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Single-machine scheduling to minimize a function of two or three maximum cost criteria. (English) Zbl 0857.68012
Summary: We consider the problem of scheduling \(n\) jobs on a single machine that is continuously available from time zero onward and that can handle no more than one job at a time. Each job requires processing during a given positive uninterrupted time. The cost of each job is measured by \(K\) \((K = 2,3)\) nondecreasing penalty functions; the quality of a schedule is computed on the basis of \(K\) performance criteria, the \(k\)th one being given by the maximum value of the \(k\)th penalty function over all jobs. We wish to minimize an objective function that is a nondecreasing function of these \(K\) performance criteria. We present a polynomial algorithm for both problems and we show that these can also be used if precedence constraints exist between the jobs or if all penalty functions are nonincreasing in the job completion times.

68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
68W10 Parallel algorithms in computer science
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