A bi-objective model for the single-machine scheduling problem with rejection cost and total tardiness minimization

Résumé : We study the problem of scheduling jobs on a single machine with a rejection possibility, concurrently minimizing the total tardiness of the scheduled jobs and the total cost of the rejected ones. The model we consider is fully bi-objective, i.e. its aim is to enumerate the Pareto front. We tackle the problem both with and without the presence of hard deadlines. For the case without deadlines, we provide a pseudo-polynomial time algorithm, based on the dynamic program of [25], thereby proving that the problem is weakly NP-hard. For the case with deadlines, we propose a branch-and-bound algorithm and prove its efficiency by comparing it to an µ-constrained approach on benchmark instances based on those proposed in the literature on similar problems.
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Submitted on : Thursday, January 17, 2019 - 4:53:18 PM
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Roberto Cordone, Pierre Hosteins. A bi-objective model for the single-machine scheduling problem with rejection cost and total tardiness minimization. Computers and Operations Research, Elsevier, 2019, 102, pp130-140. ⟨10.1016/j.cor.2018.10.006⟩. ⟨hal-01985204⟩

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