Dynamic Relocations in Car-Sharing Networks

We propose a novel dynamic car relocation policy for a car-sharing network with centralized control and uncertain, unbalanced demand. The policy is derived from a reformulation of the linear programming fluid model approximation of the dynamic problem. We project the full-dimensional fluid approximation onto the lower-dimensional space of relocation decisions only. This projection results in a characterization of the problem as n + 1 linear programs, where n is the number of nodes in the network. The reformulation uncovers structural properties that are interpretable using absorbing Markov chain concepts and allows us to write the gradient with respect to the relocation decisions in closed form. Our policy exploits these gradients to make dynamic car relocation decisions. We provide extensive numerical results on hundreds of random networks where our dynamic car relocation policy consistently outperforms the standard static policy. Our policy reduces the optimality gap in steady state by more than 23% on average. Also, in a short-term, time-varying setting, the lookahead version of our dynamic policy outperforms the static lookahead policy slightly more than in the time-homogeneous tests.