Ourari, SamiaYalaoui, Farouk2024-10-242024-10-2420241757-5850https://www.inderscienceonline.com/doi/abs/10.1504/IJMOR.2024.142135https://doi.org/10.1504/IJMOR.2024.142135https://dspace.univ-boumerdes.dz/handle/123456789/14537In 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.enDominance conditionsNested or perfect intervalsOptimality conditionScheduling rulesSingle-machine schedulingArticle