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spoilage. The objective of the cost-based overbooking model is to find the optimal AU that minimizes the total combined costs of denied boardings and spoilage: MINCost of DB Cost of SP (4.5) Probability calculations of the normal distribution allow the following measures to be calculated for each value of AU, given CAP and estimates of NSR and STD: Total cost = $DB ? EDB $SP ? ESP (4.6) where: $DB and $SP = cost per DB and SP, respectively E DB = expected number of DB, given AU E SP = expected number of SP, given AU Finding the optimal AU in this approach requires calculations of Gaussian probabilities and expected values, followed by a mathematical search over a reasonable range of AU values to find the minimum total cost. As shown in Figure 4.13 for our flight example, the total costs of denied boardings increase as the AU is increased above the physical capacity (CAP) of 100 seats. At the same time, each increase in AU results in a lower total spoilage cost. In the example shown, the cost per denied boarding is assumed to be $200 while the cost per spoiled seat is assumed to be $300. The minimum cost AU in Figure 4.13 is therefore 123. Some RM systems provide airline RM analysts with a graph Denied Boarding and Spoilage Costs Airline Revenue Management 97 very similar to that shown in Figure 4.13, allowing them to determine the sensitivity of total overbooking costs to their own judgmental modifications to the optimal AU. The cost-based overbooking model has an explicit objective that matches the proper objective of airline overbooking (i.e., minimize the total costs of denied boardings and spoilage). However, the current “state of the practice” among most airlines does not reflect complete and widespread adoption of this model. Instead, many airlines continue to use the probabilistic/risk framework, due both to its relative simplicity and because the estimation of cost inputs required by the cost-based model can be difficult. The costs of a denied boarding on a given flight can include a variety of elements, some of which are not readily quantifiable in monetary terms: • Cash compensation paid to involuntary denied boardings. • Free travel vouchers as incentives for voluntary denied boardings. • Meal and hotel costs for displaced passengers. • Space on other airlines to accommodate displaced passengers.



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