Serial Nesting and Revenue Optimality

1. Serial Nesting and Revenue Optimality Ronald Menich Presentation to AGIFORS Res&YM Study Group Bangkok May 2001 ©2001 Manugistics, Inc. and Manugistics Atlanta, Inc. ("Manugistics"). All rights reserved. This document is confidential, contains trade secrets of Manugistics and may not be used by recipient except as expressly authorized by Manugistics.

2. Outline • Define serial nesting • Display serial nesting availability computations found in different inventory control systems • Discuss revenue implications of serial nesting in different demand scenarios

3. Some Definitions Availability or Seats Available A function AV( t, i; G(t) ), defined at time t for class or bucket i, such that a booking request of type i and size b can be accepted at time t only if b <= AV( t, i; G(t) ). The G(t) is a set of parameter values (e.g., seats sold, booking limits, protection levels) at time t upon which the availability computation depends. Inventory control system A computerized system that computes availability.

4. Serial Nesting • Serial nesting is a particular type of availability computation embodied in many inventory control systems • Serial nesting protects seats for ‘higher’ classes from consumption by ‘lower’ classes • Two basic categories of serial nesting: • Strong serial nesting • Weak serial nesting

5. Variations • Some inventory control systems permit • Classes outside the serial nest • Multiple nests and different types of serial nests (e.g., protection level nests versus booking limit nests) • Booking limit or other controls to apply to classes within a serial nest • In different environments, serial nesting can apply to • Classes or buckets within one leg cabin • Classes within a segment cabin • Classes within an O&D path cabin

6. Definitions Strong serial nesting Consider an ordered set J of classes or buckets that use a common set of leg cabins and no others. If AV( t, i; G(t) ) >= AV( t, j; G(t) ) for all classes i<j in J, then the function AV() is said to be strongly serially nested over J at time t. The ‘higher’ the class, the higher the availability.

7. Strong Serial Nesting Examples

8. Definitions Serial nesting or weak serial nesting If AV( t, j; G(t) ) > 0 implies AV( t, i; G(t) ) > 0 for all classes i<j in J, then AV() is said to be serially nested (or weakly serially nested) over J at time t. It is never the case that a ‘higher’ class is closed whereas a ‘lower’ class is open.

9. Weak Serial Nesting Example

10. Justification for Serial Nesting Serial nesting Revenue Management goal: • Protect seats for high value demands from consumption by low value demands How should value be defined?

11. Thought Problem 1 Classical RM demand assumptions: • Two classes, A and B, with average fares $150 and $100 • Distribution cost[A] = distribution cost[B] • All of class B’s demand arrives before any of class A’s. • Independent demand streams • Neither cancellations nor no shows • More demand than capacity Under these assumptions, it is a good idea to protect space for class A demand. Strong serial nesting can achieve this.

12. Thought Problem 2 Same assumptions as in Problem 1, except: • Class A and B booking requests intermixed • Class B bookings do not cancel. • Class A bookings cancel with probability 2/3, and receive a full refund of their $150 fare. • No overbooking allowed Value[A] = (1/3) * $150 + (2/3) * ($150 - $150) = $50 < $100 = Value[B] ??

13. Quote from the Literature Subramanian, Stidham and Lautenbacher, Transportation Science, 5/99: “In contrast to previous models, we show that … it may be optimal to accept a lower fare class and simultaneously reject a higher fare class because of differing cancellation refunds, so that the optimal booking limits may not always be nested according to fare class.”

14. Moderation Even though serial nesting may not be optimal in certain demand scenarios, users often still prefer serial nesting: • Cancellation rates for the higher class might be overestimated or have high variance • There may be some possibility that a rejected lower-class passenger may buy-up • Serial nesting may have other benefits such as robustness in the face of forecast errors

15. Buy-Up and Recapture Assumptions same as Problem 2, except: • If a class A booking request is rejected, it is lost • If a class B booking request is rejected, then with probability • 0.3, it is lost • 0.4, it is recaptured on another flight at $100 • 0.3, it buys-up to a class A fare on the same flight at $150 • If a rejected class B request is recaptured or buys-up, it retains its zero cancellation rate

16. Buy-Up (cont.) • Value[A, accepted] = (1/3)*$150 + (2/3)*$0 = $50 • Value[A, rejected] = $0 • Value[B, accepted] = $100 • Value[B, rejected] = (0.4)*$100 + (0.3)*$150 = $85 In this case, A has ‘higher value’ ($50) than B ($15)

17. Summary • There are many interpretations of the serial nesting concept • Serial nesting makes sense under classical RM demand assumptions, assumptions that are often realistic • Occasionally, classical demand assumptions are violated. When this is the case, the economic value for a class or bucket that is fed to an RM optimization --- or the optimization itself --- should ideally include consideration of cancellation, refunds, recapture, and buy-up