Approximation Results for Makespan Minimization with Budgeted Uncertainty

  • Marin BougeretEmail author
  • Klaus Jansen
  • Michael Poss
  • Lars Rohwedder
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11926)


We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to [3], once the schedule is defined an adversary can pick a scenario where deviation is added to some of the jobs’ processing times. Given only the maximal cardinality of these jobs, and the magnitude of potential deviation for each job, the goal is to optimize the worst-case scenario. We consider both the cases of identical and unrelated machines. Our main result is an EPTAS for the case of identical machines. We also provide a 3-approximation algorithm and an inapproximability ratio of \(2-\epsilon \) for the case of unrelated machines.


Makespan minimization Robust Optimization Approximation algorithms EPTAS Parallel machines Unrelated machines 


  1. 1.
    Aloulou, M.A., Croce, F.D.: Complexity of single machine scheduling problems under scenario-based uncertainty. Oper. Res. Lett. 36(3), 338–342 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Basu Roy, A., Bougeret, M., Goldberg, N., Poss, M.: Approximating robust bin packing with budgeted uncertainty. In: Friggstad, Z., Sack, J.-R., Salavatipour, M.R. (eds.) WADS 2019. LNCS, vol. 11646, pp. 71–84. Springer, Cham (2019). Scholar
  3. 3.
    Bertsimas, D., Sim, M.: Robust discrete optimization and network flows. Math. Program. 98(1–3), 49–71 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bougeret, M., Pessoa, A.A., Poss, M.: Robust scheduling with budgeted uncertainty. Discrete Appl. Math. 261, 93–107 (2019)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Daniels, R.L., Kouvelis, P.: Robust scheduling to hedge against processing time uncertainty in single-stage production. Manag. Sci. 41(2), 363–376 (1995)CrossRefGoogle Scholar
  7. 7.
    Jansen, K., Klein, K., Verschae, J.: Closing the gap for makespan scheduling via sparsification techniques. In: 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, 11–15 July 2016, Rome, Italy, pp. 72:1–72:13 (2016)Google Scholar
  8. 8.
    Jansen, K., Maack, M.: An EPTAS for scheduling on unrelated machines of few different types. Algorithms and Data Structures. LNCS, vol. 10389, pp. 497–508. Springer, Cham (2017). Scholar
  9. 9.
    Kasperski, A., Kurpisz, A., Zielinski, P.: Approximating a two-machine flow shop scheduling under discrete scenario uncertainty. Eur. J. Oper. Res. 217(1), 36–43 (2012)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kasperski, A., Kurpisz, A., Zieliński, P.: Parallel machine scheduling under uncertainty. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012. CCIS, vol. 300, pp. 74–83. Springer, Heidelberg (2012). Scholar
  11. 11.
    Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(1–3), 259–271 (1990)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Mastrolilli, M., Mutsanas, N., Svensson, O.: Approximating single machine scheduling with scenarios. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX/RANDOM -2008. LNCS, vol. 5171, pp. 153–164. Springer, Heidelberg (2008). Scholar
  13. 13.
    Tadayon, B., Smith, J.C.: Algorithms and complexity analysis for robust single-machine scheduling problems. J. Scheduling 18(6), 575–592 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Marin Bougeret
    • 2
    Email author
  • Klaus Jansen
    • 1
  • Michael Poss
    • 2
  • Lars Rohwedder
    • 1
  1. 1.Department of Computer ScienceKiel UniversityKielGermany
  2. 2.LIRMMUniversity of Montpellier, CNRSMontpellierFrance

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