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Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration. (English) Zbl 1145.90389
Summary: This article considers a single machine scheduling problem with an availability constraint under simple linear deterioration. The non-preemptive case is taken into account as well. The objective is to minimize the makespan in the system. The addressed problem is first described as a 0-1 integer programming model, and is then solved optimally. Subsequently, we prove that the addressed problem belongs to NP-hard. Thus, some heuristic algorithms based on the bin packing concepts are provided for solving the addressed problem. Computational results show that the proposed algorithm H3 performs well. In addition, a good strategy that sets the maintenance to start epoch when half the jobs have been already processed is suggested as well.

MSC:
90B35 Deterministic scheduling theory in operations research
90B25 Reliability, availability, maintenance, inspection in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90C10 Integer programming
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