Location Optimization Of Carsharing Systems Under Stochastic And Dynamic Supply And Demand Environments

Carsharing is attracting wide attention as a new mode of transportation between public transportation and private cars.Compared with private cars,carsharing enables users to enjoy comfortable and flexible travel without bearing high vehicle purchase costs,insurance and parking fees.Compared with online ride-hailing and taxis,carsharing can better protect users’ personal and privacy security,and have higher driving autonomy and greater price advantages.However,it is difficult for users to find and return cars due to unreasonable station distribution,parking space and vehicle configuration.The dynamic and random supply and demand environments lead to the dilemma that users’ demand cannot be matched in time.Thus,largescale vehicle relocations are needed which result in the increase of operating costs and difficulty in making profits.These problems directly lead to the slow development and shrinking market of the carsharing industry in recent years.This paper conducts a joint optimization model to study the planning,configuration and operation of carsharing systems to provide theoretical basis for the development of carsharing systems.Firstly,the fluid queuing network model is constructed to reveal the interactions among sharing cars,users,staff and other vehicles on the road under the dynamic random supply and demand environments.Then,based on the fluid queuing network model,a joint optimization model is constructed to maximize the operators’ profit,considering the user demand satisfaction rate,vehicle utilization rate and road congestion constraints.The optimization model decides the number,location and capacity of stations at the planning level;optimizes the fleet size and initial vehicle allocation,the number of staff and initial staff distribution at the configuration level;determines vehicle relocations and staff movements at the operational level.Because the joint optimization model is a complex mixed integer nonlinear non-convex model and the location problem is NP hard,a greedy location algorithm based on simultaneous perturbation stochastic approximation(SPSA)is proposed.The algorithm divides the joint optimization model into three sub-problems: first,the greedy algorithm is used to select the stations with high economic benefits;then,the initial solution of station capacity and configuration is obtained by log barrier algorithm,and the relocation schemes are taken as the input parameters.Then SPSA algorithm based on elite strategy is used to solve the optimal station capacity and configuration scheme under the current station.Finally,by comparing greedy algorithm with violent search algorithm,and SPSA algorithm with other heuristic algorithms,the computational performance of the proposed algorithm is verified.Finally,the example of Chengdu city is analyzed.Firstly,the data is cleaned and the initial candidate stations are obtained by K-means clustering algorithm.By comparing the optimal carsharing systems obtained by considering the dynamic random environment or not,we conclude that the system tends to choose the stations with large demands when the supply and demand are relatively balanced.However,when the carsharing systems obtained under the condition of equilibrium supply and demand is applied to the dynamic random supply and demand environments,the operator’s profits and demand satisfaction rate will be reduced.When the imbalance between supply and demand of the carsharing systems is serious and a large number of vehicle relocation are needed,the system will prefer to choose the stations with relatively balanced supply and demand,even though the total demands for sharing cars are small.Then,the effects of fuel price,price elastic demands and road congestion elastic demands on carsharing systems are analyzed.Fuel price increase will reduce operators’ profits and demand satisfaction rate,and increase the vehicle utilization rate and then reduce.As the impact of fuel price fluctuations on the carsharing systems is significant,it is necessary to consider introducing electric sharing cars or using hybrid vehicles to reduce the impact.The sensitivity analysis of price elasticity demand verifies the feasibility and economy of adaptive relocation strategy which adopts dynamic pricing to guide user demands.The sensitivity analysis of congestion elastic demand shows that the road congestion constraint will exclude the stations connected to congested roads,even though these stations have higher economic benefits,thus affecting the profits of operators.When urban roads are moderately congested(when road occupancy rate is around 0.5-0.6),the introduction of carsharing systems can achieve a triple win for operators,users and urban traffic management departments.