Abstract
Car-sharing, electrification, and autonomous driving are greatly revolutionizing the future of the transportation system. This study proposes a location routing problem for the car-sharing system with autonomous electric vehicles to determine optimal station location and vehicle routing, where each station is both a depot and a charging station. A mathematical model is formulated and then extended to three variants, while simultaneously considering different recharging and service options. The proposed mixed-integer nonlinear models are separately solved by general algebraic modeling system (GAMS) and genetic algorithm (GA), and the efficiency of the GA is demonstrated. The comparative experimental results of instances are presented, and the benefits of allowing partial recharge are obtained. More significant savings in cost can be achieved if partial service is simultaneously allowed. Furthermore, the trade-off between the operator’s interests and the interests of users, as well as the operator’s immediate profits and future profits, are explored through sensitivity analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
02 June 2021
Additional “0” on online date during original publication.
Abbreviations
- ae ik :
-
The remaining energy of vehicle k when arriving point i
- at ik :
-
The arrival time of vehicle k at point i
- C distance :
-
Unit distance cost of a vehicle
- C reject :
-
Unit penalty cost incurred by rejecting a travel demand
- C station :
-
Construction cost of the station, including installation cost of charging facilities
- C vehicle :
-
Acquisition cost of a vehicle
- D:{1−,2−,⋯m −}:
-
Set of destinations of m travel demands, that is the set of delivery nodes
- de ik :
-
The remaining energy of vehicle k when leaving point i
- d ij :
-
Distance from point i to point j
- dt ik :
-
The departure time of vehicle k at point i
- E :
-
The battery capacity of the vehicle
- et m :
-
Allowed earliest pick-up time of travel demand m
- g :
-
The charging rate of charging infrastructure
- H: {1, 2,⋯, h}:
-
Set of candidate locations, it’s just regarded as a set of depots
- K:{1, 2, ⋯, k}:
-
Set of vehicles, k is the upper bound of the number of vehicles
- lt m :
-
Allowed latest pick-up time of travel demand m, ltm =etm + ω, ω is the width of the time window
- M: {1, 2,⋯, m}:
-
Set of travel demands, where m is the total number of travel demands N= Set of all points (N = H∪P∪O∪D)
- O:{1+, 2+, ⋯, m +}:
-
Set of origins of m travel demands, that is the set of pickup nodes
- P :
-
Set of all dummy nodes (∪h∈HPh), that is the set of all charging nodes
- P h :
-
Set of dummy nodes for vertex h ∈ H, it’s regarded as the set of charging nodes corresponding to the vertex h ∈ H
- r :
-
The consumption rate of the electric vehicle
- t ij :
-
Travel time from point i to point j
- T max :
-
Maximum operation time
- x ijk :
-
Binary: if vehicle k travel from point i to point j
- y i :
-
Binary: if candidate location i ∈ H is open as SAEVs’ station
References
Bongiovanni C, Kaspi M, Geroliminis N (2019) The electric autonomous dial-a-ride problem. Transportation Research Part B: Methodological 122:436–456, DOI: https://doi.org/10.1016/j.trb.2019.03.004
Boyacı B, Zografos KG, Geroliminis N (2015) An optimization framework for the development of efficient one-way car-sharing systems. European Journal of Operational Research 240(3):718–733, DOI: https://doi.org/10.1016/j.ejor.2014.07.020
Chen G, Hu D, Chien S (2020) Optimizing battery-electric-feeder service and wireless charging locations with nested genetic algorithm. IEEE Access 8(99):67166–67178, DOI: https://doi.org/10.1109/ACCESS.2020.2985168
Cordeau J-F, Laporte G (2003) A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transportation Research Part B: Methodological 37(6):579–594, DOI: https://doi.org/10.1016/s0191-2615(02)00045-0
