Modeling Sell-up in PODS

1. Modeling Sell-up in PODS enhancements to existing sell-up algorithms, etc. Hopperstad March 00

2. Subjects • What is sell-up? • Belobaba/Weatherford model • Revised model • A little experiment • So really, what is sell-up? • Next?

3. What is sell-up? • Passengers when they find that their first choice class on a path is unavailable, take the next higher class (on that path). • The RM system can take advantage of this phenomena by increasing the chance that the first choice class is unavailable.

4. Belobaba/Weatherford (B/W) model • At AGIFORS RM (Zurich) 1996 and in a Decision Sciences article Belobaba & Weatherford proposed a revision to EMSRbFor two fare classes (Y, Q), the optimum protection of Y against Q (bprot*) is defined to be that at which: • where: ydem = Y class demand (normally distributed) • yfare = Y class fare • qfare = Q class fare • psup = sell-up probability

5. Belobaba/Weatherford (B/W) model • The argument for the optimality of B/W model is that by increasing any bprot by e: • In terms of Q, given the demand is greater than blim, the loss of revenue is: • In terms of Y, capacity is increased by the non sell-up resulting in a revenue gain, in the limit, of: • Optimality occurs at that bprot where the gain equals the loss

6. Revised sell-up model • The current model accounts for the sell-up associated with increasing bprot, not for that sell-up already induced by the current setting. The revised B/W model accounts for this iteratively: 1. Solve for bprot/blim assuming no ‘previous’ sell-up. 2. Solve for the conditional (on qdem > blim) Q spill & Q spill sell-up 3. Define revised Y demand including Q spill sell-up 4. Re-solve for bprot/blim. 5. Repeat steps 2 – 4 until convergence criteria (change in bprot of < 0.5) is met.

7. Revised sell-up model (example) • Basic parameters: booking capacity = 100 k-factor = 0.3 z-factor = 2 • Y demand = 50 • Y fare = 200 • Q fare = 100 • sell-up probability = 0.25 Conclusion: revised model important for high demand cases, otherwise not

8. A little experiment • Special PODS runs • 1 market, 2 airlines, 6 non-stop paths • 3 fare classes, fares = 400, 200, 100 • standard passenger descriptions by type • capacity large enough that no classes are closed by the RM systems • artificially closed down classes on one path • observed the change in loads for open path/classes

9. A little experiment • Of the pax whose first choice was airline A, path 2, class 3 • 6% sold-up to path 2, class 2 • 2% sold-up to path 2, class 1 • 61% sold-over to class 3 on another airline A path • 31% sold-over to class 3 on an airline B path • Of the pax whose choice now was airline A, path 2, class 2 • 16% sold-up to path 2, class 1 • 33% sold-over to class 2 on another airline A path • 36% sold-over to class 2 on an airline B path • 5% sold-down to class 3 on another airline A path • 9% sold-down to class 3 on an airline B path

10. So really, what is sell-up? • Sell-up is sell-up for modest rates • For relatively high rates it appears that sell-up is primarily a surrogate for class closures (own and competitors) • It has a nice self-fulfilling prophecy feature • the higher the sell-up rate estimate, the lower the booking limits, the more closures, the higher the sell-up rate

11. Next? • Try some forecast adjustment heuristics based on the state of the the market (class closures) • Try some bidprice heuristics • rules for causing all paths to either be open or closed for a class • rules for adjusting bidprices in a market based on competitor class closures