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Competitive Analysis of Online Booking: Dynamic Policies

Competitive Analysis of Online Booking: Dynamic Policies. Michael Ball, Huina Gao, Itir Karaesman R. H. Smith School of Business University of Maryland and Maurice Queyranne Sauder School of Business University of British Columbia. Motivation: Assemble-to-Order Products. production

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Competitive Analysis of Online Booking: Dynamic Policies

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  1. Competitive Analysis of Online Booking: Dynamic Policies Michael Ball, Huina Gao, Itir Karaesman R. H. Smith School of Business University of Maryland and Maurice Queyranne Sauder School of Business University of British Columbia

  2. Motivation: Assemble-to-Order Products production capacity components Some particular features: • Multiple capacity constraints • Time dimension – production capacity and components replenish over time • Time dimension – product differentiation based on delivery time • No low before high products Very simple case: 1 key component 2 products

  3. Competitive Analysis i1, i2, i3, … Algorithm algorithm input Evil Designer stream Adversary Competitive Ratio = Min input streams {(alg performance)/(best performance)} • “Traditional” revenue management analysis has assumed: • Demand can be forecast reasonably well • Risk neutrality • Are these valid??

  4. Sample Result • Flight has 95 available seats, three fare classes: $1,000, $750, $500 • Policy that guarantees at least 63% of the max possible revenue: • Protect 15 high fare seats • Protect 35 seats for two higher fare classes (i.e. sell at most 60 lowest fare seats)

  5. Two-Fare Analysis • n = number of seats • f1 = higher fare; f2 = lower fare. • r = f2/f1 = discount ratio. • Key quantity: b(r) = 1 / (2 – r) Policy intuition: Always best to accept any high fare (H) that comes along  Adversary will start off with low fare requests (L): Question – how many to accept before only H’s are accepted??

  6. Basic Trade Off Note: must accept first order, o.w. adversary will stop after submitting one order with algorithm performance = 0. L L L L L L L L L L L L L L L L available seats Stop accepting L’s Accept too few L’s  adversary will only send additional L’s L L L L L L L L L L L L L H H H H H H H H H Stop accepting L’s Accept too many L’s  adversary will only send additional H’s

  7. Best Two-Fare Policy Proposal: protect (1 – b(r)) n = (1 – 1/(2 – r)) n … assume for the moment that b(r) n is integer .. L L L L L L L L L L L L L L L L L L L All L’s after stopping  Performance = (f2 b(r) n ) / (f2 n) = b(r) L L L L L L L L L L L L L H H H H H All H’s after stopping  Performance = [f2 b(r) n + f1 (1 – b(r)) n] / (f1 n) = b(r)

  8. More General Cases f = price f1=fmax f2 f3 f4 = fmin q = total order quantity accepted n protection levels: (f3) (f2) (f1)

  9. m Fare Classes Define:  = m - {i=2,m} fi / f i-1 Theorem: For the continuous m-fare problem, no booking policy, deterministic or random, has a competitive ratio larger than 1 / . Define: i = (n / ) (i - {j=1,i} fj+1 / f j) Theorem: For the continuous m-fare problem, the protection level policy using protection levels i achieves a competitive ratio of at least 1 / . e.g. f1 = 1000, f2 = 750, f3 = 500, 1 /   63 %

  10. Approach to alternate type of policy Optimal adversary strategy f = price f1=fmax f2 f3 f4 = fmin q = total order quantity accepted n protection levels: (f3) (f2) (f1)

  11. Order Quantity Control Fcn f = price P’(q) q = total order quantity accepted n

  12. Order Quantity Control Policy • Order quantity control policy: • after q orders have been accepted, accept next order if price of order > P’(q) f = price q = total order quantity accepted n

  13. Order Quantity Control Policy • Order quantity control policy: • after q orders have been accepted, accept next order if price of order > P’(q) f = price q = total order quantity accepted n Accept!! Reject!! or

  14. Numerical Experiments • Compare against another approach that does not require a-priori demand information: Van Ryzin & McGill, “Revenue Management without Forecasting or Optimization: an Adaptive Algorithm for Determining Airline Seat Protection Levels” • Two categories of demand generation: • Stationary – demand in each fare class is normally distributed • Non-stationary – for a given day/flight, demand is normally distributed but mean demand jumps between one of three mean pairs with a certain probability: .9 30 65 30 65 .1 .05 48 48 48 48 .9 .05 .1 65 30 65 30 .9

  15. Comparison: capacity: 100 High: fare -- $2000, mean demand -- 15 Low: fare -- $1000, mean demand -- 81 Van Ryzin & McGill Robust Low before High Random Ave diff: -$7210 -$10140

  16. Comparison: capacity: 100 High: fare -- $2000, mean demand -- 15 Low: fare -- $1500, mean demand -- 81 Van Ryzin & McGill Robust Low before High Random Ave diff: -$1760 -$6130

  17. Comparison: capacity: 100 High: fare -- $2000, mean demand -- 48 Low: fare -- $1000, mean demand -- 48 Van Ryzin & McGill Robust Low before High Random Ave diff: +$ 2750 +$6550

  18. Comparison of protection levels Van Ryzin & McGill Robust Low before High Random

  19. Comparison: capacity: 100 High: fare -- $2000, mean demand -- 65 Low: fare -- $1500, mean demand -- 31 Van Ryzin & McGill Robust Low before High Random Ave diff: +$1620 +$8130

  20. Comparison: capacity: 100 High: fare -- $2000, mean demand -- 81 Low: fare -- $1000, mean demand -- 15 Van Ryzin & McGill Robust Low before HighRandom Ave diff: -$650 +$7320

  21. Comparison: capacity: 100 Non-stationary demand: High: fare -- $2000, mean demand -- 65 48 30 Low: fare -- $1000, mean demand -- 30 48 65 Van Ryzin & McGill Robust Low before High Random Ave diff: +$4170 +$8080

  22. Comparison of protection levels Van Ryzin & McGill Robust Low before High Random

  23. Comparison: capacity: 100 Non-stationary demand: High: fare -- $2000, mean demand -- 65 48 30 Low: fare -- $1500, mean demand -- 30 48 65 Van Ryzin & McGill Robust Low before High Random Ave diff: +$1150 +$8740

  24. Observations • Random vs low-before-high makes a difference – for random, lower protection levels seem better. • Robust policy works well across range of demand scenarios – demand distribution most useful in cases of unbalanced demand.

  25. Dynamic Policy Motivation:Taking advantage of an inferior adversary • Optimal Adversary Policies: • Start low • After threshold: • Stay low • Or jump to high and stay high nb(r) n

  26. Dynamic Policy Motivation:Taking advantage of an inferior adversary nb(r) n

  27. Dynamic Policy Motivation:Taking advantage of an inferior adversary Having 2 (or more) high’s “in the bank” leads to a problem on a smaller n  threshold can be smaller & overall guarantee is improved. n’b(r) nb(r) n’ n

  28. Dynamically Revising Threshold orig threshold: n b(r) = n / (2-r) let: h’ = # high fare request accepted so far  = h’/n  = ( f1 +(1 - ) f2 ) / f2 revised threshold: n (1 + (1 – r) /r ) / (1 +  (1 – r) )

  29. Dynamic Policy: numerical test n = 100; r = .5

  30. Final Thoughts • Many implicit and explicit assumptions in airline revenue management problems – relaxing these can lead to novel problems. • Online algorithm approach shows significant promise: • No risk neutrality assumption. • Demand information not required. • Policies are practical and seem to work well across range of demand distributions.

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