This paper considers a single machine scheduling problem with preventive maintenance. In many cases, a machine must be maintained after it continuously works for a period of time. But most papers in the literature ignore non-availability of the machine. For this reason, this paper studies the problem of scheduling processing of jobs and maintenance of machine simultaneously. The objective is to minimise total completion time of jobs. The problem is proved to be NP-hard in the strong sense. Three heuristic algorithms and a branch and bound algorithm are proposed. Computational experiments are done to evaluate the effectiveness of the algorithms.

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In this paper, we present a strict bounded real lemma for linear time-varying systems in the infinite-horizon case. Using some operator methods, we show that the strict bounded realness for the related IrO operators is equivalent to the solvability of a semidefinite or definite Riccati equation. We also apply this result to the problem of disturbance attenuation and H -optimization. All our results

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