Revenue Management under Competition and Uncertainty

Tao Yao

Assistant ProfessorThe Harold and Inge Marcus Department ofIndustrial and Manufacturing Engineering

Penn State Universitytaoyao@psu.edu

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� Self-Introduction� Project summary: Revenue Management� Proposed Research

Outline

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Self-Introduction

� Education– PhD, Management Science and Engineering, Stanford University, 2005– MS, Engineering Economics System & Operations Research, Stanford University– MS, Mathematics, UCLA– BS, Mathematics, Peking University

� Research Interests– Methodology: stochastic models, optimization, and game theory– Applications: decision making under uncertainty, real options,

manufacturing, service and supply chain operations, informationand technology management, energy and environment

� Hobby– Soccer

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Revenue Management

� Service packages– Revenue maximization– Dynamic pricing– Demand Management

� Features– Uncertainty– Competition

� Application– Fashion, Retail, Air Travel, Hotel, Seasonal Products etc.

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Project Summary: Revenue Managementunder Uncertainty and Competition

� Strength:– Computability– Dynamic Game: Variational method

– Rules of thumb � Real time decision support

� Proposed Work:– Forecasting and Optimization– Robust optimization– Data-driven, Risk– Customer Contact Center

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Related Fields

� Dynamic Optimization and Game� Control Theory� Mathematical Programming� Simulation� Risk Management

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Research Goals, Impacts

� Comprehensive models, computational techniques� Real time data, realistic assumption� Application� General approach, whole service engineering community� Managerial insights, revenue management, randomness,

competition

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Revenue Management

� Review– McGill and van Ryzin 1999 Transportation Science– Bitran and Caldentey 2003 Manufacuting & Service Operations

Mangament– Boyd and Bilegan 2003 Management Science– Elmaghraby and Keskinocak 2003 Management Science– Chiang, Chen and Xu 2007 International Journal of Revenue

Management� Book

– Talluri and van Ryzin 2004 The Theory and Practice of RevenueManagment

– Phillips 2005 Pricing and Revenue Optimization

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Revenue Management

� Pricing� Auctions� Capacity control (inventory)� Overbooking� Forecasting� Economics� Customer behavior and perception� Techniques� Competition and alliance

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Classical example: newsvendor

� Profit maximization, stock decision, uncertain demand– Porteus 1990– Petruzzi and Dada 1999

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Seller 1 Seller i Seller f

Period 1 Period t Period T

πfπ1 π2

Market

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Assumptions

� Perfect information (imperfect information)� Demand is deterministic (uncertainty via learning, robust

optimization, data driven)� Single product (network)� Single resource (network)� Single period (multiple period, continuous time)� Sellers optimization, pricing (resource allocation)� Single seller (game)� Complete market, risk neutral (incomplete market, risk

averse)

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Questions

� How should sellers price the product and allocate resourcewith competition?

� What are the equilibrium prices in the market?� How to handle demand uncertainty?� How to handle demand learning?� How to handle risk preference?

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Proposed Research: Revenue Managementunder Uncertainty and Competition

� Forecasting and Optimization� Robust optimization� Data-driven, Risk Management

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Goals

� Modeling of competition and dynamics� Modeling of demand uncertainty and robust optimization� Modeling of primitive data and risk attitude� Numerical study� Application

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Forecasting and optimization

� Demand uncertainty– Demand distribution and parameters– Revealed over time

� High frequency of data– Information technology– Rich information

� Simultaneously forecast the demand and optimize thepricing strategy.

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Literature Summary

Linear demand, MPECYesSingleDirectYesYesPrice onlyKachani, Perakis& Simon, 2004

Discrete time Kalman filter,Optimal control/VI perspectiveYesMultiDirectYesYes

Price &Allocation

Kwon, Friesz,Mookherjee, Yao,Feng (2006)

Optimal control/VI perspectiveNoMultiDirectYesYes

Price &Allocation

Friesz,Mookherjee,Rigdon, (2005)

Yes

Yes

No

Learning

Price &Allocation

Price &Allocation

Price &Allocation

Decisions

Continuous time Kalman filter,Multiplicative demand,Simultaneous forecasting andoptimization, Optimal control/VIperspective

MultiDirectYesYesThis work (2007)

Linear demand, Learningalgorithm; quasi-VI formulationMulti

Indirect(robust

opt)YesYes

Perakis & Sood(2005)

MonopolyMultiDirectYesNoBerstimas & deBoer (2005)

FeaturesSingle /multi

service

Stochas-ticity

Multiperiod

(dynamic)

Comp-etition(game)

Articles

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Literature Review

� Dynamic Optimization and Game– Differential Variational Inequalities. Pang and Stewart (2003),

Friesa et al. (2006)– Friesz et al. (2005) consider joint pricing and resource allocation in

network revenue management markdown optimization with knowndemand dynamics and parameters.

