Bike-sharing systems are becoming increasingly prevalent in urban environments. They provide a low-cost, environmentally-friendly transportation alternative for cities. The management of these systems gives rise to many optimization problems. Chief among these problems is the issue of bicycle rebalancing. Users imbalance the system by creating demand in an asymmetric pattern. This necessitates action to put the system back in balance with the requisite levels of bicycles at each station to facilitate future use. In this paper, we tackle the problem of maintaing system balance during peak rush-hour usageas well as rebalancing overnight to prepare the systemfor rush-hour usage. We provide novel problem formulationsthat have been motivated by both a close collaborationwith the New York City bike share (Citibike) and a careful analysisof system usage data. We analyze system data to discover the best placement of bikes tofacilitate usage. We solve routing problems forovernight shifts as well as clustering problems for handlingmid rush-hour usage. The tools developed from this research are currently in daily use at NYC Bike Share LLC, operators of Citibike.

Inference in constraint programming is usually based on the deductions generated by individual constraints which are then communicated to other constraints through domain filtering. Frequently we find that this is a too coarse-grained form of communication since constraints could exchange more powerful forms of deductions that could help reduce the search effort. In this paper we propose a particular technique for enhancing inference in constraint programming, by generating deductions that involve tighter interleaving of constraints. We apply our method to the market split problem and obtain massive speed-ups which brings a new order of market split problems into the realm of solvability by means of constraint programming.