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This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integer programming formulation, this paper shows how good-quality lower and upper bounds can be computed. Numerical experiments are provided for assessing the proposed approach.

Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds