Energy-Aware Production Scheduling with Power-Saving Modes

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)


This study addresses optimization of production processes where machines have high energy consumption. One efficient way to reduce the energy expenses in production is to turn a machine off when it is not being used or switch it into an energy-saving mode. If the production has several machines and production demand that varies in time, the energy saving can be substantial; the cost reduction can be achieved by an appropriate production schedule that could control the switching between the energy modes with respect to the required production volume. Therefore, inspired by real production processes of glass tempering and steel hardening, this paper addresses the scheduling of jobs with release times and deadlines on parallel machines. The objective is to find a schedule of the jobs and a switching between the power modes of the machines so that the total energy consumption is minimized. Moreover, to further generalize the scheduling problem to other production processes, we assume that the processing time of the jobs is mode-dependent, i.e., the processing time of a job depends on the mode in which a machine is operating. The study provides an efficient Branch-and-Price algorithm and compares two approaches (based on Integer Linear Programming and Constraint Programming) for solving the subproblem.


Production scheduling Energy Branch-and-Price Integer Linear Programming Constraint Programming 



The work in this paper was supported by the Technology Agency of the Czech Republic under the Centre for Applied Cybernetics TE01020197, and partially by the Charles University, project GA UK No. 158216.


  1. 1.
    Mouzon, G., Yildirim, M.B., Twomey, J.: Operational methods for minimization of energy consumption of manufacturing equipment. Int. J. Prod. Res. 45(18–19), 4247–4271 (2007)CrossRefGoogle Scholar
  2. 2.
    Shrouf, F., Ordieres-Meré, J., García-Sánchez, A., Ortega-Mier, M.: Optimizing the production scheduling of a single machine to minimize total energy consumption costs. J. Cleaner Prod. 67(Suppl. C), 197–207 (2014)CrossRefGoogle Scholar
  3. 3.
    Gong, X., der Wee, M.V., Pessemier, T.D., Verbrugge, S., Colle, D., Martens, L., Joseph, W.: Integrating labor awareness to energy-efficient production scheduling under real-time electricity pricing: an empirical study. J. Cleaner Prod. 168(Suppl. C), 239–253 (2017)CrossRefGoogle Scholar
  4. 4.
    Ángel González, M., Oddi, A., Rasconi, R.: Multi-objective optimization in a job shop with energy costs through hybrid evolutionary techniques (2017)Google Scholar
  5. 5.
    Selmair, M., Claus, T., Trost, M., Bley, A., Herrmann, F.: Job shop scheduling with flexible energy prices. In: European Conference for Modelling and Simulation (2016)Google Scholar
  6. 6.
    Mitra, S., Sun, L., Grossmann, I.E.: Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices. Energy 54(Suppl. C), 194–211 (2013)CrossRefGoogle Scholar
  7. 7.
    Kong, F., Wang, Y., Deng, Q., Yi, W.: Minimizing multi-resource energy for real-time systems with discrete operation modes. In: 2010 22nd Euromicro Conference on Real-Time Systems, pp. 113–122, July 2010Google Scholar
  8. 8.
    Lenstra, J., Kan, A.R., Brucker, P.: Complexity of machine scheduling problems. In: Hammer, P., Johnson, E., Korte, B., Nemhauser, G. (eds.) Studies in Integer Programming. Annals of Discrete Mathematics, vol. 1, pp. 343–362. Elsevier (1977)CrossRefGoogle Scholar
  9. 9.
    Feillet, D.: A tutorial on column generation and branch-and-price for vehicle routing problems. 4OR 8(4), 407–424 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Desrosiers, J., Lübbecke, M.E.: A primer in column generation. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds.) Column Generation, pp. 1–32. Springer, Boston (2005). Scholar
  11. 11.
    Vilím, P., Barták, R., Čepek, O.: Extension of o (n log n) filtering algorithms for the unary resource constraint to optional activities. Constraints 10(4), 403–425 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Laborie, P., Rogerie, J., Shaw, P., Vilím, P.: Reasoning with conditional time-intervals. Part II: an algebraical model for resources. In: FLAIRS conference, pp. 201–206 (2009)Google Scholar
  13. 13.
    Václavík, R., Novák, A., Šůcha, P., Hanzálek, Z.: Accelerating the branch-and-price algorithm using machine learning. Eur. J. Oper. Res. (2017). under reviewGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Czech Technical University in PraguePragueCzech Republic
  2. 2.Charles UniversityPragueCzech Republic

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