arXiv subjects

Michael L. Pinedo

Publications and source records attributed to Michael L. Pinedo.

2 recordsLinked to original sources

arXiv2026

New Complexity Results for Fair Repetitive Scheduling

We revisit the problem of finding fair solutions to repetitive scheduling problems with a single machine. In this problem, we are given a set of $n$ clients and a planning horizon consisting of $q$ periods (days). Each day, every client submits a single job that must be processed by the machine. The objective is to construct a set of $q$ schedules, one for each day, such that the quality of service (QoS) received by each client meets a predefined threshold. The QoS measure may be any standard scheduling criterion, such as the total waiting time or total completion time of a client's jobs over the entire planning horizon. This problem has been studied in the literature, with previous works providing complexity classifications and approximation algorithms for various QoS measures. Nevertheless, several important questions remain open. In this paper, we resolve three of these questions and identify several additional directions for future research.

cs.DS↗

arXiv2025

Minimizing the Number of Tardy Jobs and Maximal Tardiness on a Single Machine is NP-hard

This paper resolves a long-standing open question in bicriteria scheduling regarding the complexity of a single machine scheduling problem which combines the number of tardy jobs and the maximal tardiness criteria. We use the lexicographic approach with the maximal tardiness being the primary criterion. Accordingly, the objective is to find, among all solutions minimizing the maximal tardiness, the one which has the minimum number of tardy jobs. The complexity of this problem has been open for over thirty years, and has been known since then to be one of the most challenging open questions in multicriteria scheduling. We resolve this question by proving that the problem is strongly NP-hard. We also prove that the problem is at least weakly NP-hard when we switch roles between the two criteria (i.e., when the number of tardy jobs is the primary criterion). Finally, we provide hardness results for two other approaches (constraint and a priori approaches) to deal with these two criteria.

cs.DS↗