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

## Presentation on theme: "Modeling Sell-up in PODS enhancements to existing sell-up algorithms, etc. Hopperstad March 00."— Presentation transcript:

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

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

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.

Belobaba/Weatherford (B/W) model At AGIFORS RM (Zurich) 1996 and in a Decision Sciences article Belobaba & Weatherford proposed a revision to EMSRb For 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

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

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.

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

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

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

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

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