optimal pricing and seat allocation in airline industry...

Optimal Pricing and Seat Allocation in Airline Industry Under Market Competition

PhD Thesis Oral Exam PresentationSyed Asif Raza

Outline

Revenue Management (RM)Background and LiteratureModel and ResultsConclusion and Future WorksQuestions

Airline RM

Airline Schedule Design and Fleet Assignment

Airline Revenue Management

Forecasting

Pricing

OverbookingResearch

Seat Inventory

Static Seat Inventory Control

Dynamic SeatInventory Control

Static Pricing

Dynamic Pricing

Revenue Management is simply the practice of maximising Revenue from Perishable assets (seats) through a combination of Pricing & Inventory controls

Fares

Revenue Management

Pricing Reservation Control

Services/ Restrictions

Seat Inventory Control Overbooking

Itinerary Control Fare Class Mix

Segment OD Point-of-Sale

No Direct Connection

Market Competition

Ignored

Missing Connections in Airline RM Studies

Review Articles:McGill and Van Ryzin (1999)- Revenue Management: Research overview and prospects.Pak and Piersma (2002)- Overview of OR techniques in airline RM.Silver (2004)- An overview of heuristic solution methodsBarnhart et al. (2003) – Application of operations research in the air transport industry.Elmagraby and Keskinocak (2003) -Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directionsBitran and Caldentey (2003)- An overview of pricing models for Revenue Management.

Cote et al. (2003)- Mathematical optimization approach for integrated seat allocation and pricing in airline industry.

Bi-level mathematical optimization model is presented for joint determination of fare pricing and seat allocationThe customer demand is considered price insensitive and the model is non dynamic

Dai et al. (2005)- Multiple firms competition in RM context.Competitive prices are determined for both the deterministic and stochastic price sensitive demand for a known capacity. Mostly the analysis consider duopoly competition

Chen et al.(2005) – Newsvendor pricing gameJointly determined the competitive pricing and capacity for the competing firms for a single commodity Unique Nash equilibrium is determined analytically

Competition in RM

Competition in Airline RM:Hotelling (1929)-Scheduling decision under competition Borenstein et al. (2003)- An empirical paper, focus on broad competition problem but ignore any seat allocation/ pricing modeling.Belobaba and Wilson (1997)- Simulation model to study scheduling strategy under market competition.Lippman and McCardle (1997)- two-firm pricing competition.Teodorovic and Krcmar-Nozic (1989)- Multi-criteria model to determine flight frequencies on an airline network under competitive conditions.

Objectives of thesis

Develop new models for joint determination of competitive fare pricing and seat allocation in airline IndustryDevelop new solution methodologies for joint determination of pricing and capacity in RM

Airline RM Competition Models

Airline RM game is developed mainly in duopoly marketTwo game theoretic models are presentedThe models are studied for both the cooperative and non-cooperative game settings.Numerical analysis with statistical DOE

Distribution Free Approach is RMAn alternative approach for joint determination of pricing and capacity under monopolyDetermines lower bound (worst possible) revenue estimateThe approach is addressed to:

Standard Newsvendor problem Extension to Shortage cost PenaltyExtension to Shortage and Holding costExtension to recourse caseExtension random yieldExtension to multiple items

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Competition Models in Airline RM:

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Multiplicative Model

Game Theory

Environment Certain

Dynamic

Static

1 DM

> 1 DM

1 DM

> 1 DMNon

Cooperative

Non Cooperative

Cooperative

Cooperative

Optimal Control

Optimization

No Side Payments

Side Payments

Side Payments

No Side Payments

Competition Analysis

Non-cooperative analysisUniqueness of Nash Equilibrium (NE) Numerical analysis with a Statistical Design Of Experiment (s) (DOE).

Cooperative analysisBargaining game with No Side Payment options (NSP)Bargaining game with Side Payment options (SP)

mequilibriuNash Unique

mequilibriuNash Unique

commitment-prelimit booking aFor ly.respective 2player

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Nash Bargain Solution

Numerical Analysis

}2,1{,]2,0[],[],[ModeltiveMultiplicaFor

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13355.11200.26171.5685.88Airline 2

13355.13200.26171.5685.91Airline 1Normal

13608.25208.32175.5084.90Airline 2

13608.25208.32175.5084.90Airline 1UniformMultiplicative

13349.00200.04171.4772.90Airline 2

13349.00200.04171.4772.89Airline 1Normal

13570.21205.18176.5372.35Airline 2

13570.21205.18176.5372.35Airline 1UniformAdditive

PayoffHigh Fare PriceLow Fare PriceBooking

LimitAirlineDistributionModel

Non-Cooperative Analysis (Symmetric market)

[Additive (-), Multiplicative (+)]Model Type (I)

[0.05 (-), 0.15 (+)]H21

[0.1(-), 0.2 (+)]L21

[0.1(-), 0.2 (+)]βH2

[0.2 (-), 0.3 (+)]βL2

[80 (-), 120 (+)]C2

LevelsParameters

Non-Cooperative Analysis (Asymmetric market)

