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Robust Multi-period Fleet Allocation Models for Bike-Sharing Systems

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Abstract

This paper presents mathematical programming models that generate optimal daily allocation of bicycles to the stations of a bike-sharing system. First, a time-space network is constructed to describe time-dependent bike flows in the system. Next, a bike fleet allocation model that considers average historical demand and fixed fleet size is established based on the time-space network. In addition to fleet allocation in multiple periods, this model generates least cost empty bicycle redistribution plans to meet demand in subsequent time periods. The model aims to correct demand asymmetry in bike-sharing systems, where flow from one station to another is seldom equal to the flow in the opposing direction. An extension of the model that relaxes the fleet size constraint to determine optimal fleet size in supporting planning stage decisions is also presented in the paper. Moreover, we describe uncertain bike demands using some prescribed uncertainty sets and develop robust bike fleet allocation models that minimize total system cost in the worst-case or maximum demand scenarios derived from the uncertainty sets. Numerical experiments were conducted based on the New Taipei City’s public bike system to demonstrate the applicability and performance of the proposed models. In addition, this research considers two performance measures, robust price and hedge value, in order to investigate the tradeoff between robustness and optimality, as well as the benefit of applying robust solutions relative to nominal optimal solutions in uncertain demand situations.

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References

  • Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ben-Tal A, Chung BD, Mandala SR, Yao T (2011) Robust optimization for emergency logistics planning: risk mitigation in humanitarian relief supply chains. Transp Res B 45(8):1177–1189

    Article  Google Scholar 

  • Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98:43–71

    Google Scholar 

  • Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52(1):35–53

    Article  Google Scholar 

  • Brons M, Givoni M, Rietveld P (2009) Access to railway stations and its potential in increasing rail use. Transp Res A 43(2):136–149

    Google Scholar 

  • Chen C-H, Yan S, Tseng C-H (2010) Inter-city bus scheduling for allied carriers. Transportmetrica 6(3):161–185

    Article  Google Scholar 

  • Chung BD, Yao T, Xie C, Thorsen A (2011) Robust optimization model for a dynamic network design problem under demand uncertainty. Netw Spat Econ 11(2):371–389

    Article  Google Scholar 

  • Chung BD, Yao T, Zhang B (2012) Dynamic traffic assignment under uncertainty: a distributional robust chance-constrained approach. Netw Spat Econ 12(1):167–181

    Article  Google Scholar 

  • DeMaio P (2009) Bicycle-sharing: history, impacts, models of provision, and future. J Public Transp 12(4):41–56

    Article  Google Scholar 

  • Dill J, Carr T (2003) Bicycle commuting and facilities in major US Cities: if you build them, commuters will use them. Transp Res Rec 1828:116–123

    Article  Google Scholar 

  • García-Palomares JC, Gutiérrez J, Latorre M (2012) Optimizing the location of stations in bike-sharing programs: a GIS approach. Appl Geogr 35(1–2):235–246

    Article  Google Scholar 

  • Hunt J, Abraham J (2007) Influences on bicycle use. Transportation 34:453–470

    Article  Google Scholar 

  • Li M, Gabriel SA, Shim Y, Azarm S (2011) Interval uncertainty-based robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning. Netw Spat Econ 11(1):159–191

    Article  Google Scholar 

  • Lin J-R, Yang T-H (2011) Strategic design of public bicycle sharing systems with service level constraints. Transp Res E 47(2):284–294

    Article  Google Scholar 

  • Lin J-R, Yang T-H, Chang Y-C (2013) A hub location inventory model for bicycle sharing system design: formulation and solution. Comput Ind Eng 65(1):77–86

    Google Scholar 

  • Lou Y, Yin Y, Lawphongpanich S (2009) Robust approach to discrete network design with demand uncertainty. Transp Res Rec 2090:86–94

    Article  Google Scholar 

  • Lu C-C (2012) Robust optimization approach for system optimal dynamic traffic assignment with demand uncertainty. J Chin Inst Ind Eng 29(2):136–147

