OIT 247 BlueSky Airlines Simulation Maria Oktopodaki, the head of revenue management at BlueSky Airlines, has been struggling with one particularly problematic flight, between Lincoln (Nebraska) and New York. On that flight, the airline operates a small plane, with a capacity of 200 seats, and is offering two different fare classes: a full fare (FF), for $850, and a super saver (SS) fare, for $350. To qualify for the SS fare, customers must purchase at least 2 months in advance (before the flight date), and are required to have a Saturday-night stay in New York. In contrast, FF is very flexible, and is offered up until the date of the flight, if seats are still available. In fact, historically, the FF customers are almost exclusively business travelers, who always make last-minute purchases, and are not price-sensitive Using historical data, Maria estimated that the mean demand for SS fares is roughly 130, and the mean demand for FF fares is roughly 55. She would like to build a model to guide her decisions. A key operational lever under her control is the booking limit for the SS fare, i.e., how many seats to make available to SS customers. Historically, that value was set at 120, but Maria is not sure thats right. She knows that, the larger that limit is, the fewer seats she might have available for (higher-paying) FF customers

Treat each of the following questions independently. A template is available to get you started, in BlueSky Simulation template.xlsx. Question 1. Build a spreadsheet model that predicts the revenue for one Lincoln-NYC flight when the booking limit (for SS fare) is set to 120. Question 2. Using additional data, Maria has been able to estimate that the demand for SS fares actually follows a normal distribution, with mean 130 and standard deviation 45, and the demand for FF follows a normal distribution, with mean 55 and standard deviation 20. Update the model in Question 1 to predict the expected revenue for one Lincoln-NYC flight when the booking limit for SS fare is set to 120. How does this number compare with the one you got in Question 1? Question 3. Draw a histogram for the revenue in Question 2, displaying the mean and the net revenue values found 1 standard deviation away from the mean. What are the standard deviation and median? What is the probability that the revenue exceeds a value of $100,000? Question 4. What would the expected revenue be in Question 2 if the distribution of SS demand was characterized by Table 1 below? (the FF demand distribution remains the same)

Value Probability

160 0.1

140 0.3

128 0.4

104 0.2

Table 1 Demand Distribution for SS Demand

Question 5. Maria collected historical SS demand data, shown in the tab Historical SS Demand Values of the spreadsheet BlueSky-Template.xlsx. What would the expected revenue be if she used these values to estimate the distribution of the open market price? (Note. Using historical data amounts to constructing a Custom distribution, with values exactly corresponding to the historical values, and probabilities equal to 1/N, where N is the number of records.)

Question 6. Consider now the following change in the model you constructed in Question 2: the demand for SS fares and FF fares is positively correlated, with a correlation coefficient of 0.6. How would the mean and variance of the revenue compare with the values in Question 2?

Question 7. Using the model in Question (2), find the booking limit that maximizes the expected revenue for one Lincoln-NYC flight. Question 8. Maria realizes that some of the passengers who inquire about SS tickets after the booking limit is reached may actually be convinced to buy up, i.e., purchase an FF ticket. This demand stream would be in addition to the regular demand for FF tickets. Using historical data, she estimates that any customer that is turned away buys-up with a probability of roughly 30%. Change the model in (Q2) to address this issue. What should the new booking limit be to maximize the expected revenue for one Lincoln-NYC flight? Hint. A first-cut approach might be to simply look at the number of SS customers turned away, and take 30% of those as extra demand. However, a more appropriate assumption is to consider that the number of customers turned away is a Binomial Random Variable. This can be selected from the familiar gallery of Assumptions in Crystal Ball. Two parameters must be specified, the number of trials (N), and the probability of success in a given trial (p). To understand this random variable, it is easiest to think about N coin tosses, where each toss gives heads with probability p (this is a biased coin toss!. The Binomial Random Variable corresponds to the total number of outcomes that are heads in the N coin tosses. Warning! The number of trials for a Binomial must always be a positive integer! Question 9. Returning to the model in Question 2, after considerable internal debate, Maria decided to fix the booking limit at 160. Talking to her peers, however, she realized that overbooking is actually a common practice in the industry. In particular, instead of accepting reservations up to the actual capacity of the airplane (200), she could accept reservations up to a virtual capacity, which could potentially be larger than 200, in the hope that some of the customers do not show up on the day of the flight. Using historical data, she estimates that the fraction of SS fare customers (with confirmed tickets) who actually show up for the flight is uniformly distributed, between 85% and 100%. Similarly, the fraction of FF customers (with confirmed tickets) who show up for the flight follows a triangular distribution, with a minimum of 90%, a maximum of 100%, and a likeliest value of 95%. When the plane is overbooked and more than 200 passengers show up for the flight, the airline is ruthless: the first passengers to be bumped (i.e., denied boarding) are among the SS fare. They each receive a $450 coupon, and are rebooked on another flight, in the SS fare class. Only as a last resort, the airline also denies boarding to FF customers, who receive a coupon for $1,000, and are also rebooked on another flight, in the FF class. Change the model in Question 2 to reflect the practice of overbooking as described above.

What would be the expected net revenues on one Lincoln NYC flight (i.e., the revenues net of any fees associated with overbooking) if the virtual capacity used were 220? What is the probability that more than 10 customers are bumped? What would be the expected total overbooking costs paid by the airline? Question 10. Stephanie is aware that there is a very small chance that the plane might fail the mechanical tests just before the flight, in which case all passengers would have to be rebooked, and costs would be incurred as in Question 9. She estimates that the likelihood of that event is roughly 1 in 10,000. Change the model in Question 9 to accommodate for this. What would be the resulting net revenues (for the same virtual capacity of 220)?