Repositioning in bike sharing systems with broken bikes considering on-site repairs
研究了同时使用车辆搬运和维修工现场维修来重新定位故障自行车与可用自行车的问题，建立了混合整数线性规划模型，并设计了混合遗传算法求解，以最小化用户不满和碳排放成本。
• We introduce a bike repositioning problem with broken bikes and on-site repairers. • We propose a time-indexed mixed integer linear program for the problem. • We develop an effective hybrid algorithm to solve the problem. • The algorithm relies a new concept of station budgets to determine loading and repair instructions. • Hybrid genetic search is used to determine truck and repair routes. On-site repairs by repairers can handle broken bikes in a bike-sharing system and simultaneously satisfy usable bike demand without requiring vehicle repositioning for off-site repairs. However, this option has not been jointly considered with vehicle-based repositioning for both usable and broken bikes in the literature to improve repositioning performance. This paper presents a mixed-integer linear programming model for a static bike repositioning problem that combines vehicle-based bike delivery/collection with labor-based on-site repairs, aiming to minimize the total cost of user dissatisfaction and carbon emissions within a time budget. A hybrid algorithm, consisting of hybrid genetic search with adaptive diversity control and a station budget constrained heuristic, is proposed to solve the problem. This method introduces a station budget concept to limit the time spent at each station by considering the benefit-cost ratio function of each station along the route. The proposed algorithm is evaluated on networks of various sizes and configurations of the number of trucks and repairers. The results demonstrate that the algorithm can obtain optimal solutions on small instances and can outperform a commercial solver on larger networks in achieving superior solutions within a fraction of the computational time. Moreover, we investigated the cost-effectiveness of introducing repairers, revealing that long repair times and a low percentage of broken bikes diminish the effectiveness of introducing them.