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AIRLINE SEAT ALLOCATION
Yield Management was born with the application of overbooking with the first published work by Beckman (1958). Overbooking arose as airlines oversold capacity to mitigate losses from the arrival uncertainty of customers. In the post airline deregulation environment in the United States, airlines started to offer fares a multiple prices and in addition to dealing with arrival uncertainty, airlines focused on the allocation of capacity across price or fare classes. Littlewood (1972) is the seminal work on fare class allocation or airline seat allocation as it is more commonly called. Littlewood presented the simple decision rule for a two-fare model; continue to sell discount seats as long as r [> or =, slanted](1-P )R where r is the revenue from low-fare passengers, R revenue from full fare, and P the probability that full-fare demand exceeds remaining capacity. Indicating that an airline would continue to sell discounted seats; until such a time, the marginal revenue of full-fare seats fare times probability of selling at least that many seats (to that fare class) exceeds the revenues from selling the discounted seat.
Littlewood's rule is extended to multiple-fare classes in Belobaba (1987) with Belobaba introducing the term expected marginal seat revenue (EMSR). For more than two-fare classes, EMSR is Littlewood's rule applied sequentially in increasing fare order. The method is only optimal for two fare classes. EMSR is later refined by Belobaba into EMSRb (Belobaba and Weatherford, 1996). EMSRb works as follows: given estimates of mean demands, μi , and standard deviations, σi , for each fare class i with fare fi , the EMSRb heuristic sets a protection level (the number of seats to reserve for this and higher yielding fare classes) [theta]i so that (Formula Omitted: See PDF) where [Xmacr ]i is a normal random variable with mean μ ≡∑μi and variance ∑σi2 and [fmacr]i is the weighted average fare ∑μi /μ fi .
EMSRb is logically the same as Littlewood's rule; continue selling discounted seats until such a time that the expected marginal revenue of future sales in higher fare classes exceeds the discounted fare. These future sales are for a weighted average fare from...