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New conditions of dominance and optimality for single-machine scheduling problems with nested execution intervals

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  • Samia Ourari
  • Farouk Yalaoui

Abstract

In this paper, we consider the problem of scheduling a set of n + 1 jobs on a single disjunctive machine. Each job has a fixed processing time and a temporal execution interval. Pre-emption is not allowed. Temporal execution intervals are assumed to have a perfect pyramidal structure, i.e., the execution intervals of the jobs are nested within each other, or none two of them are contained within each other. The objective is to find a feasible sequence that minimises the maximum lateness under some particular constraints. In order to do so, new dominance properties under known necessary and sufficient conditions are established, and optimality conditions of certain job sequences are given.

Suggested Citation

  • Samia Ourari & Farouk Yalaoui, 2024. "New conditions of dominance and optimality for single-machine scheduling problems with nested execution intervals," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 29(2), pages 191-213.
    • Handle: RePEc:ids:ijmore:v:29:y:2024:i:2:p:191-213
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