� Kalman Filter– Kwon, Friesz, Mookherjee, Yao and Feng(2006) present discrete

Kalman-Filter model to forecast the demand and a differentialvariational inequality model for pricing the service. We alsopropose an algorithm based on a gap function to efficientcomputing the optimal pricing strategies.

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Sellers’ Decentralized Problem

Sellers Maximize profit over whole time horizon

Decisions PricesAllocation of capacity

Constraint Demand dynamicsLearning dynamicsBounds on priceBounds on capacityBounds on demand

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Proposed Research

� Our objective in this research is to develop pricing modelswhich simultaneously forecast demand and optimize thepricing strategy under uncertainty.

� More specifically, we propose a continuous timeestimation of parameters using Kalman Filter andmarkdown dynamic pricing optimization model.

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Current Status

� We present a differential variational inequality model and an algorithmbased on a gap function.

� We have described the dynamics of demand as a continuous timedifferential equation based on an evolutionary game theoryperspective.

� Realized sales data are refined on a discrete time scale and used toobtain estimates of parameters that govern the evolution of demand.

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Numerical Example (Competition)

� Revenue Changes

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Looking Forward

� Combine markdown optimization with continuous time parameter estimation.– Develop and experiment nonlinear estimation for continuous time system with

discrete measure by extending Kalman Filter method for complex revenuemanagement models using insights gained from the discrete time of the model.

� Fright Service Network– Service lever guarantee, product differentiation– Future contract market and spot market– Both standard analytical approach and computational (numerical) approach

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Robust Optimization

� Literature:– Soyster (1973)– Ben-Tal and Nemirovski (1998, 1999, 2000)– Bertsimas and Sim (2002)

� Unknown data distribution, parameters uncertain, within an uncertainty set.

� Stochastic dynamic programming, curse of dimensionality

� Robust optimization, optimal payoff, robust within the uncertainty set(Bertsimas and Thiele 2004)

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Robust Optimization

� Robust optimization

– Uncertainty

– Competition

– Perakis and Sood 2006

– Adida and Perakis 2006

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Risk Management, Data-Driven

� Imperfect market, Risk preference– Review, Van Mieghem 2003– Utility, Lau 1980, Eeckhoudt et al. 1995– Data-driven, Bertsimas and Thiele 2005– Risk Measure, Brown, Ben-Tal, & Bertsimas 06

� Data-driven, profit maximization, risk management,network revenue management, competition– Risk averse– Dynamic game– Data information

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Risk Management, Data-Driven

� Imperfect market, Risk preference– Review, Van Mieghem 2003– Utility, Lau 1980, Eeckhoudt et al. 1995– Data-driven, Bertsimas and Thiele 2005

� Data-driven, profit maximization, risk management,network revenue management, competition– Risk averse– Dynamic game– Data information

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Customer Contact Center

� Penn State SEE Board, Industry Data, Call Center– Naren Gursahaney, president of Tyco EPS– John J. Brennan, chairman and CEO of ICT group

� Service Engineering– Telephone Call Venters: Tutorial, Review and Research Prospects

(Gans, koole, Mandelbaum, 2003)– Statistical Analysis, Queueing Science (Brown, Gans,

Mandelbaum, Sakov, Shen, Zeltyn, Zhao, 2005)– Ticket Queue (Xu, Gao, Ou, 2006)

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Contributions

� Model for competitive pricing and resource allocating in amulti-period, oligopolistic market– DVI framework

� Extended to demand learning– Discrete time Kalman filter– Continuous time estimation

� Extended to robust optimization� Extended to data driven, risk management� Form of equilibrium pricing rules.

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Conclusion

� Project Summary:– Revenue Management under Uncertainty and Competition

� Strength: Computability– Rules of thumb � Real time decision support

� Proposed work:– Forecasting and Optimization– Robust optimization– Data-driven, Risk– Customer Contact Center

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Thank you!

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Overview of Service Science, Management and Engineering

� The scope of Service:– Service sector is very crucial in our lives. It includes

transportation, information, banking, insurance, real-estate,medical, education, government, wholesale and retail trade, etc.

� The importance of Service to economics:– The service industry has grown to dominate developed economies.

In USA, 80% of GDP was from the service sector in 2005.

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� Service Science, Management, and Engineering (SSME) isthe application of science, management, and engineeringdisciplines to service sector.

� Service is the least-studied part of the economy. SSMEcalls for actions from academia.

Overview of Service Science, Management and Engineering

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Robust Optimization

� Linear demand

� Robust Constraint