Advertisement

Online Scheduling with Machine Cost and a Quadratic Objective Function

  • J. CsirikEmail author
  • Gy. Dósa
  • D. Kószó
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

We will consider a quadratic variant of online scheduling with machine cost. Here, we have a sequence of independent jobs with positive sizes. Jobs come one by one and we have to assign them irrevocably to a machine without any knowledge about additional jobs that may follow later on. Owing to this, the algorithm has no machine at first. When a job arrives, we have the option to purchase a new machine and the cost of purchasing a machine is a fixed constant. In previous studies, the objective was to minimize the sum of the makespan and the cost of the purchased machines. Now, we minimize the sum of squares of loads of the machines and the cost paid to purchase them and we will prove that 4/3 is a general lower bound. After this, we will present a 4/3-competitive algorithm with a detailed competitive analysis.

Keywords

Scheduling Online algorithms Analysis of algorithms 

References

  1. 1.
    Dósa, Gy., He, Y.: Better online algorithms for scheduling with machine cost. SIAM J. Comput. 33(5), 1035–1051 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Dósa, Gy., He, Y.: Scheduling with machine cost and rejection. J. Comb. Optim. 12(4), 337–350 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Dósa, Gy., Imreh, Cs.: The generalization of scheduling with machine cost. Theoret. Comput. Sci. 510, 102–110 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dósa, Gy., Tan, Z.: New upper and lower bounds for online scheduling with machine cost. Discrete Optim. 7(3), 125–135 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Han, S., Jiang, Y., Hu, J.: Online algorithms for scheduling with machine activation cost on two uniform machines. J. Zhejiang Univ.-Sci. A 8(1), 127–133 (2007)CrossRefGoogle Scholar
  6. 6.
    He, Y., Cai, S.: Semi-online scheduling with machine cost. J. Comput. Sci. Technol. 17(6), 781–787 (2002)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Imreh, Cs.: Online scheduling with general machine cost functions. Discrete Appl. Math. 157(9), 2070–2077 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Imreh, C., Noga, J.: Scheduling with machine cost. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds.) APPROX/RANDOM -1999. LNCS, vol. 1671, pp. 168–176. Springer, Heidelberg (1999).  https://doi.org/10.1007/978-3-540-48413-4_18CrossRefGoogle Scholar
  9. 9.
    Nagy-György, J., Imreh, Cs.: Online scheduling with machine cost and rejection. Discrete Appl. Math. 155(18), 2546–2554 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Szwarc, W., Mukhopadhyay, S.K.: Minimizing a quadratic cost function of waiting times in single-machine scheduling. J. Oper. Res. Soc. 46(6), 753–761 (1995)CrossRefGoogle Scholar
  11. 11.
    Townsend, W.: The single machine problem with quadratic penalty function of completion times: a branch-and-bound solution. Manage. Sci. 24(5), 530–534 (1978)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of SzegedSzegedHungary
  2. 2.Department of MathematicsUniversity of PannoniaVeszprémHungary

Personalised recommendations