Classical Combinatorial and Single Machine Scheduling Problems with Opposite Optimality Criteria

by E.R. Gafarov, A.A. Lazarev, F. Werner


Preprint series: 10-11, Preprints

90B35 Scheduling theory, See also {68M20}
90C27 Combinatorial optimization
68Q25 Analysis of algorithms and problem complexity


Abstract; In this paper, we consider some scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. We present some complexity results for such maximization problems with classical objective functions (e.g. total tardiness, number of tardy jobs and total completion time) and various additional constraints (e.g. deadlines, weights and/or release dates of jobs may be given). As a generalization, we consider a classical combinatorial problem with an opposite optimization criterion, namely a minimization version of the knapsack problem, for which we give an NP-hardness proof and an exact pseudo-polynomial algorithm.

Keywords: Scheduling, Single machine problems, Scheduling maximization problems, Total tardiness, Number of tardy jobs, Knapsack minimization problem

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Letzte Änderung: 01.03.2018 - Ansprechpartner:

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