Advertisement

Minimizing Multimodular Functions and Allocating Capacity in Bike-Sharing Systems

  • Daniel Freund
  • Shane G. Henderson
  • David B. Shmoys
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)

Abstract

The growing popularity of bike-sharing systems around the world has motivated recent attention to models and algorithms for the effective operation of these systems. Most of this literature focuses on their daily operation for managing asymmetric demand. In this work, we consider the more strategic question of how to allocate dock-capacity in such systems. Our main result is a practically fast polynomial-time allocation algorithm to compute optimal solutions for this problem, that can also handle a number of practically motivated constraints, such as a limit on the number of docks moved from a given allocation. Our work further develops connections between bike-sharing models and the literature on discrete convex analysis and optimization.

Keywords

Allocation Algorithm Operational Constraint Submodular Function Citi Bike Increase Customer Satisfaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Altman, E., Gaujal, B., Hordijk, A.: Multimodularity, convexity, and optimization properties. Math. Oper. Res. 25(2), 324–347 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Capital Bikeshare: Bikeshare member survey report (2014)Google Scholar
  3. 3.
    Datner, S., Raviv, T., Tzur, M., Chemla, D.: Setting inventory levels in a bike sharing network (2015)Google Scholar
  4. 4.
    Forma, I.A., Raviv, T., Tzur, M.: A 3-step math heuristic for the static repositioning problem in bike-sharing systems. Transp. Res. Part B: Methodological 71, 230–247 (2015)CrossRefGoogle Scholar
  5. 5.
    Freund, D., Henderson, S.G., Shmoys, D.B.: Minimizing multimodular functions and allocating capacity in bike-sharing systems. arXiv preprint arXiv:1611.09304 (2016)
  6. 6.
    Freund, D., Norouzi-Fard, A., Paul, A., Henderson, S.G., Shmoys, D.B.: Data-driven rebalancing methods for bike-share systems, working paper (2016)Google Scholar
  7. 7.
    Hajek, B.: Extremal splittings of point processes. Math. Oper. Res. 10(4), 543–556 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ho, S.C., Szeto, W.: Solving a static repositioning problem in bike-sharing systems using iterated tabu search. Transp. Res. Part E: Logistics Transp. Rev. 69, 180–198 (2014)CrossRefGoogle Scholar
  9. 9.
    Jian, N., Freund, D., Wiberg, H.M., Henderson, S.G.: Simulation optimization for a large-scale bike-sharing system. In: Proceedings of the 2016 Winter Simulation Conference, pp. 602–613. IEEE Press (2016)Google Scholar
  10. 10.
    Jian, N., Henderson, S.G.: An introduction to simulation optimization. In: Proceedings of the 2015 Winter Simulation Conference, pp. 1780–1794. IEEE Press (2015)Google Scholar
  11. 11.
    Kaspi, M., Raviv, T., Tzur, M.: Bike-sharing systems: user dissatisfaction in the presence of unusable bicycles. IISE Trans. 49(2), 144–158 (2017). http://dx.doi.org/10.1080/0740817X.2016.1224960 CrossRefGoogle Scholar
  12. 12.
    Lee, Y.T., Sidford, A., Wong, S.C.W.: A faster cutting plane method and its implications for combinatorial and convex optimization. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 1049–1065. IEEE (2015)Google Scholar
  13. 13.
    Murota, K.: Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10. Society for Industrial and Applied Mathematics, Philadelphia (2003)CrossRefGoogle Scholar
  14. 14.
    Murota, K.: On steepest descent algorithms for discrete convex functions. SIAM J. Optim. 14(3), 699–707 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    O’Mahony, E.: Smarter Tools For (Citi) Bike Sharing. Ph.D. thesis, Cornell University (2015)Google Scholar
  16. 16.
    Parikh, P., Ukkusuri, S.V.: Estimation of optimal inventory levels at stations of a bicycle sharing system (2014)Google Scholar
  17. 17.
    Raviv, T., Kolka, O.: Optimal inventory management of a bike-sharing station. IIE Trans. 45(10), 1077–1093 (2013)CrossRefGoogle Scholar
  18. 18.
    Raviv, T., Tzur, M., Forma, I.A.: Static repositioning in a bike-sharing system: models and solution approaches. EURO J. Transp. Logistics 2(3), 187–229 (2013)CrossRefGoogle Scholar
  19. 19.
    Schuijbroek, J., Hampshire, R., van Hoeve, W.J.: Inventory rebalancing and vehicle routing in bike sharing systems. Eur. J. Oper. Res. 257, 992–1004 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Daniel Freund
    • 1
  • Shane G. Henderson
    • 1
  • David B. Shmoys
    • 1
  1. 1.Cornell UniversityIthacaUSA

Personalised recommendations