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Algorithms 2018, 11(6), 80; https://doi.org/10.3390/a11060080

Scheduling a Single Machine with Primary and Secondary Objectives

Centro de Investigación en Ciencias, Universidad Autonoma del Estado de Morelos, 62210 Cuernavaca, Mexico
Received: 27 February 2018 / Revised: 30 May 2018 / Accepted: 31 May 2018 / Published: 5 June 2018
(This article belongs to the Special Issue Algorithms for Scheduling Problems)
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Abstract

We study a scheduling problem in which jobs with release times and due dates are to be processed on a single machine. With the primary objective to minimize the maximum job lateness, the problem is strongly NP-hard. We describe a general algorithmic scheme to minimize the maximum job lateness, with the secondary objective to minimize the maximum job completion time. The problem of finding the Pareto-optimal set of feasible solutions with these two objective criteria is strongly NP-hard. We give the dominance properties and conditions when the Pareto-optimal set can be formed in polynomial time. These properties, together with our general framework, provide the theoretical background, so that the basic framework can be expanded to (exponential-time) implicit enumeration algorithms and polynomial-time approximation algorithms (generating the Pareto sub-optimal frontier with a fair balance between the two objectives). Some available in the literature experimental results confirm the practical efficiency of the proposed framework. View Full-Text
Keywords: scheduling single machine; release time; lateness; makespan; bi-criteria scheduling; Pareto-optimal solution scheduling single machine; release time; lateness; makespan; bi-criteria scheduling; Pareto-optimal solution
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Vakhania, N. Scheduling a Single Machine with Primary and Secondary Objectives. Algorithms 2018, 11, 80.

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