Bid Price Controls for Car Rental Network Revenue Management

Abstract

Car rental network revenue management (RM), despite its prevalence for a long time, has received much less attention in the literature than airline RM does and we aim to fill this gap. The key operational characteristics of car rental services include multi-day length of rentals and mobility of inventories, which requires the car rental booking control to account for the inter-temporal and spatial correlations of demands for capacities across different locations and days. We formulate the car rental network RM problem into an infinite-horizon cyclic stochastic dynamic program. To tackle the curse of dimensionality, we propose a Lagrangian relaxation (LR) approach with product- and time-dependent Lagrangian multipliers to decomposing the network problem into multiple single-station single-day sub-problems, which breaks the inter-temporal and spatial correlations simultaneously. We characterize the structural properties of the decomposed problems in terms of the Lagrangian multipliers and then assemble the optimal value functions of the decomposed problems into an approximate value function. We show that the Lagrangian dual problem is a convex program and its minimum value provides an upper bound on the optimal value functions of the original problem. A subgradient-based algorithm is developed to solve the dual problem and derive an LR-based bid price policy. To increase the scalability of the method, we further propose a simpler LR approach with location- and leadtime-dependent Lagrangian multipliers. Our numerical study indicates that both LR-based bid price policies significantly outperform other commonly used heuristics, and that the second LR approach, though slightly worse than the first one, is much faster. Using a set of real-world booking data, we empirically demonstrate the characteristics of car rental service and perform a case study in which we calibrate the arrival process as a Poisson regression model and show that both LR-based bid price policies indeed outperform other heuristics consistently in both in-sample and out-of-sample tests.