Estimating Primary Demand in Bike-sharing Systems

We consider the problem of estimating the primary (first-choice) demand in a bike-sharing system. Such estimates are crucial for various operational decisions, such as the allocation and rebalancing of bikes to meet demand over a planning horizon. A key challenge in estimating the demand is to account for the choice substitution effect, where a commuter may substitute a trip for close alternatives when the first-choice location for picking up or returning a bike is not available. In this paper, we propose a method for estimating the primary demand using a rank-based demand model. The model accounts for choice substitutions by treating each observed trip as the best available option in a latent ranking over origin-destination (OD) pairs. To solve the high-dimensional estimation problem that arises from the combinatorial growth of origindestination rankings, we propose algorithms that (i) find sparse representations of the model parameters efficiently, and (ii) restrict station substitutions spatially according to the bike-sharing network. We prove consistency results of the model and develop efficient, first-order methods based on difference of convex (DCP) programming. Our approach is tractable on a city scale, which we demonstrate on a bike-sharing system in the Boston metropolitan area. Experimental evaluations on both simulated and real-world data sets show that our method can significantly reduce biases in ridership prediction and primary demand estimation, which results in increased ridership when used as inputs to an operational model for bike allocation.