The one-station bike repositioning problem

TL;DR

This paper addresses the complex bike repositioning problem in bike sharing systems by modeling it as a mixed integer linear programming problem and providing an optimal, linear-time algorithm for vehicle loading and unloading at stations.

Contribution

It introduces a novel linear-time optimal algorithm for the specific problem of vehicle loading/unloading at stations within bike sharing systems.

Findings

The algorithm efficiently minimizes bike demand loss and free stand loss.

The problem is effectively modeled as a mixed integer linear programming problem.

The solution runs in linear time relative to the time horizon size.

Abstract

In bike sharing systems the quality of the service to the users strongly depends on the strategy adopted to reposition the bikes. The bike repositioning problem is in general very complex as it involves different interrelated decisions: the routing of the repositioning vehicles, the scheduling of their visits to the stations, the number of bikes to load or unload for each station and for each vehicle that visits the station. In this paper we study the problem of optimally loading/unloading vehicles that visit the same station at given time instants of a finite time horizon. The goal is to minimize the total lost demand of bikes and free stands in the station. We model the problem as a mixed integer linear programming problem and present an optimal algorithm that runs in linear time in the size of the time horizon.