Robust depot location and inventory management in bike-sharing systems under government supervision

Abstract

Bike-sharing systems offer an efficient and accessible option for short-distance transportation. However, the boom of bike-sharing systems also introduced challenges to urban transportation systems, such as congestion due to oversupplying bikes and low service quality caused by malfunctioning bikes. To address these challenges, government supervision has been conducted to improve operational orders in bike-sharing systems. For instance, the government may restrict the bike inventory in certain regions to avoid congestion caused by oversupplying bikes, and supervise the operational condition of the bike fleet to improve the satisfaction of users. Therefore, bike-sharing system operators should incorporate the influence of government supervision when formulating related decisions. This study introduces an optimization model for bike-sharing systems that simultaneously addresses depot location, inventory management, and bike rebalancing decisions under government supervision. Specifically, we consider government supervision aimed at controlling bike oversupply and managing the maintenance of malfunctioning bikes. Moreover, to address the uncertainty of travel demand and government supervision strategy, a distributionally robust optimization (DRO) model that incorporates both moment-based and sample-based information is developed and reformulated. The numerical results imply that the DRO model surpasses benchmark models. Furthermore, effect analyses are conducted, and we provide valuable managerial insights for government supervisors and bike-sharing system operators. For government supervisors, conducting the supervision could effectively mitigate the oversupply of bikes. While for bike-sharing system operators, we notice that the bike allocation restriction and malfunctioning bikes may significantly affect their profits. Accordingly, they should optimize the bike rebalancing operations to avoid such penalties and improve the operational profits.

Graphical abstract

Keywords

bike-sharing system / supervision strategy / depot location / inventory management / distributionally robust optimization

References

[1] Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G, (2013). Robust solutions of optimization problems affected by uncertain probabilities. Manage Sci, 59: 341–357

[2] Ben-Tal A, Nemirovski A, (1999). Robust solutions of uncertain linear programs. Oper Res Lett, 25: 1–13

[3] Bertsimas D, Sim M, (2004). The price of robustness. Oper Res, 52: 35–53

[4] Birge J RLouveaux F (2011). Introduction to stochastic programming. Springer Science & Business Media

[5] Bulhões T, Subramanian A, Erdogan G, Laporte G, (2018). The static bike relocation problem with multiple vehicles and visits. Eur J Oper Res, 264: 508–523

[6] Caggiani L, Colovic A, Ottomanelli M, (2020). An equality-based model for bike-sharing stations location in bicycle-public transport multimodal mobility. Transp Res Part A Policy Pract, 140: 251–265

[7] Chang X, Wu J, Sun H, Yan X, (2023). A smart predict-then-optimize method for dynamic green bike relocation in the free-floating system. Transp Res, Part C Emerg Technol, 153: 104220

[8] Chen Q, Fu C, Zhu N, Ma S, He Q, (2023). A target-based optimization model for bike-sharing systems: From the perspective of service efficiency and equity. Transp Res, Part B: Methodol, 167: 235–260

[9] Datner S, Raviv T, Tzur M, Chemla D, (2019). Setting inventory levels in a bike sharing network. Transport Sci, 53: 62–76

[10] Erdogan G, Battarra M, Wolfler Calvo R, (2015). An exact algorithm for the static rebalancing problem arising in cicycle sharing systems. Eur J Oper Res, 245: 667–679

[11] Mohajerin Esfahani P, Kuhn D, (2018). Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations. Math Program, 171: 115–166

[12] Fishman E, (2016). Bikeshare: A review of recent literature. Transport Reviews, 36: 92–113

[13] Frade I, Ribeiro A, (2015). Bike-sharing stations: A maximal covering location approach. Transp Res Part A Policy Pract, 82: 216–227

[14] Fu C, Ma S, Zhu N, He Q, Yang H, (2022a). Bike-sharing inventory management for market expansion. Transp Res, Part B: Methodol, 162: 28–54

[15] Fu C, Zhu N, Ma S, Liu R, (2022b). A two-stage robust approach to integrated station location and rebalancing vehicle service design in bike-sharing systems. Eur J Oper Res, 298: 915–938

[16] Guo Y, Li J, Xiao L, Allaoui H, Choudhary A, Zhang L, (2024). Efficient inventory routing for Bike-Sharing Systems: A combinatorial reinforcement learning framework. Transp Res, Part E Logist Trans Rev, 182: 103415

[17] He L, Hu Z, Zhang M, (2020). Robust repositioning for vehicle sharing. Manuf Serv Oper Manag, 22: 241–256

[18] Jiang Z, Lei C, Ouyang Y, (2020). Optimal investment and management of shared bikes in a competitive market. Transp Res, Part B: Methodol, 135: 143–155

[19] Jin Y, Ruiz C, Liao H, (2022). A simulation framework for optimizing bike rebalancing and maintenance in large-scale bike-sharing systems. Simul Model Pract Theory, 115: 102422

[20] Kaspi M, Raviv T, a Tzur M, (2016). Detection of unusable bicycles in bike-sharing systems. Omega, 65: 10–16

[21] Li L, Li G, Liang S, (2021). Does government supervision suppress free-floating bike sharing development? Evidence from Mobike in China. Inf Technol Dev, 27: 802–826

[22] Li X, Wang X, Feng Z, (2024). Dynamic repositioning in bike-sharing systems with uncertain demand: An improved rolling horizon framework. Omega, 126: 103047

[23] Lin J, Yang T, (2011). Strategic design of public bicycle sharing systems with service level constraints. Transp Res, Part E Logist Trans Rev, 47: 284–294

[24] Lin J, Yang T, Chang Y, (2013). A hub location inventory model for bicycle sharing system design: Formulation and solution. Comput Ind Eng, 65: 77–86

