Airlines use sophisticated software to determine overbooking levels as well as the appropriate number of seats to offer or protect at each fare level. This software will collect data, perform analyses, assign limits, and generate reports from which management can make decisions. Although the software will do the work, you need to understand how this information is collected and how analyses are performed. This understanding will help you decide whether or not overrides are appropriate or whether should trust the models offered by the software.

1: Probability & EMSR 2: Booking Limits & Seat Protection

Problem 1: Probability & EMSR (You may need to scroll down to see Problem 2!) Instructions: A daily flight has a cabin capacity of 70 available seats that must be divided among three fare classes: Y, M, and B, each with respective fares of $900, $750, and $600. The number of tickets sold in each fare class each day last month is shown in Table 1 below. This data was used to calculate the mean number of tickets sold daily and standard deviation for each fare class, shown in Table 2. Complete Table 3 by doing the following: 1. Use the Normal Distribution formula (NORMDIST) and data from Table 2 to calculate the probability of selling each seat in each fare class. See Excel Help if you need instructions on using the NORMDIST formula. 2. Calculate the expected marginal seat revenue (EMSR) for each seat by multiplying the probability of selling each seat by the full fare class value (e.g. $900 for Y). The probabilities and EMSR for the Y fare class have been done as an example for you. Table 1: Tickets Sold in Each Fare Class Table 2: Means & Standard Deviations Table 3: Probabilities and EMSR =N EL Fare Class Fare Class = Y ($900) M ($750) B ($600) Y ($900) M ($750) B ($600) Seat Y Probability Y EMSR VR B Probability B 1. 22 29 35 Mean 20.633 30.467 33.033 1 100.000% $900.00 1 2 22 20 41 Sigma 2 100.000% $900.00 3 23 42 38 (Standard 3 100.000% $900.00 4 24 35 27 Deviation) 2.456 9.790 8.028 4 100.000% $900.00 5 22 42 19 5; 100.000% $900.00 6 24 30 89 6 100.000% $900.00 7 18 25 28 7 100.000% $900.00 8 22 36 41 8 100.000% $900.00 9 23 16 41 9 100.000% $900.00 10 20 44 B2 10 99.999% $899.99 11 24 32 34 11 99.996% $899.96 v 2U a4 30 11 24 32 34 12 20 42 25 13 17 30 28 14 17 40 3 15 17 18 34 16 18 38 19 17 17 24 32 18 21 16 41 19 20 35 22 20 20 34 40 21 19 28 21 22 23 25 43 23 21 16 41 24 22 47 40 25 21 34 44 26 21 46 29 27 17 18 40 28 24 18 2l 29 23 20 22 30 17 34 41 1 99.999% >8Y9.9Y 11 99.996% $899.96 12 99.978% $899.80 13 99.906% $899.15 14 99.654% $896.88 15 98.909% $890.18 16 97.037% $873.34 17 93.046% $837.41 18 85.816% $772.34 19 74.696% $672.27 20 60.174% $541.56 21 44.067% $396.60 22 28.897% $260.07 23 16.764% $150.88 24 8.524% $76.72 25 3.772% $33.95 26 1.445% $13.00 27 0.477% $4.29 28 0.135% $1.22 29 0.033% $0.30 30 0.007% $0.06 31. 0.001% $0.01 32 0.000% $0.00 Problem 2: Booking Limits & Seat Protection Instructions: After calculating the probabilities and EMSR for each fare class, the airline must decide how many seats to protect and limit for each fare class in this flight. It makes sense for the airline to protect seats for a higher fare class as long as the EMSR for the additional seat is greater than the revenue received for that seat from a lower fare class