A generalized disjunctive programming model for the static bike sharing rebalancing problem with demand intervals

Solving a static bike sharing rebalancing problem requires finding the minimum-cost route for rebalancing vehicles, subject to meeting the demand at the bike sharing stations of the system. In this work, we study the variant of the problem where the demand is specified by intervals, which adds flexibility to the routing of the rebalancing vehicles. We propose a generalized disjunctive programming (GDP) model to represent the problem and its reformulation into a mixed-integer linear programming (MILP) model. We use demand splitting to duplicate stations that require multiple visits. The model is designed for single-vehicle routing but can be used jointly with a clustering approach proposed in the literature for multi-vehicle routing. The model can solve to optimality 86.8% of benchmark instances with 70 stations within two hours of computing time. On test cases derived from real process data, the model is more than two orders of magnitude faster than the reference model in the literature.