Dong X, Zhang B, Wang B, Wang Z (2020) Urban households’ purchase intentions for pure electric vehicles under subsidy contexts in China: Do cost factors matter. Transportation Research Part A: Policy and Practice 135:183–197, DOI: https://doi.org/10.1016/j.tra.2020.03.012
Folkestad CA, Hansen N, Fagerholt K, Andersson H, Pantuso G (2020) Optimal charging and repositioning of electric vehicles in a freefloating carsharing system. Computers & Operations Research 113: 104771, DOI: https://doi.org/10.1016/j.cor.2019.104771
He F, Yin Y, Zhou J (2015) Deploying public charging stations for electric vehicles on urban road networks. Transportation Research Part C: Emerging Technologies 60:227–240, DOI: https://doi.org/10.1016/j.trc.2015.08.018
Hof J, Schneider M, Goeke D (2017) Solving the battery swap station location-routing problem with capacitated electric vehicles using an AVNS algorithm for vehicle-routing problems with intermediate stops. Transportation Research Part B: Methodological 97:102–112, DOI: https://doi.org/10.1016/j.trb.2016.11.009
Jorgensen RM, Larsen J, Bergvinsdottir KB (2007) Solving the Dial-a-Ride problem using genetic algorithms. Journal of the Operational Research Society 58(10):1321–1331, DOI: https://doi.org/10.1057/palgrave.jors.2602287
Kirchler D, Wolfler Calvo R (2013) A granular tabu search algorithm for the Dial-a-Ride problem. Transportation Research Part B: Methodological 56:120–135, DOI: https://doi.org/10.1016/j.trb.2013.07.014
Krueger R, Rashidi TH, Rose JM (2016) Preferences for shared autonomous vehicles. Transportation Research Part C: Emerging Technologies 69:343–355, DOI: https://doi.org/10.1016/j.trc.2016.06.015
Liang X, Correia GHDA, An K, van Arem B (2020) Automated taxis’ dial-a-ride problem with ride-sharing considering congestion-based dynamic travel times. Transportation Research Part C: Emerging Technologies 112:260–281, DOI: https://doi.org/10.1016/j.trc.2020.01.024
Liu H, Wang DZW (2017) Locating multiple types of charging facilities for battery electric vehicles. Transportation Research Part B: Methodological 103:30–55, DOI: https://doi.org/10.1016/j.trb.2017.01.005
Loeb B, Kockelman KM (2019) Fleet performance and cost evaluation of a shared autonomous electric vehicle (SAEV) fleet: A case study for Austin, Texas. Transportation Research Part A: Policy and Practice 121:374–385, DOI: https://doi.org/10.1016/j.tra.2019.01.025
Loeb B, Kockelman KM, Liu J (2018) Shared autonomous electric vehicle (SAEV) operations across the Austin, Texas network with charging infrastructure decisions. Transportation Research Part C: Emerging Technologies 89:222–233, DOI: https://doi.org/10.1016/j.trc.2018.01.019
Lokhandwala M, Cai H (2020) Siting charging stations for electric vehicle adoption in shared autonomous fleets. Transportation Research Part D: Transport and Environment 80:102231, DOI: https://doi.org/10.1016/j.trd.2020.102231
Masmoudi MA, Braekers K, Masmoudi M, Dammak A (2017) A hybrid genetic algorithm for the heterogeneous Dial-a-Ride problem. Computers & Operations Research 81:1–13, DOI: https://doi.org/10.1016/j.cor.2016.12.008
Masmoudi MA, Hosny M, Braekers K, Dammak A (2016) Three effective metaheuristics to solve the multi-depot multi-trip heterogeneous dial-a-ride problem. Transportation Research Part E: Logistics and Transportation Review 96:60–80, DOI: https://doi.org/10.1016/j.tre.2016.10.002
Masmoudi MA, Hosny M, Demir E, Genikomsakis KN, Cheikhrouhou N (2018) The dial-a-ride problem with electric vehicles and battery swapping stations. Transportation Research Part E: Logistics and Transportation Review 118:392–420, DOI: https://doi.org/10.1016/j.tre.2018.08.005
