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Polyhedral results for position-based scheduling of chains on a single machine

Author

Listed:
  • Markó Horváth

    (Hungarian Academy of Sciences)

  • Tamás Kis

    (Hungarian Academy of Sciences)

Abstract

We consider a scheduling problem, where a set of unit-time jobs has to be sequenced on a single machine without any idle times between the jobs. Preemption of processing is not allowed. The processing cost of a job is determined by the position in the sequence, i.e., for each job and each position, there is an associated weight, and one has to determine a sequence of jobs which minimizes the total weight incurred by the positions of the jobs. In addition, the ordering of the jobs must satisfy the given chain-precedence constraints. In this paper we show that this problem is NP-hard even in a special case, where each chain consists of two jobs (2-chains). Further on, we study the polyhedron associated with the problem, and present a class of valid inequalities along with a polynomial-time separation procedure, and show that some of these inequalities are facet-defining in the special case of 2-chains. Finally, we present our computational results that confirm that separating these inequalities can significantly speed up a linear programming based branch-and-bound procedure to solve the problem with chains of two jobs.

Suggested Citation

  • Markó Horváth & Tamás Kis, 2020. "Polyhedral results for position-based scheduling of chains on a single machine," Annals of Operations Research, Springer, vol. 284(1), pages 283-322, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-019-03180-8
    DOI: 10.1007/s10479-019-03180-8
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    References listed on IDEAS

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