Bike Rebalancing Problem Considering Broken Bikes

Bike sharing systems(BSS)are developing fast with the growing popularity of sharing economy.The large scale of the bikes distributed in the cities and the stochastic behavior of customers have made the operation of BSS hard,and invoked many scientific researches.Due to customer behavior heterogeneity,bike sharing systems often grow into states where bike supply doesn't match customer demand,that is,some stations lack bikes while others have an excess.Bike rebalancing problems deal with such imbalance by scheduling trucks to move bikes between stations under limited resources,and raise customer satisfaction.Former studies only regard empty or full stations as causes for service dissatisfaction,but in fact,bikes damage is getting severer and may cost customers more time and fail their expectation,which should not be ignored.The thesis measures the cost of this new kinds of service dissatisfaction considering broken bikes by a queueing model.Then a mixed integer programming(MIP)model is built to optimize the operation of rebalancing good bikes and collecting broken bikes to the depot,minimizing the sum of traveling cost,truck acquisition cost and service dissatisfaction cost.The MIP model will decide the number of trucks used,schedule their routes and output the number of bikes loaded or unloaded at each bike station.Numerical experiments are first conducted based on Hubway BSS data to analysis the single station service dissatisfaction,the results show that,as the number of initial bikes increase,the cost will decline then followed by an increase.Moreover,it indicates that by considering broken bikes,the optimal initial number of good bikes turns bigger,and the rate of cost decreasing is faster than that of cost increasing.This means a bike shortage costs more than a surplus,which can be explained as less good bikes make broken bikes easier met by customers.As the objective function of the MIP model is non-convex and nonlinear,it is first simplified to a quadratic function so as to be solved by CPLEX,for the purpose of model validation.Then,a genetic algorithm is designed to solve the original model.The numerical instances are from the data of Hubway BSS in Boston.Repeating computations prove the effectiveness of the proposed algorithm.The average coefficient of variation of solution is 5.2%,and the initial solutions are improved by 14.4% in average.The computational time is reasonable,for example,it cost 4273 s for the instance of 150 stations and 3 trucks,and 1561 s for the instance of 50 stations and 9 trucks.Finally,by analyzing the pattern of the deduced solutions,managerial insights are given for practice in terms of the operational priorities,that is,loading broken bikes has the highest priority,then unloading good bikes,and at last loading good bikes.