Masmoudi MA, Hosny M, Demir E, Pesch E (2019) Hybrid adaptive large neighborhood search algorithm for the mixed fleet heterogeneous dial-a-ride problem. Journal of Heuristics 26(1):83–118, DOI: https://doi.org/10.1007/s10732-019-09424-x
Meyrowitz AL, Blidberg DR, Michelson RC (2002) Autonomous vehicles. Proceedings of the IEEE 84(8):1147–1164, DOI: https://doi.org/10.1109/5.533960
Miao H, Jia H, Li J, Qiu TZ (2019) Autonomous connected electric vehicle (ACEV)-based car-sharing system modeling and optimal planning: A unified two-stage multi-objective optimization methodology. Energy 169:797–818, DOI: https://doi.org/10.1016/j.energy.2018.12.066
Mozafar MR, Moradi MH, Amini MH (2017) A simultaneous approach for optimal allocation of renewable energy sources and electric vehicle charging stations in smart grids based on improved GA-PSO algorithm. Sustainable Cities and Society 32:627–637, DOI: https://doi.org/10.1016/j.scs.2017.05.007
Parragh SN, Pinho de Sousa J, Almada-Lobo B (2014) The Dial-a-Ride problem with split requests and profits. Transportation Science 49(2):311–334, DOI: https://doi.org/10.1287/trsc.2014.0520
Schiffer M, Walther G (2017) The electric location routing problem with time windows and partial recharging. European Journal of Operational Research 260(3):995–1013, DOI: https://doi.org/10.1016/j.ejor.2017.01.011
Schiffer M, Walther G (2018) An adaptive large neighborhood search for the location-routing problem with intra-route facilities. Transportation Science 52(2):331–352, DOI: https://doi.org/10.1287/trsc.2017.0746
Shaheen SA, Cohen AP (2013) Carsharing and personal vehicle services: Worldwide market developments and emerging trends. International Journal of Sustainable Transportation 7(1):5–34, DOI: https://doi.org/10.1080/15568318.2012.660103
Steck F, Kolarova V, Bahamondebirke FJ, Trommer S, Lenz B (2018) How autonomous driving may affect the value of travel time savings for commuting. Transportation Research Record 2672(46):11–20, DOI: https://doi.org/10.1177/0361198118757980
US EPA (2020) United states environmental protection agency (US EPA). US EPA, Retrieved September 1, 2020, https://www.fueleconomy.gov
Vosooghi R, Puchinger J, Bischoff J, Jankovic M, Vouillon A (2020) Shared autonomous electric vehicle service performance: Assessing the impact of charging infrastructure. Transportation Research Part D: Transport and Environment 81:102283, DOI: https://doi.org/10.1016/j.trd.2020.102283
Weikl S, Bogenberger K (2013) Relocation strategies and algorithms for free-floating car sharing systems. IEEE Intelligent Transportation Systems Magazine 5(4):100–111, DOI: https://doi.org/10.1109/ITSC.2012.6338869
Yang J, Sun H (2015) Battery swap station location-routing problem with capacitated electric vehicles. Computers & Operations Research 55:217–232, DOI: https://doi.org/10.1016/j.cor.2014.07.003
Zhang H, Sheppard CJR, Lipman TE, Moura SJ (2019) Joint fleet sizing and charging system planning for autonomous electric vehicles. IEEE Transactions on Intelligent Transportation Systems 99:1–14, DOI: https://doi.org/10.1109/TITS.2019.2946152
Zhang H, Sheppard CJR, Lipman TE, Zeng T, Moura SJ (2020) Charging infrastructure demands of shared-use autonomous electric vehicles in urban areas. Transportation Research Part D: Transport and Environment 78:102210, DOI: https://doi.org/10.1016/j.trd.2019.102210
Acknowledgments
This work was supported by the Fundamental Research Funds for the Central Universities under Grant 300102229111.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ma, B., Hu, D. & Wu, X. The Location Routing Problem of the Car-Sharing System with Autonomous Electric Vehicles. KSCE J Civ Eng 25, 3107–3120 (2021). https://doi.org/10.1007/s12205-021-1605-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-021-1605-5