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A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times

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  • Koulamas, Christos
  • Gupta, Sushil
  • Kyparisis, George J.

Abstract

We present a unified analysis for single-machine scheduling problems in which the actual job processing times are controlled by either a linear or a convex resource allocation function and also vary concurrently depending on either the job's position in the sequence and/or on the total processing time of the already processed jobs. We show that the problem is solvable in O(nlogn) time by using a weight-matching approach when a convex resource allocation function is in effect. In the case of a linear resource allocation function, we show that the problem can be solved in O(n3) time by using an assignment formulation. Our approach generalizes the solution approach for the corresponding problems with controllable job processing times to incorporate the variability of the job processing times stemming from either the job's position in the sequence and/or the total processing time of the already processed jobs.

Suggested Citation

  • Koulamas, Christos & Gupta, Sushil & Kyparisis, George J., 2010. "A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times," European Journal of Operational Research, Elsevier, vol. 205(2), pages 479-482, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:2:p:479-482
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    2. Grundel, Soesja & Çiftçi, Barış & Borm, Peter & Hamers, Herbert, 2013. "Family sequencing and cooperation," European Journal of Operational Research, Elsevier, vol. 226(3), pages 414-424.
    3. Oron, Daniel, 2016. "Scheduling controllable processing time jobs with position-dependent workloads," International Journal of Production Economics, Elsevier, vol. 173(C), pages 153-160.
    4. S.S. Panwalkar & Christos Koulamas, 2015. "On equivalence between the proportionate flow shop and single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 595-603, October.
    5. Yunqiang Yin & Du-Juan Wang & T C E Cheng & Chin-Chia Wu, 2016. "Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(9), pages 1169-1183, September.
    6. Qian, Jianbo & Steiner, George, 2013. "Fast algorithms for scheduling with learning effects and time-dependent processing times on a single machine," European Journal of Operational Research, Elsevier, vol. 225(3), pages 547-551.

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