隨著都市快速發展，人口密集及私有汽車的增加，造成環境污染及停車位一位難求的問題，擁有私人車輛也必須負擔購買及後續產生的高花費，由此，共享電動車系統在近年來因其帶來對於環境、交通便利及社會的相關益處，而受到廣大的關注。本研究探討結合有樁及無樁式形態的共享電動汽車系統中的車輛部署及車輛調度問題，並且考慮需求及停車位數之隨機性。我們將該問題建立為整數兩階段隨機規劃問題，在第一階段透過歷史資料，以利潤最大化為目標，求得初始車輛部署分配量，第二階段將隨機需求及路邊停車位數不確定之情況納入考量，以利潤最大化為目標，求得車輛與人員之最佳調度。為求解此問題，本研究採用整數L-shaped方法，透過加入限制式以縮限可行解空間並得到品質佳的求解結果。實驗結果顯示本研究之求解方法能有效求解問題，且透過與商業求解軟體比較，能有較佳的求解表現。

As the population in the city grows, the amount of private gasoline vehicles increases accordingly. Excess gasoline vehicles cause the air pollution, lower chance of finding an unoccupied parking space. Also, purchasing a vehicle and associated expenses are another issue. Therefore, electric vehicle (EV) sharing systems have received increasing attention because of their environmental, mobility, and societal benefits. In this research, we investigate the vehicle deployment and relocation problem for hybrid one-way station-based and free-floating electric vehicle sharing systems considering demand and parking space stochasticity. The problem is formulated as a two-stage stochastic program. In the first stage, the EVs are deployed into a sharing system based on historical customer data to maximize the resulting profit. The second stage maximizes the expected profit by relocating the EVs in the system using relocation staff in response to uncertain demand parking space availability. To solve the resulting complicated problem, an integer L-shaped method is proposed so that the cuts can efficiently fathom the solution space and identify solutions with a reasonable optimality gap. The proposed solution framework is empirically applied to cases of various sizes. The empirical results demonstrate the effectiveness of the proposed solution scheme in compared with optimization solver package.

[1] Aguilera-García, Á., Gomez, J., & Sobrino, N. (2020). Exploring the adoption of moped scooter-sharing systems in Spanish urban areas. Cities, 96, 102424. doi:https://doi.org/10.1016/j.cities.2019.102424
[2] Ahmed, S. (2011). Two-Stage Stochastic Integer Programming: A Brief Introduction. In Wiley Encyclopedia of Operations Research and Management Science.
[3] Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252. doi:10.1007/BF01386316
[4] Bertsimas, D., & Tsitsiklis, J. N. (1997). Introduction to linear optimization. Belmont, Mass.: Athena Scientific.
[5] Bian, Y., Cui, Y., Yan, S., & Han, X. (2021). Optimal strategy of a customer-to-customer sharing platform: Whether to launch its own sharing service? Transportation Research Part E: Logistics and Transportation Review, 149, 102288. doi:https://doi.org/10.1016/j.tre.2021.102288
[6] Biesinger, B., Hu, B., & Raidl, G. (2016). An Integer L-shaped Method for the Generalized Vehicle Routing Problem with Stochastic Demands. Electronic Notes in Discrete Mathematics, 52, 245-252. doi:https://doi.org/10.1016/j.endm.2016.03.033
[7] Boyaci, B., Zografos, K. G., & Geroliminis, N. (2017). An integrated optimization-simulation framework for vehicle and personnel relocations of electric carsharing systems with reservations. Transportation Research Part B-Methodological, 95, 214-237. doi:10.1016/j.trb.2016.10.007
[8] Brandstätter, G., Kahr, M., & Leitner, M. (2017). Determining optimal locations for charging stations of electric car-sharing systems under stochastic demand. Transportation Research Part B: Methodological, 104, 17-35. doi:https://doi.org/10.1016/j.trb.2017.06.009
[9] Cepolina, E. M., & Farina, A. (2012). A new shared vehicle system for urban areas. Transportation Research Part C: Emerging Technologies, 21(1), 230-243. doi:https://doi.org/10.1016/j.trc.2011.10.005
[10] Chen, T. D., & Kockelman, K. M. (2016). Carsharing's life-cycle impacts on energy use and greenhouse gas emissions. Transportation Research Part D-Transport and Environment, 47, 276-284. doi:10.1016/j.trd.2016.05.012
[11] Correia, G. H. d. A., & Antunes, A. P. (2012). Optimization approach to depot location and trip selection in one-way carsharing systems. Transportation Research Part E: Logistics and Transportation Review, 48(1), 233-247. doi:https://doi.org/10.1016/j.tre.2011.06.003
[12] Deng, Y. H., & Cardin, M. A. (2018). Integrating operational decisions into the planning of one-way vehicle-sharing systems under uncertainty. Transportation Research Part C-Emerging Technologies, 86, 407-424. doi:10.1016/j.trc.2017.11.018
[13] Fan, W. (2014). Optimizing Strategic Allocation of Vehicles for One-Way Car-sharing Systems Under Demand Uncertainty. Journal of the Transportation Research Forum. doi:10.5399/osu/jtrf.53.3.4252