[25] Liu S, Shen Z M, Ji X, (2022). Urban bike lane planning with bike trajectories: Models, algorithms, and a real-world case study. Manuf Serv Oper Manag, 24: 2500–2515

[26] Long D Z, Sim M, Zhou M, (2023). Robust satisficing. Oper Res, 71: 61–82

[27] Lu C, (2016). Robust multi-period fleet allocation models for bike-sharing systems. Netw Spat Econ, 16: 61–82

[28] Lv C, Liu Q, Zhang C, Ren Y, Zhou H, (2024). A feature correlation reinforce clustering and evolutionary algorithm for the green bike-sharing reposition problem. Comput Oper Res, 166: 106627

[29] Lv C, Zhang C, Lian K, Ren Y, Meng L, (2022). A two-echelon fuzzy clustering based heuristic for large-scale bike sharing repositioning problem. Transp Res, Part B: Methodol, 160: 54–75

[30] Maggioni F, Cagnolari M, Bertazzi L, Wallace SW, (2019). Stochastic optimization models for a bike-sharing problem with transshipment. Eur J Oper Res, 276: 272–283

[31] Ministry of Transport in Singapore (2022). Written reply to parliamentary question on measures taken to ensure non-dumping or illegal parking of shared bicycles from granting of new licence for bike sharing. Available at the website of mot.gov.sg

[32] Nikiforiadis A, Aifadopoulou G, Salanova Grau JM, Boufidis N, (2021). Determining the optimal locations for bike-sharing stations: methodological approach and application in the city of Thessaloniki, Greece. Transp Res Procedia, 52: 557–564

[33] Pu D, Xie F, Yuan G, (2020). Active supervision strategies of online ride-hailing based on the tripartite evolutionary game model. IEEE Access, 8: 149052–149064

[34] Qin M, Wang J, Chen WM, (2023). Reducing CO₂ emissions from the rebalancing operation of the bike-sharing system in beijing. Frontiers of Engineering Management, 10(2): 262–284

[35] Raviv T, Kolka O, (2013). Optimal inventory management of a bike-sharing station. IIE Trans, 45: 1077–1093

[36] Raviv T, Tzur M, Forma IA, (2013). Static repositioning in a bike-sharing system: models and solution approaches. EURO J Transp Logist, 2: 187–229

[37] Schuijbroek J, Hampshire R C, Van Hoeve W J, (2017). Inventory rebalancing and vehicle routing in bike sharing systems. Eur J Oper Res, 257: 992–1004

[38] Shenzhen Municipal Transportation Bureau (2017). Policy interpretation of the “implementation plan for the regulation and rectification of internet rental bicycles in shenzhen”. Available at the website of jtys.sz.gov.cn

[39] Shu J, Chou MC, Liu Q, Teo C, Wang I, (2013). Models for effective deployment and redistribution of bicycles within public bicycle-sharing systems. Oper Res, 61: 1346–1359

[40] Shui CS, Szeto W, (2018). Dynamic green bike repositioning problem—A hybrid rolling horizon artificial bee colony algorithm approach. Transp Res Part D Transp Environ, 60: 119–136

[41] Shui CS, Szeto WY, (2020). A review of bicycle-sharing service planning problems. Transp Res, Part C Emerg Technol, 117: 102648

[42] Silva M C M, Aloise D, Jena S D, (2024). Data-driven prioritization strategies for inventory rebalancing in bike-sharing systems. Omega, 129: 103141

[43] Smith J E, Winkler R L, (2006). The optimizer’s curse: Skepticism and postdecision surprise in decision analysis. Manage Sci, 52: 311–322

[44] Song J, Li B, Szeto W, Zhan X, (2024). A station location design problem in a bike-sharing system with both conventional and electric shared bikes considering bike users’ roaming delay costs. Transp Res, Part E Logist Trans Rev, 181: 103350

[45] Wang Y, Jin H, Zheng S, Shang W, Wang K, (2023). Bike-sharing duopoly competition under government regulation. Appl Energy, 343: 121121

[46] Wiesemann W, Kuhn D, Sim M, (2014). Distributionally robust convex optimization. Oper Res, 62: 1358–1376

[47] Wu L, Gu W, Fan W, Cassidy M J, (2020). Optimal design of transit networks fed by shared bikes. Transp Res, Part B: Methodol, 131: 63–83

[48] Xiamen Municipal Law Enforcement Bureau of Urban Management (2025). Public consultation on the “2025 implementation plan for the assessment of internet rental bicycle operating companies in xiamen (draft for public comment)”. Available at the website of cg.xm.gov.cn

[49] Xiao G, Wang Z, (2020). Empirical study on bikesharing brand selection in china in the post-sharing era. Sustainability (Basel), 12: 3125

[50] Yan S, Lin J, Chen Y, Xie F, (2017). Rental bike location and allocation under stochastic demands. Comput Ind Eng, 107: 1–11

[51] Yin Z, Hardaway K, Feng Y, Kou Z, Cai H, (2023). Understanding the demand predictability of bike share systems: A station-level analysis. Frontiers of Engineering Management, 10: 551–565

[52] Zhang D, Yu C, Desai J, Lau H, Srivathsan S, (2017). A time-space network flow approach to dynamic repositioning in bicycle sharing systems. Transp Res, Part B: Methodol, 103: 188–207

[53] Zhao SHou WWang ZHe Q (2022). Bikes detention game in free-float bike sharing systems. In: INFORMS International Conference on Service Science: 251–26

[54] Zhong Y, Yang T, Cao B, Cheng T, (2022). On-demand ride-hailing platforms in competition with the taxi industry: Pricing strategies and government supervision. Int J Prod Econ, 243: 108301

Rights & permissions

Higher Education Press