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Inverse interval scheduling via reduction on a single machine

Author

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  • Yim, Seho
  • Hong, Sung-Pil
  • Park, Myoung-Ju
  • Chung, Yerim

Abstract

We consider an inverse counterpart of the interval scheduling problem. In the problem, we are given a set of machines and the objective is to reduce the non-preemptive job intervals with a least cost so that all jobs with positive processing times may be scheduled on the machines. The paper focuses on the single machine case. We establish the strong NP-hardness of the problem and show however it admits a polynomial time approximation scheme.

Suggested Citation

  • Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.
    • Handle: RePEc:eee:ejores:v:303:y:2022:i:2:p:541-549
    DOI: 10.1016/j.ejor.2022.02.046
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    References listed on IDEAS

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    1. Ilya Gertsbakh & Helman I. Stern, 1978. "Minimal Resources for Fixed and Variable Job Schedules," Operations Research, INFORMS, vol. 26(1), pages 68-85, February.
    2. Leo G. Kroon & Marc Salomon & Luk N. Van Wassenhove, 1997. "Exact and Approximation Algorithms for the Tactical Fixed Interval Scheduling Problem," Operations Research, INFORMS, vol. 45(4), pages 624-638, August.
    3. Chung, Yerim & Culus, Jean-François & Demange, Marc, 2015. "Inverse chromatic number problems in interval and permutation graphs," European Journal of Operational Research, Elsevier, vol. 243(3), pages 763-773.
    4. Dijkstra, Matthijs C. & Kroon, Leo G. & van Nunen, Jo A. E. E. & Salomon, Marc, 1991. "A DSS for capacity planning of aircraft maintenance personnel," International Journal of Production Economics, Elsevier, vol. 23(1-3), pages 69-78, October.
    5. T.C.E. Cheng & Zhi‐Long Chen & Chung‐Lun Li & B.M.‐T. Lin, 1998. "Scheduling to minimize the total compression and late costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 67-82, February.
    6. Julia Chuzhoy & Rafail Ostrovsky & Yuval Rabani, 2006. "Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 730-738, November.
    7. Janiak, Adam & Kovalyov, Mikhail Y. & Kubiak, Wieslaw & Werner, Frank, 2005. "Positive half-products and scheduling with controllable processing times," European Journal of Operational Research, Elsevier, vol. 165(2), pages 416-422, September.
    8. Matteo Fischetti & Silvano Martello & Paolo Toth, 1992. "Approximation Algorithms for Fixed Job Schedule Problems," Operations Research, INFORMS, vol. 40(1-supplem), pages 96-108, February.
    9. Chung-Yee Lee & Lei Lei, 2001. "Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases," Annals of Operations Research, Springer, vol. 102(1), pages 287-307, February.
    10. Kroon, Leo G. & Salomon, Marc & Van Wassenhove, Luk N., 1995. "Exact and approximation algorithms for the operational fixed interval scheduling problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 190-205, April.
    11. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    12. Kailiang Xu & Zuren Feng & Liangjun Ke, 2010. "A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates," Annals of Operations Research, Springer, vol. 181(1), pages 303-324, December.
    13. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    14. Michael W. Carter & Craig A. Tovey, 1992. "When Is the Classroom Assignment Problem Hard?," Operations Research, INFORMS, vol. 40(1-supplem), pages 28-39, February.
    15. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    16. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
    17. Du-Juan Wang & Yunqiang Yin & Mengqi Liu, 2016. "Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3691-3705, June.
    18. G. B. Dantzig & D. R. Fulkerson, 1954. "Minimizing the number of tankers to meet a fixed schedule," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(3), pages 217-222, September.
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