[14] Fang, K., Wang, S., Pinedo, M. L., Chen, L., & Chu, F. (2021). A combinatorial Benders decomposition algorithm for parallel machine scheduling with working-time restrictions. European Journal of Operational Research, 291(1), 128-146. doi:https://doi.org/10.1016/j.ejor.2020.09.037
[15] Fishman, E., Washington, S., Haworth, N., & Watson, A. (2015). Factors influencing bike share membership: An analysis of Melbourne and Brisbane. Transportation Research Part A: Policy and Practice, 71, 17-30. doi:https://doi.org/10.1016/j.tra.2014.10.021
[16] Folkestad, C. A., Hansen, N., Fagerholt, K., Andersson, H., & Pantuso, G. (2020). Optimal charging and repositioning of electric vehicles in a free-floating carsharing system. Computers & Operations Research, 113. doi:UNSP 104771
10.1016/j.cor.2019.104771
[17] Fuller, M. (2016). Wireless charging in California: Range, recharge, and vehicle electrification. Transportation Research Part C: Emerging Technologies, 67, 343-356. doi:https://doi.org/10.1016/j.trc.2016.02.013
[18] Gössling, S. (2020). Integrating e-scooters in urban transportation: Problems, policies, and the prospect of system change. Transportation Research Part D: Transport and Environment, 79, 102230. doi:https://doi.org/10.1016/j.trd.2020.102230
[19] Gambella, C., Malaguti, E., Masini, F., & Vigo, D. (2018). Optimizing relocation operations in electric car-sharing. Omega-International Journal of Management Science, 81, 234-245. doi:10.1016/j.omega.2017.11.007
[20] Golalikhani, M., Oliveira, B. B., Carravilla, M. A., Oliveira, J. F., & Antunes, A. P. (2021). Carsharing: A review of academic literature and business practices toward an integrated decision-support framework. Transportation Research Part E: Logistics and Transportation Review, 149, 102280. doi:https://doi.org/10.1016/j.tre.2021.102280
[21] Han, J., Zhang, J., Zeng, B., & Mao, M. (2021). Optimizing dynamic facility location-allocation for agricultural machinery maintenance using Benders decomposition. Omega, 105, 102498. doi:https://doi.org/10.1016/j.omega.2021.102498
[22] Heilporn, G., Cordeau, J.-F., & Laporte, G. (2011). An integer L-shaped algorithm for the Dial-a-Ride Problem with stochastic customer delays. Discrete Applied Mathematics, 159(9), 883-895. doi:https://doi.org/10.1016/j.dam.2011.01.021
[23] Huang, K., Correia, G. H. d. A., & An, K. (2018). Solving the station-based one-way carsharing network planning problem with relocations and non-linear demand. Transportation Research Part C: Emerging Technologies, 90, 1-17. doi:https://doi.org/10.1016/j.trc.2018.02.020
[24] Huo, X., Wu, X. K., Li, M., Zheng, N., & Yu, G. Z. (2020). The allocation problem of electric car-sharing system: A data-driven approach. Transportation Research Part D-Transport and Environment, 78. doi:ARTN 102192
10.1016/j.trd.2019.11.021
[25] Illgen, S., & Höck, M. (2019). Literature review of the vehicle relocation problem in one-way car sharing networks. Transportation Research Part B: Methodological, 120, 193-204. doi:https://doi.org/10.1016/j.trb.2018.12.006
[26] Jacquillat, A., & Zoepf, S. (2017). Deployment and Utilization of Plug-in Electric Vehicles in Round-trip Carsharing Systems. International Journal of Sustainable Transportation, 12. doi:10.1080/15568318.2017.1328624
[27] Jiang, B., & Fan, Z.-P. (2020). Optimal allocation of shared parking slots considering parking unpunctuality under a platform-based management approach. Transportation Research Part E: Logistics and Transportation Review, 142, 102062. doi:https://doi.org/10.1016/j.tre.2020.102062
[28] Ko, Y. D. (2019). An efficient integration of the genetic algorithm and the reinforcement learning for optimal deployment of the wireless charging electric tram system. Computers & Industrial Engineering, 128, 851-860. doi:https://doi.org/10.1016/j.cie.2018.10.045
[29] Laporte, G., & Louveaux, F. V. (1993). The Integer L-Shaped Method for Stochastic Integer Programs with Complete Recourse. Operations Research Letters, 13(3), 133-142. doi:Doi 10.1016/0167-6377(93)90002-X
[30] Laporte, G., Louveaux, F. V., & Hamme, L. v. (2002). An Integer L-Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands. Operations Research, 50(3), 415-423. doi:10.1287/opre.50.3.415.7751
[31] Lu, M., Chen, Z., & Shen, S. (2017). Optimizing the Profitability and Quality of Service in Carshare Systems Under Demand Uncertainty. Manufacturing & Service Operations Management, 20. doi:10.1287/msom.2017.0644
