Competitive Algorithms for Demand Response Management in Smart Grid

  • Vincent Chau
  • Shengzhong Feng
  • Nguyen Kim Thang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)


We consider a scheduling problem which abstracts a model of demand-response management in Smart Grid. In the problem, there is a set of unrelated machines and each job j (representing a client demand) is characterized by a release date, and a power request function representing its request demand at specific times. Each machine has an energy power function and the energy cost incurred at a time depends on the load of the machine at that time. The goal is to find a non-migration schedule that minimizes the total energy (over all times).

We give a competitive algorithm for the problem in the online setting where the competitive ratio depends (only) on the power functions of machines. In the setting with typical energy function \(P(z) = z^{\nu }\), the algorithm is \(\varTheta (\nu ^{\nu })\)-competitive, which is optimal up to a constant factor. Our algorithm is robust in the sense that the guarantee holds for arbitrary request demands of clients. This enables flexibility on the choices of clients in shaping their demands — a desired property in Smart Grid.

We also consider a special case in offline setting in which jobs have unit processing time, constant power request and identical machines with energy function \(P(z) = z^{\nu }\). We present a \(2^{\nu }\)-approximation algorithm for this case.



We thank Prudence W. H. Wong for insightful discussions and anonymous reviewers for useful comments that helps to improve the presentation.


  1. 1.
    Albers, S.: Energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)CrossRefGoogle Scholar
  2. 2.
    Alford, R., Dean, M., Hoontrakul, P., Smith, P.: Power systems of the future: the case for energy storage, distributed generation, and microgrids. Zpryme Research & Consulting, Technical report (2012)Google Scholar
  3. 3.
    Azar, Y., Epstein, A.: Convex programming for scheduling unrelated parallel machines. In: Proceedings 37th Annual ACM Symposium on Theory of Computing, pp. 331–337 (2005)Google Scholar
  4. 4.
    Bell, P.C., Wong, P.W.H.: Multiprocessor speed scaling for jobs with arbitrary sizes and deadlines. J. Comb. Optim. 29(4), 739–749 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Burcea, M., Hon, W., Liu, H.H., Wong, P.W.H., Yau, D.K.Y.: Scheduling for electricity cost in a smart grid. J. Sched. 19(6), 687–699 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chen, C., Nagananda, K., Xiong, G., Kishore, S., Snyder, L.V.: A communication-based appliance scheduling scheme for consumer-premise energy management systems. IEEE Trans. Smart Grid 4(1), 56–65 (2013)CrossRefGoogle Scholar
  7. 7.
    Cohen, J., Dürr, C., Thang, N.K.: Smooth inequalities and equilibrium inefficiency in scheduling games. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 350–363. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  8. 8.
    Fang, K., Uhan, N.A., Zhao, F., Sutherland, J.W.: Scheduling on a single machine under time-of-use electricity tariffs. Ann. OR 238(1–2), 199–227 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Feng, X., Xu, Y., Zheng, F.: Online scheduling for electricity cost in smart grid. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, D.-Z. (eds.) COCOA 2015. LNCS, vol. 9486, pp. 783–793. Springer, Cham (2015). CrossRefGoogle Scholar
  10. 10.
    Hamilton, K., Gulhar, N.: Taking demand response to the next level. IEEE Power Energy Mag. 8(3), 60–65 (2010)CrossRefGoogle Scholar
  11. 11.
    Koutsopoulos, I., Tassiulas, L.: Control and optimization meet the smart power grid: scheduling of power demands for optimal energy management. In: e-Energy, pp. 41–50. ACM (2011)Google Scholar
  12. 12.
    Lenstra, J.K., Shmoys, D.B., Tardos, É.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(1), 259–271 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Liu, F., Liu, H.H., Wong, P.W.H.: Optimal nonpreemptive scheduling in a smart grid model. In: Proceedings 27th Symposium on Algorithms and Computation, vol. 64, pp. 53:1–53:13 (2016)Google Scholar
  14. 14.
    Liu, F., Liu, H.H., Wong, P.W.H.: Optimal nonpreemptive scheduling in a smart grid model. CoRR abs/1602.06659 (2016).
  15. 15.
    Lui, T.J., Stirling, W., Marcy, H.O.: Get smart. IEEE Power Energy Mag. 8(3), 66–78 (2010)CrossRefGoogle Scholar
  16. 16.
    Maharjan, S., Zhu, Q., Zhang, Y., Gjessing, S., Basar, T.: Dependable demand response management in the smart grid: a stackelberg game approach. IEEE Trans. Smart Grid 4(1), 120–132 (2013)CrossRefGoogle Scholar
  17. 17.
    Roughgarden, T.: Intrinsic robustness of the price of anarchy. J. ACM 62(5), 32 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Salinas, S., Li, M., Li, P.: Multi-objective optimal energy consumption scheduling in smart grids. IEEE Trans. Smart Grid 4(1), 341–348 (2013)CrossRefGoogle Scholar
  19. 19.
    Thang, N.K.: Online primal-dual algorithms with configuration linear programs. CoRR abs/1708.04903 (2017)Google Scholar
  20. 20.
    US Department of Energy: The smart grid: an introduction (2009).
  21. 21.
    Yao, F.F., Demers, A.J., Shenker, S.: A scheduling model for reduced CPU energy. In: FOCS, pp. 374–382. IEEE Computer Society (1995)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Vincent Chau
    • 1
  • Shengzhong Feng
    • 1
  • Nguyen Kim Thang
    • 2
  1. 1.Shenzhen Institutes of Advanced Technology, Academy of SciencesShenzhenChina
  2. 2.IBISCUniv Évry, Université Paris-SaclayÉvryFrance

Personalised recommendations