1 / 30

Competitive Analysis of Online Booking: Dynamic Policies

This study analyzes dynamic policies for online booking in assemble-to-order products to optimize revenue management strategies based on competitive ratios, protection levels, and order quantity control. The research assesses the performance of various algorithms and proposes optimal policy recommendations.

Download Presentation

Competitive Analysis of Online Booking: Dynamic Policies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related