[32] Mardan, E., Govindan, K., Mina, H., & Gholami-Zanjani, S. M. (2019). An accelerated benders decomposition algorithm for a bi-objective green closed loop supply chain network design problem. Journal of Cleaner Production, 235, 1499-1514. doi:https://doi.org/10.1016/j.jclepro.2019.06.187
[33] Mounce, R., & Nelson, J. D. (2019). On the potential for one-way electric vehicle car-sharing in future mobility systems. Transportation Research Part a-Policy and Practice, 120, 17-30. doi:10.1016/j.tra.2018.12.003
[34] Mubarak, M., Üster, H., Abdelghany, K., & Khodayar, M. (2021). Strategic network design and analysis for in-motion wireless charging of electric vehicles. Transportation Research Part E: Logistics and Transportation Review, 145, 102179. doi:https://doi.org/10.1016/j.tre.2020.102179
[35] Ngo, H., Kumar, A., & Mishra, S. (2020). Optimal positioning of dynamic wireless charging infrastructure in a road network for battery electric vehicles. Transportation Research Part D: Transport and Environment, 85, 102385. doi:https://doi.org/10.1016/j.trd.2020.102385
[36] Nourinejad, M., Zhu, S. R., Bahrami, S., & Roorda, M. J. (2015). Vehicle relocation and staff rebalancing in one-way carsharing systems. Transportation Research Part E-Logistics and Transportation Review, 81, 98-113. doi:10.1016/j.tre.2015.06.012
[37] Panchal, C., Stegen, S., & Lu, J. (2018). Review of static and dynamic wireless electric vehicle charging system. Engineering Science and Technology, an International Journal, 21(5), 922-937. doi:https://doi.org/10.1016/j.jestch.2018.06.015
[38] Roni, M. S., Yi, Z. G., & Smart, J. G. (2019). Optimal charging management and infrastructure planning for free-floating shared electric vehicles. Transportation Research Part D-Transport and Environment, 76, 155-175. doi:10.1016/j.trd.2019.09.021
[39] Shaheen, S., Cohen, A., & Chung, M. (2008). North American Carsharing: A Ten-Year Retrospective. Institute of Transportation Studies, UC Davis, Institute of Transportation Studies, Working Paper Series.
[40] TENG, S. Y., ONG, H. L., & HUANG, H. C. (2004). AN INTEGER L-SHAPED ALGORITHM FOR TIME-CONSTRAINED TRAVELING SALESMAN PROBLEM WITH STOCHASTIC TRAVEL AND SERVICE TIMES. Asia-Pacific Journal of Operational Research, 21(02), 241-257. doi:10.1142/s0217595904000229
[41] Van Slyke, R. M., & Wets, R. (1969). L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming. Siam Journal on Applied Mathematics, 17(4), 638-663. Retrieved from http://www.jstor.org/stable/2099310
[42] Vanslyke, R. M., & Wets, R. (1969). L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming. Siam Journal on Applied Mathematics, 17(4), 638-+. doi:Doi 10.1137/0117061
[43] Wang, L., Liu, Q., & Ma, W. J. (2019). Optimization of dynamic relocation operations for one-way electric carsharing systems. Transportation Research Part C-Emerging Technologies, 101, 55-69. doi:10.1016/j.trc.2019.01.005
[44] Wang, M., & Zhou, X. (2017). Bike-sharing systems and congestion: Evidence from US cities. Journal of Transport Geography, 65, 147-154. doi:https://doi.org/10.1016/j.jtrangeo.2017.10.022
[45] Wang, Q., McCalley, J. D., Zheng, T., & Litvinov, E. (2016). Solving corrective risk-based security-constrained optimal power flow with Lagrangian relaxation and Benders decomposition. International Journal of Electrical Power & Energy Systems, 75, 255-264. doi:https://doi.org/10.1016/j.ijepes.2015.09.001
[46] Weikl, S., & Bogenberger, K. (2015). A practice-ready relocation model for free-floating carsharing systems with electric vehicles - Mesoscopic approach and field trial results. Transportation Research Part C: Emerging Technologies, 57, 206-223. doi:10.1016/j.trc.2015.06.024
[47] Zekang, L., He, S., & Xu, Y. (2020). Combining Benders decomposition and column generation for scheduled service network design problem in rail freight transportation. Transportmetrica A: Transport Science, 17, 1-30. doi:10.1080/23249935.2020.1863505
[48] Zhang, D., Liu, Y., & He, S. C. (2019). Vehicle assignment and relays for one-way electric car-sharing systems. Transportation Research Part B-Methodological, 120, 125-146. doi:10.1016/j.trb.2018.12.004
[49] Zhao, M., Li, X. P., Yin, J. T., Cui, J. X., Yang, L. X., & An, S. (2018). An integrated framework for electric vehicle rebalancing and staff relocation in one-way carsharing systems: Model formulation and Lagrangian relaxation-based solution approach. Transportation Research Part B-Methodological, 117, 542-572. doi:10.1016/j.trb.2018.09.014