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DOE-Non Cooperative Game

2162.22162.2Gain Of Cooperation

15732.42368.2820070.0015732.42368.2820070NBS with side payments

13570.21259.43156.0455.1113570.21255.81169.5754.05NBS no side payments

13570.21205.18176.5372.3513570.21205.18176.5372.35Non-cooperative

PayoffPH2PL2B2PayoffPH1PL1B1

Airline 2Airline 1

Cooperative Analysis (Bargaining Game)Additive

1604.001604.00Gain Of Cooperation

15212.24310.10200.0080.0015212.24310.10220080NBS with side payments

15212.24310.10200.0080.0015212.24310.10220080NBS no side payments

13608.25208.32175.5084.9013608.25208.32175.5084.90Non-cooperative

PayoffPH2PL2B2PayoffPH1PL1B1

Airline 2Airline 1

Cooperative Analysis (Bargaining Game)

Multiplicative

Comparing NSP with NE

Airline 1Revenue improves about 5.4%1.9% more seats for High fare customersLow and high fare prices increase by 4.8% and 35% respectively

Airline 2Revenue improves 6.5%5.3% more seats for high fare classLow and high fare prices increase is 9.6% and 28.4%

Comparing SP with NSP

Airline 1Revenue improves about 6%1.9% more seats for High fare customersLow and high fare prices increase by 6.7% and 8.6% respectively

Airline 2Revenue improves 5.2%1.6% more seat to high fare class but not significant.Low and high fare prices increase is 6.3% and 5.8% respectively

-300

-200

-100

0

100

200

300

80 85 90 95 100 105 110 115 120

C2

Side

Pay

men

tSide Payments

Newsvendor Problem and RMYao (2002)’ s thesis investigates newsvendor problem (NVP) with pricing in the context of SCM and reported that the elegant structure of the problem also finds applications in RM.In standard newsvendor problem optimal quantity is determined for a single perishable asset with stochastic demand having an objective to maximize the revenue

Proposed Extension to NVP

Investigate alternative solution approach to NVP with pricing using Distribution Free Approach.Using Distribution Free approach study several extensions to NVP with application in RM

Distribution Based Vs. Distribution Free Approach

Distribution BasedModeling requires precise information about demand distributionIt maximizes the revenue under a known distribution

Distribution FreeModeling requires only the mean and standard error estimate of the demand.It maximizes the revenue under the worst possible demand distribution.

Newsvendor problem with Pricing

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−=Π+=

+

+

σ

σξ

ξ

ξ

Newsvendor problem with Pricing

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2/122

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−=Π=

+

+

σ

σξξ

ξ

ξ

Proving concavity

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modeltiveMultiplicaFor'4

),);

modelAdditiveFor

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if,concavequasiisΠ

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2

2LB

2

2LB

2

2LB

2LB

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−≥≥−Π

≥∂∂

∂−

∂∂

∂∂

=

≤∂∂

≤∂∂

−

σσ

σ

DDPiiDQDiifconcavequasiis

DPiiDQiifconcavequasiis

QPQPHii

QPi

LBLB

LBLB

LBLBLBLB

LBLB

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)(

),(

][)(

]][][},min{[),(

2/122

**

LBLBLB

LBLBLBLBLB

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DSQCSPQP

DSRDQEGSPQCSP

DRDSRDQGQCRDQPEQP

−−−+++−

−−+=Π

−−++−−+=

−−−−−=Π+

++

σ

ξ

ξ

Proving concavity

( )

( )SGDDPiiDQDiifconcavequasiis

DSGPiiDQiifconcavequasiis

LBLB

LBLB

+−−

≥≤≤−Π

−+≥≥−Π

)2('2),2);

modeltiveMultiplicaFor'4

),);

modelAdditiveFor

LB

LB

σσ

σ

Extension to Shortage cost case:

( )( )

( ) ( )( )

'4),);

2)(

),(

][)(

]][},min{[),(

:ModelAdditive

LB

2/122

**

DSPiiDQiifconcavequasiis

QDQDSP

DSQCSPQP

DSRDQESPQCSP

DRDSQCRDQPEQPξDRD

LBLB

LBLBLB

LBLBLBLBLB

σ

σ

ξ

ξ

−≥≥−Π

−−−++−

−−+=Π

−−+−−+=

−−−=Π

+=

+

+

Recourse case:

( )( )

( ) ( )( )

LBrLBLB

LBLBrLB

rLBrLBLBLBLB

rrr

PCiiiD

PiiDQiifconcavequasiis

QDQDCP

DCQCCPQP

DCRDQECPQCCPQPξDRD

<−≥≥−Π

−−−++−

−−+=Π

−−+−+−=Π

+=+

)'4

),);

2)(

),(

][)(),(

:ModelAdditive

LB

2/122

**

σ

σ

ξ

Random yield case:

( )( ) ( )( )

IPEis,;0Π)

2/1;0Π)

