Optimal Airline Seat Allocation with Fare Classes Nested by Origins and Destinations

Abstract

Previous research in the optimal allocation of airline seats has followed one of two themes: marginal seat revenue or mathematical programming. Both approaches capture important elements of the revenue management problem. The marginal seat revenue approach accounts for the “nesting” of fare classes in computer reservation systems, but can only control seat inventory by bookings on legs. The mathematical programming approach will handle realistically large problems and will account for multiple origin–destination itineraries and side constraints, but it does not account for fare class nesting in the reservation systems. This paper combines both approaches by developing equations to find the optimal allocation of seats when fare classes are nested on an origin–destination itinerary and the inventory is not shared among origin–destinations. These results are applicable to seat allocation in certain reservations systems, point-of-sale control, and acceptance of groups over their entire itinerary. A special case of the analysis produces the optimal booking limits for leg-based seat allocation with nested fare classes.

Revenue Management Under a General Discrete Choice Model of Consumer Behavior

“…On a theoretical level, single-leg models in which demand for each fare product is assumed to occur in non-overlapping periods have been developed and analyzed by Brumelle and McGill [13], Curry [16], Robinson [35] and Wollmer [45]. A key result of this work is that the optimal policy can be implemented using a set of so-called nested allocations.…”

“…For further work on single-leg allocation problems, see Brumelle et al [14], Kleywegt and Papastavrou [24], Lautenbacher and Stidham [25], Liang [27], Stone and Diamond [38], Subramanian et al [39] and Zhao [48]. For analysis of multiple-leg (network) allocation problems, see Cooper [15], Curry [16], Dror et al [18], Glover et al [22], Simpson [36], Talluri [40], Talluri and van Ryzin [41], [42] and Williamson [43], [44]. A recent surveys of yield management research is provided by McGill and van Ryzin [32]; Talluri and Barnhart [3] provide an overview of yield management and other airline operation research areas.…”

Asymptotic Behavior of an Allocation Policy for Revenue Management

“…The advantage of such approaches is that they yield easy-to-compute and easy-to-implement policies. For models with a single-leg flight, see (among many) Belobaba (1989), Curry (1990), or Brumelle and McGill (1993). Recent studies have considered more realistic models for the demand process.…”

“…Here, however, the so-called "curse of dimensionality" makes the computation and storage of optimal policies difficult or impossible for even moderate-sized problems. In these cases, it is often necessary to fall back on optimization methods that ignore much of the randomness in the demand; see Curry (1990), Glover et al (1982), Simpson (1989), or Williamson (1992). Mathematical programming approaches for railway and rental car revenue management problems can be found in, respectively, Ciancimino et al (1999) and Geraghty and Johnson (1997).…”

Optimization Applications in the Airline Industry

“…Curry [35] combined the marginal seat revenue and mathematical programming approaches to find the optimal seat allocations when fare classes are nested on an origin-destination itinerary, and the seats are not shared among different origin-destinations. Classes with different fares and the same origin-destination are allocated to nests, with higher fare classes' nests containing lower fares.…”