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A scheduling problem with job values given as a power function of their completion times

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  • Janiak, Adam
  • Krysiak, Tomasz
  • Pappis, Costas P.
  • Voutsinas, Theodore G.

Abstract

This paper deals with a problem of scheduling jobs on the identical parallel machines, where job values are given as a power function of the job completion times. Minimization of the total loss of job values is considered as a criterion. We establish the computational complexity of the problem - strong NP-hardness of its general version and NP-hardness of its single machine case. Moreover, we solve some special cases of the problem in polynomial time. Finally, we construct and experimentally test branch and bound algorithm (along with some elimination properties improving its efficiency) and several heuristic algorithms for the general case of the problem.

Suggested Citation

  • Janiak, Adam & Krysiak, Tomasz & Pappis, Costas P. & Voutsinas, Theodore G., 2009. "A scheduling problem with job values given as a power function of their completion times," European Journal of Operational Research, Elsevier, vol. 193(3), pages 836-848, March.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:3:p:836-848
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    References listed on IDEAS

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    1. M.I. Dessouky & B.J. Lageweg & J.K. Lenstra & S.L. van de Velde, 1990. "Scheduling identical jobs on uniform parallel machines," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(3), pages 115-123, September.
    2. Wlodzimierz Szwarc & Marc E. Posner & John J. Liu, 1988. "The Single Machine Problem with a Quadratic Cost Function of Completion Times," Management Science, INFORMS, vol. 34(12), pages 1480-1488, December.
    3. Voutsinas, Theodore G. & Pappis, Costas P., 2002. "Scheduling jobs with values exponentially deteriorating over time," International Journal of Production Economics, Elsevier, vol. 79(3), pages 163-169, October.
    4. Federico Della Croce & Wlodzimierz Szwarc & Roberto Tadei & Paolo Baracco & Raffaele di Tullio, 1995. "Minimizing the weighted sum of quadratic completion times on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1263-1270, December.
    5. Bachman, Aleksander & Janiak, Adam, 2000. "Minimizing maximum lateness under linear deterioration," European Journal of Operational Research, Elsevier, vol. 126(3), pages 557-566, November.
    6. W. Townsend, 1978. "The Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch-and-Bound Solution," Management Science, INFORMS, vol. 24(5), pages 530-534, January.
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    Cited by:

    1. Nikos P. Rachaniotis & Theodore G. Voutsinas & Costas P. Pappis, 2013. "Scheduling periodic preventive maintenance with a single server in a finite horizon," International Journal of Decision Sciences, Risk and Management, Inderscience Enterprises Ltd, vol. 5(1), pages 80-87.
    2. Janiak, Adam & Krysiak, Tomasz, 2012. "Scheduling jobs with values dependent on their completion times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 231-241.

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