2)(1

),(

])([)(

]}),(min{[),(

:ModelAdditive

2LB

2

2LB

2

2/122

**

DDQifQ

ii

ifP

i

DQDQQP

QCPQP

RDQGEPQCP

QCRDQGPEQPξDRD

LBLB

LB

LBLBLBLB

LBLBLBLBLB

ρ

σ

ρρρρσ

ρ

ρ ξ

ξ

≥≤∂∂

≥≤∂∂

−+−+−+−

−=Π

−−−=

−=Π+=

+

Multiple Product case:

( ) ( )( ) ( )

∑

∑

∑

∑

=

=

=

=

≤

−−−+−−=Π

≤

−=Π

n

1ii

2/122

1

**

1

1

C

:toSubject2

),(

:toSubject

]},min{[),(

BQ

QDQDPQCPQP

BQC

QCRDQPEQP

i

ii

iii

i

LB

LBiLBiiLB

n

iLBiLBLBLBLB

n

iii

n

iiiiii

σ

ξ

Numerical Analysis

2] U(0,~,],[ model, tivemultiplicaFor

30] U(0,~,],[ model, additiveFor

P - D 15,000],U[10,000,~B 0.9], U[0.5,~C1.4] U[1.2,~CC,0.3] U[0.2,~GC,0.2] U[0.1,~S

0.3]U[0.05,~ 200],U[100,~ 100], U[20,~Cproblems generatedrandomly 100

:followsextension each ation withExperiment

r

ξξξξ

ξξξξ

βαρ

βα

=

=

=×××

Standard Newsvendor Problem

Additive Model

UniformEVAI Improves revenue 0.25%

13% over-stocking

0.85% under-pricing

NormalEVAI Improves revenue 0.13%

3% over-stocking

0.81% under-pricing



0.59% under-stocking

0.01% over-pricing

Normal

EVAI Improves revenue 0.60%

0.13% over-stocking

0.30% over-pricing

Extension to Shortage and Holding Cost

Additive Model



0.89% under-pricing


2.3% over-stocking

0.85% under-pricing




0.19% over-pricing


1.68% over-stocking

0.30% over-pricing

Extension …

Recourse Case


0.86% over-stocking

0.81% under-pricing


3.5% over-stocking

0.77% under-pricing

Random Yield Case


0.53% over-stocking

0.80% under-pricing

Normal

EVAI Improves revenue 0.22%

3.27% over-stocking

0.76% under-pricing

Conclusion

Competition models in Airline Revenue Management (RM) are proposed using game theoretic approach.The models enable us to jointly determine the booking limits and fare pricing for airlines in the game.Both non-cooperative and cooperative bargaining games are considered.

Conclusion (Contd.)

Numerical study shows that cooperation results superior revenue gain to airlinesCooperation with side payments is also

found superior to cooperation with no side payments option in the bargaining game.The use of distribution free approach for pricing in RM is explored

Conclusion (Contd.)

The approach establishes lower bound estimate on revenue and enables maximizing the revenue under worst possible demand distribution.The approach is applied to standard

newsvendor problem and many other extension

Conclusion (Contd.)

It is also reported that the use of the approach on extensions of standard newsvendor problem has direct implications on RM practice in aviation and other service industries

Future Works

Dynamic pricing with seat allocation Pricing with:

Re-saleable returnCustomer choice model

A typo on page 82

22

22

22

21by 1 Replace σσ λλ +⎟

⎠⎞

⎜⎝⎛ −=+⎟

⎠⎞

⎜⎝⎛ −=

DQ

DQ LBLB

Research ArticlesA. S. Raza, M. U. Al-Turki, S. Z. Selim: 2007, “Early Tardy Minimization of Joint Scheduling of Jobs and Maintenance Operations on a Single Machine” special issue on scheduling in manufacturing, information and service industries in International Journal of Operations Research, 4, 1-10A. S. Raza, A. Akgunduz, M.Y. Chen: 2006, “A TabuSearch Algorithm for Solving Economic Lot Scheduling Problem” Journal of Heuristics, 12, 413-426A. S. Raza, A. Akgunduz: 2005, “The Use of Meta-Heuristics to Solve Economic Lot Scheduling Problem”, Lecture Notes in Computer Science, 3448, 190-201

Research Articles (Under review)

A. S. Raza, A. Akgunduz, “An Airline Revenue Management Fare Pricing Game with Seat Allocation”under second revision with International Journal of Revenue ManagementA. S. Raza, A. Akgunduz, “A Comparative Study of Heuristic Algorithms on Economic Lot Scheduling Problem” submitted to Computers and Industrial EngineeringA. S. Raza, A. Akgunduz, “A Distribution Free Approach for Jointly Controlling Price and Capacity in Revenue Management”, submitted to International Journal of Production EconomicsA. S. Raza, A. Akgunduz, “The Impact of Fare Pricing Cooperation in Airline Revenue Management”, submitted to INFOR

optimal pricing and seat allocation in airline industry...

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