A Novel Robust Optimization Method for Fleet Sizing and Differentiated Pricing in Bike-Sharing Systems

Abstract

This study proposes an integrated fleet sizing and dynamic pricing (IFSDP) problem for bike-sharing systems to alleviate the imbalanced distribution of bikes during operations. In the IFSDP problem, the number of bikes deployed at each area in the system and the differentiated trip prices for different origin-destination pairs in different periods are optimized collaboratively with the consideration of uncertain demand and user sensitivity. A bi-level robust mixed-integer programming model is developed. The model is reformulated into a tractable mixed-integer quadratic programming model. Furthermore, the mixed-integer model is relaxed to trade off the robustness of the solution and the loss of the objective value. The proposed methods are validated and evaluated using extensive numerical experiments. Results demonstrate that the reformulated model is applicable in practice in terms of computational efficiency, and that the decisions can help increase both the profit and the number of served users, compared to the deterministic benchmark. The superiority of the proposed methods is independent of the type of uncertainty.