1 Sensitivity Studies of Network Optimization with Displacement Adjusted Virtual Nesting using PODS. Thomas Fiig, Revenue Management Development, Scandinavian.

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1 Sensitivity Studies of Network Optimization with Displacement Adjusted Virtual Nesting using PODS. Thomas Fiig, Revenue Management Development, Scandinavian Airlines System, Denmark. Hedegaardsvej 88, DK-2300 Copenhagen. AGIFORS Reservations and Yield Management Conference, BKK 2001

2 Simulation Set-up in PODS H1(41) H2(42) Network D 2 Airlines 2 hubs 20 Cities (west & east). 482 markeds paths. Realistic fares. Realistic disutilities. Airline A: O&D methods Airline B: FCYM

3 DAVN-METHODS Emsrb DAVN(LP) Forecast by leg (iterate until convergence) LP opt. NETBID DC ProBPDAVN(ProBP) Path demand and fares Forecast by path & fares NETBID Path demand and fares Forecast by path & fares LP opt. NETBID DC

4 DAVN-METHODS Emsrb DAVN(LP) Forecast by leg (iterate until convergence) LP opt. NETBID DC ProBPDAVN(ProBP) Path demand and fares Forecast by path & fares DAVN(LP) Emsrb DAVN(LP) Forecast by leg Path demand and fares Forecast by path & fares LP opt. DC

5 DAVN-METHODS Emsrb DAVN(LP) Forecast by leg (iterate until convergence) LP opt. NETBID DC ProBPDAVN(ProBP) Path demand and fares Forecast by path & fares ProBP (iterate until convergence) ProBP Emsrb Forecast by leg Forecast by path & fares DC Path demand and fares

6 DAVN-METHODS Emsrb DAVN(LP) Forecast by leg (iterate until convergence) LP opt. NETBID DC ProBPDAVN(ProBP) Path demand and fares Forecast by path & fares DAVN(ProBP) (iterate until convergence) DAVN(ProBP) Emsrb Forecast by leg Forecast by path & fares DC Path demand and fares

7 Overview Effect of reoptimization frequencyProBP bidprice IV Properties of displacement costs (DC) DAVN (LP, ProBP) Sensitivity of bucket location, and number of buckets DAVN (LP)I DESCRIPTIONYM-METHODSERIE S II III Effect of noise in displacement costs. Robustness and optimality. DAVN (LP, ProBP)

8 Simulation Study I –Airline A, DAVN (LP-Method) vs. Airline B EMSRb –Sensitivity on the number of buckets 6-40, fixed and demand equalized. –Demand factor 1.0

9 DAVN(LP) Sensitivity on # buckets System wide buckets. Fixed values through legs and timeframes. Equidistant buckets. Demand equalized buckets. Leg specific. Recalculated at each timeframe. DAVN LP (8 buckets), demand equalized, corresponds to the base 0%

10 Summary of Study I Sensitivity on the number of buckets. –Large sensitivity on the number of buckets. Revenue difference between 8 and 30 buckets = %. –Fixed system wide buckets limits is not a good idea.

11 Simulation Study II –Airline A, DAVN (LP, ProBP) vs. Airline B EMSRb –Buckets are demand equalized and number=8. –Properties of displacement costs. –Demand factors 1.0

12 Displacement Costs in LP Distribution of displacement cost by timeframe (TF) Early Time Frame Departure

13 Properties DC (LP) Average DC as function of TF. Note that flights open at intermediate TF and then closes at departure. PCT of Displacement costs that are zero as function of TF. Note that 40% - 90% of the flights are wide open. Departure

14 Displacement Costs in PROBP Distribution of displacement cost by timeframe (TF) Departure

15 Properties DC (PROBP) Average DC as function of TF. Note that DC are much more stable, although DC tends to increase towards dep. PCT of Displacement costs that are zero as function of TF. Note that approx. 10%-70% of the flights are wide open. Departure

16 Summary of Study II Displacement Cost from LP –Distribution ragged. Approx 40%-90% of the DC are zero. –Average of DC decrease at intermediate timeframes and increases towards departure. Displacement Cost from ProBP –Distribution smooth. Between 10%-70% of the DC are zero. –Average of DC is almost constant.

17 Simulation Study III –Airline A, DAVN (LP, ProBP) vs. Airline B EMSRb –Buckets are demand equalized and number=8. –Demand factors 1.0 –Sensitivity of random noise to the displacement costs k-factor between 0 and 0.5. –Temporal dependence of DC. In the simulation study the noise are introduced as:

18 Random Noise to DC ProBP is robust to addition of random noise. Even k-factors as high as 0.5. LP is sensitive. Let us look at the distributions for k=0.3 DAVN LP (8 buckets), demand equalized, corresponds to the base 0%

19 DC in LP The noise has a smoothing effect on the distribution of the DC. The revenue is redu- ced by 0.03 %

20 DC in ProBP Again the noise has a smoothing effect on the distribution.

21 LP AVG(DC) with noise DAVN(LP) with k=0.0; k=0.3; and k=0.5. Revenue is decreasing with noise. k=0 The revenue is decreasing with increasing noise. k=0.3 k=0.5 k=0

22 ProBP AVG(DC) with noise DAVN(ProBP) with k=0.0; k=0.3; and k=0.5. Revenue is max in k=0.3. The slope goes from (+) to (-) as maximum revenue is attained. k=0 k=0.3 k=0.5

23 Summary of Study III Random noise to DC for DAVN (LP, ProBP) –Identified that revenue maximum coincides with constant DC as function of timeframe. –ProBP actually gets stabilized by random noise. –LP is very sensitive to noise, since most of the DC are zero. –The time dependence of the DC can be used as a quality measure. –Active use of smoothing techniques to forecasts are possibly a way to generate smoother DC distributions, which in turns stabilizes convergence of the DC.

24 Simulation Study IV –Airline A, Bidprice (ProBP) vs. Airline B EMSRb –Demand factors 1.0 –Study the revenue dependence of the frequency of network optimization.

25 Revenue as function of reopt. Breakeven for ProBP is <2 bookings per leg. Points correspond to reopt = 10, 100, 200, 500 and 1000 DAVN LP (8 buckets), demand equalized, corresponds to the base 0%

26 Benchmarking EMSRb corresponds to the base 0% BIDPRICE BOOKING LIMITS