Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration.

*(English)*Zbl 1145.90389Summary: 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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\textit{C. Low} et al., Comput. Math. Appl. 56, No. 1, 257--265 (2008; Zbl 1145.90389)

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