A Dynamic Programming Approach for Integrating Dynamic Pricing and Capacity Decisions in a Rental Context

  • Beatriz B. Oliveira
  • Maria Antónia Carravilla
  • José Fernando Oliveira
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 223)


Car rental companies have the ability and potential to integrate their dynamic pricing decisions with their capacity decisions. Pricing has a significant impact on demand, while capacity, which translates fleet size, acquisition planning and fleet deployment throughout the network, can be used to meet this price-sensitive demand. Dynamic programming has been often used to tackle dynamic pricing problems and also to deal with similar integrated problems, yet with some significant differences as far as the inventory depletion and replenishment are considered. The goal of this work is to understand what makes the car rental problem different and hinders the application of more common methods. To do so, a discrete dynamic programming framework is proposed, with two different approaches to calculate the optimal-value function: one based on a Mixed Integer Non Linear Program (MINLP) and one based on a Constraint Programming (CP) model. These two approaches are analyzed and relevant insights are derived regarding the (in)ability of discrete dynamic programming to effectively tackle this problem within a rental context when realistically sized instances are considered.


Car rental Dynamic programming Dynamic pricing Fleet deployment Optimization model Constraint programming 



The first author was supported by grant SFRH/BD/103362/2014 from FCT—Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology). This work was also partially financed by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by National Funds through the FCT—Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2013.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Beatriz B. Oliveira
    • 1
  • Maria Antónia Carravilla
    • 1
  • José Fernando Oliveira
    • 1
  1. 1.INESC TEC and Faculty of EngineeringUniversity of PortoPortoPortugal

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