Column-and-constraint-generation-based approach to a robust reverse logistic network design for bike sharing

Dockless bike-sharing systems have grown rapidly in China in recent years. A large number of shared bikes have been put into use, which results in a serious problem of uncollected faulty bikes. However, since the exact number of faulty shared bikes cannot be known a priori, a reverse logistic network must be designed strategically to reduce the total costs of the collection process. This paper studies a robust reverse logistic network design problem of shared bikes that integrates the locations of recycling centres and the planning of collection routes in uncertain collection demand situations. A two-stage robust location routing model is presented to capture the uncertainty of collection demands, and then a set-partition reformulation is presented to address the computationally intractable model. We develop a column-and-constraint-generation-based algorithm combining a tailored column generation algorithm to efficiently solve the proposed model. Numerical experiments and parameter analyses, which are based on real data from bike-sharing companies, are conducted to evaluate the performance of the proposed algorithm. A case study is presented to further analyse the spatial features of the reverse logistic network of shared bikes. Benefits of applying robust optimization are demonstrated experimentally in terms of total cost under uncertain collection demand.