Scheduling deteriorating jobs subject to job or machine availability constraints

• Published in: European journal of operational research Vol. 180; no. 1; pp. 472 - 478
• Main Author: Gawiejnowicz, Stanisław
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2007; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Complexity theory; Deteriorating jobs; Exact sciences and technology; Job shops; Machinery; Operational research and scientific management; Operational research. Management science; Scheduling; Scheduling, sequencing; Studies; Scheduling; Deteriorating jobs; Complexity theory; Availability; Deadline; Task scheduling; Independent set; NP complete problem; Optimality criterion; Single machine; Workload; Completion time
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2006.04.021

We consider two problems of scheduling a set of independent, non-preemptable and proportionally deteriorating jobs on a single machine. In the first problem, the machine is not continuously available for processing but the number of non-availability periods, the start time and end time of each period are known in advance. In the second problem, the machine is available all the time but for each job a ready time and a deadline are defined. In both problems the criterion of schedule optimality is the maximum completion time. We show that the decision version of the first (the second) problem is NP-complete in the ordinary or in the strong sense, depending on the number of non-availability periods (the number of ready times and deadlines).