Public bike-sharing systems have the characteristics of the unbalanced station inventory,multiple depots,and multiple heterogeneous vehicles.This paper investigates the static bike repositioning problem with multiple depots and heterogeneous vehicles.Describing the user demand based on the nonlinear penalty func-tion of station inventory,a mixed-integer nonlinear programming model is proposed to minimize the weighted sum of operational time and nonlinear penalty function,and a cluster-first route-second algorithm is designed to solve it.The cluster-first route-second algorithm decomposes the station network by k-means algorithm,then the reduced network is re-modeled and solved based on heuristic rules.Numerical results illustrate the effectiveness of the model and algorithm,the flexibility of multiple depots and heterogeneous vehicles,and the efficiency of demand satisfaction.Our model can provide an effective repositioning method for operators.
维普
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