some time in advance, and interested riders contact the drivers to arrange pickup details. BlaBlaCar algorithms suggest prices to drivers (usually enough to cover travel costs), and BlaBlaCar makes money by charging drivers 15% of the fare.

One of your first tasks is to estimate the number of drivers and passengers needed to make BlaBlaCar’s market “thick.” To do so, you devise a simple stylized model of this platform to gain some intuition. To simplify things, in this “first cut” model, you make a few assumptions:

1. A day is divided into 24 slots, each one hour in length;
2. You consider only one route on one specific day (for example, The Hague to Rotterdam and the 24 1-hour slots on February 27th);
3. You assume that, at some point before the specific day you are analyzing, drivers and riders arrive simultaneously on the platform. Furthermore, each rider and driver choose only one slot on that day.
4. The platform matching mechanics are as follows: (a) riders and drivers enter the platform and choose specific slots. (b) In each slot, drivers and riders are matched at random. (c) unmatched rivers and riders leave the platform. For example, if there are 5 riders and 7 drivers in a given slot, there will be 5 matches, and 2 drivers will be unmatched and will leave the platform. Similarly, if there are 1 rider and 0 drivers, the rider will not be matched (and will not change time slots) and leave.
5. Each driver can only take one passenger. For example, if there are two drivers in one slot and only one passenger, or two passengers in a slot and only one driver, only one ride occurs.
6. Drivers and passengers choose slots with the same probability – all slots in a day are equally likely to be selected (they are selected uniformly at random).

Question 1 (10 points)

If a single passenger arrives on the platform and is looking for a ride on a specific slot and route on a given day, what is the minimum number of drivers that should be in the system offering rides for that route so that they find a ride with a probability of at least 80%?

Question 2 (20 points)

Note: This question is more advanced, and I suggest using Excel, R, Python, Matlab (or your preferred programming language) to solve it.

Note that the scenario in Question 1 is great for the passenger but terrible for the drivers. A well-managed platform with many matches depends not only on the number of drivers and passengers but also on the balance between them. A liquid platform is one where many matches occur, and a small number of people are unmatched. This concept is also known as market thickness. Thus, with the same assumptions as before, what is the minimum number of drivers and passengers that must arrive at the platform searching for a trip on a day and route such that, in expectation, at least 80% of passengers and 80% of drivers find a match?

Question 3 (5points)

Of course, this model is somewhat unrealistic. However, do you think it provides an upper bound or lower bound on the actual number of drivers needed?

Question 4 (5 points)

How could you make this model more realistic? What other data would you need?