    Google Scholar 

  • Lu C-C, Mahmassani HS, Zhou X (2009) Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem. Transp Res B 43(3):345–364

    Article  Google Scholar 

  • Martens K (2004) The bicycle as a feedering mode: experiences from three European countries. Transp Res D 9:281–294

    Article  Google Scholar 

  • Martens K (2007) Promoting bike-and-ride: the Dutch experience. Transp Res A 41(4):326–338

    Google Scholar 

  • Moudon A, Lee C, Cheadle A, Collier C, Johnson D, Schmid T (2005) Cycling and the built environment, a US perspective. Transp Res D 10:245–261

    Article  Google Scholar 

  • Petritsch TA, Landis BW, Huang HF, Challa SK (2006) Sidepath safety model – bicycle sidepath design factors affecting crash rates. Transp Res Rec 1982:194–201

    Article  Google Scholar 

  • Pucher J, Buehler R, Seinen M (2011) Bicycling renaissance in North American? An update and re-appraisal of cycling trends and policies. Transp Res A 45(6):451–475

    Google Scholar 

  • Sayarshad H, Tavassoli S, Zhao F (2012) A multi-periodic optimization formulation for bike planning and bike utilization. Appl Math Model 36(10):4944–4951

    Article  Google Scholar 

  • Shaheen S, Guzman S, Zhang H (2010) Bikesharing in Europe, the Americas, and Asia: past, present, and future. Transp Res Rec 2143:159–167

    Article  Google Scholar 

  • Sungur I, Ordonez F, Dessouky M (2008) A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. IIE Trans 40:509–523

    Article  Google Scholar 

  • Szeto WY, Wong SC (2012) Dynamic traffic assignment: model classifications and recent advances in travel choice principles. Central Eur J Eng Educ 2(1):1–18

    Google Scholar 

  • Tang C-H, Yan S, Chen Y-H (2008) An integrated model and solution algorithms for passenger, cargo, and combi flight scheduling. Transp Res E 44(6):1004–1024

    Article  Google Scholar 

  • Taylor D, Mahmassani H (1996) Analysis of state preferences for intermodal bicycle-transit interfaces. Transp Res Rec 1556:86–95

    Article  Google Scholar 

  • Vandenbulcke G, Dujardin C, Thomas I, de Geus B, Degraeuwe B, Meeusen R, Int Panis L (2011) Cycle commuting in Belgium: spatial determinants and re-cycling strategies. Transp Res A 45(2):118–137

    Google Scholar 

  • Wardman M, Tight M, Page M (2007) Factors influencing the propensity to cycle to work. Transp Res A 41:339–350

    Google Scholar 

  • Yan S, Tang C-H, Hou Y-Z (2011) Airport gate reassignments considering deterministic and stochastic flight departure/arrival times. J Adv Transp 45(4):304–320

    Article  Google Scholar 

  • Yao T, Mandala SR, Chung BD (2009) Evacuation transportation planning under uncertainty: a robust optimization approach. Netw Spat Econ 9(2):171–189

    Article  Google Scholar 

  • Yin Y, Madanat SM, Lu X (2009) Robust improvement schemes for road networks under demand uncertainty. Eur J Oper Res 198(2):470–479

    Article  Google Scholar 

Download references

Acknowledgments

This paper is based on a project (NSC 102-2410-H-027-011-MY3) sponsored by the National Science Council, Taiwan. The authors are grateful to three anonymous reviewers for many insightful and constructive comments and suggestions which help improve the quality of this paper. The authors are solely responsible for the content of this paper.

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  1. Graduate Institute of Information and Logistics Management, National Taipei University of Technology, Taipei City, 106, Taiwan

    Chung-Cheng Lu

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  1. Chung-Cheng Lu
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Correspondence to Chung-Cheng Lu.

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Lu, CC. Robust Multi-period Fleet Allocation Models for Bike-Sharing Systems. Netw Spat Econ 16, 61–82 (2016). https://doi.org/10.1007/s11067-013-9203-9

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