Modeling Sell-up in PODSenhancements to existing sell-up

algorithms, etc.

HopperstadMarch 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:

( *)

qfare yfare psupP ydem bprot

yfare 1 psup

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

qfare yfare psup

( ) ( )P ydem bprot yfare 1 psup

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

Current model Revised modelQ demand Q blim Revenue Q blim Revenue Rev change

25 44 12399 43(2 cycles)

12399 0.0%

50 44 13761 39(3 cycles)

13786 0.1%

100 44 14855 23(4 cycles)

15384 3.6%

Y demand = 50Y fare = 200Q fare = 100sell-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