Revenue Management Under the Markov Chain Choice Model

We consider revenue management problems when customers choose among the offered products according to the Markov chain choice model. In this choice model, a customer arrives into the system to purchase a particular product. If this product is available for purchase, then the customer purchases it. Otherwise, the customer transitions to another product or to the no purchase option, until she reaches an available product or the no purchase option. We consider three classes of problems. First, we study assortment problems, where the goal is to find a set of products to offer to maximize the expected revenue obtained from each customer. We give a linear program to obtain the optimal solution. Second, we study single resource revenue management problems, where the goal is to adjust the set of offered products over a selling horizon when the sale of each product consumes the resource. We show how the optimal set of products to offer changes with the remaining resource inventory. Third, we study network revenue ...

[1]  Huseyin Topaloglu,et al.  Constrained Assortment Optimization for the Nested Logit Model , 2014, Manag. Sci..

[2]  Srikanth Jagabathula,et al.  Nonparametric choice modeling: applications to operations management , 2011 .

[3]  Paat Rusmevichientong,et al.  Technical Note : A Simple Greedy Algorithm for Assortment Optimization in the Two-Level Nested Logit Model , 2012 .

[4]  P. Rusmevichientong,et al.  Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters , 2014 .

[5]  Juan José Miranda Bront,et al.  A Branch-and-Cut Algorithm for the Latent Class Logit Assortment Problem , 2010, Electron. Notes Discret. Math..

[6]  Richard Ratliff,et al.  Estimating Primary Demand for Substitutable Products from Sales Transaction Data , 2011, Oper. Res..

[7]  Kenneth E. Train,et al.  Discrete Choice Methods with Simulation , 2016 .

[8]  G. Gallego,et al.  A general attraction model and an efficient formulation for the network revenue management problem , 2011 .

[9]  Kalyan T. Talluri,et al.  A Randomized Concave Programming Method for Choice Network Revenue Management , 2010 .

[10]  J. Blanchet,et al.  A markov chain approximation to choice modeling , 2013, EC '13.

[11]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[12]  Guang Li,et al.  A greedy algorithm for the two-level nested logit model , 2014, Oper. Res. Lett..

[13]  Ruxian Wang,et al.  Capacitated Assortment and Price Optimization under the Multinomial Logit Model , 2012, Oper. Res. Lett..

[14]  Ruxian Wang.  Assortment Management under the Generalized Attraction Model with a Capacity Constraint , 2012 .

[15]  G. Iyengar,et al.  Managing Flexible Products on a Network , 2004 .

[16]  Arne Strauss,et al.  Network revenue management with inventory-sensitive bid prices and customer choice , 2012, Eur. J. Oper. Res..

[17]  K. Talluri,et al.  A new compact linear programming formulation for choice network revenue management , 2012 .

[18]  Dan Zhang,et al.  Reductions of Approximate Linear Programs for Network Revenue Management , 2015, Oper. Res..

[19]  Dan Zhang,et al.  An Approximate Dynamic Programming Approach to Network Revenue Management with Customer Choice , 2009, Transp. Sci..

[20]  Kalyan T. Talluri,et al.  An Enhanced Concave Program Relaxation for Choice Network Revenue Management , 2013 .

[21]  Jose H. Blanchet,et al.  A markov chain approximation to choice modeling , 2013, EC.

[22]  Guang Li,et al.  The d-Level Nested Logit Model: Assortment and Price Optimization Problems , 2015, Oper. Res..

[23]  Huseyin Topaloglu,et al.  A refined deterministic linear program for the network revenue management problem with customer choice behavior , 2008 .

[24]  David B. Shmoys,et al.  Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint , 2010, Oper. Res..

[25]  Garrett J. van Ryzin,et al.  On the Choice-Based Linear Programming Model for Network Revenue Management , 2008, Manuf. Serv. Oper. Manag..

[26]  Devavrat Shah,et al.  A Nonparametric Approach to Modeling Choice with Limited Data , 2009, Manag. Sci..

[27]  Guillermo Gallego,et al.  WORKING PAPER SERIES , 2011 .

[28]  Garrett J. van Ryzin,et al.  Revenue Management Under a General Discrete Choice Model of Consumer Behavior , 2004, Manag. Sci..

[29]  Dan Zhang,et al.  Revenue Management for Parallel Flights with Customer-Choice Behavior , 2005, Oper. Res..

[30]  Hongmin Li,et al.  Pricing Multiple Products with the Multinomial Logit and Nested Logit Models: Concavity and Implications , 2011, Manuf. Serv. Oper. Manag..

[31]  Juan José Miranda Bront,et al.  A Column Generation Algorithm for Choice-Based Network Revenue Management , 2008, Oper. Res..

[32]  Huseyin Topaloglu,et al.  Assortment Optimization Under Variants of the Nested Logit Model , 2014, Oper. Res..