Exact loading and unloading strategies for the static multi-vehicle bike repositioning problem

This study investigates a bike repositioning problem (BRP) that determines the routes of the repositioning vehicles and the loading and unloading quantities at each bike station to firstly minimize the positive deviation from the tolerance of total demand dissatisfaction (TDD) and then service time. The total demand dissatisfaction of a bike-sharing system in this study is defined as the sum of the difference between the bike deficiency and unloading quantity of each station in the system. Two service times are considered: the total service time and the maximum route duration of the fleet. To reduce the computation time to solve the loading and unloading sub-problem of the BRP, this study examines a novel set of loading and unloading strategies and further proves them to be optimal for a given route. This set of strategies is then embedded into an enhanced artificial bee colony algorithm to solve the BRP. The numerical results demonstrate that a larger fleet size may not lead to a lower total service time but can effectively lead to a lower maximum route duration at optimality. The results also illustrate the trade-offs between the two service times, between total demand dissatisfaction and total service time, and between the number of operating vehicles provided and the TDD. Moreover, the results demonstrate that the optimal values of the two service times can increase with the TDD and introducing an upper bound on one service time can reduce the optimal value of the other service time.