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Stochastic single machine scheduling with quadratic early-tardy penalties. (English) Zbl 0782.90055
Summary: We address the problem of scheduling \(n\) jobs on a single machine, which is subject to random breakdowns, to minimize an expected sum of nonregular penalty functions. A simple recourse model is considered when the penalty function is the squared deviation of job completion times from a common due date, and a deterministic equivalent objective function is developed. Characterizations of optimal schedules for this quadratic objective function are established both when the common due date is a decision variable and when it is given and fixed. Most importantly, the \(V\)-shaped nature of optimal schedules is investigated for a class of Poisson processes, \(\{N(t), t>0\}\), describing the number of breakdowns in the interval \((0,t)\). In addition, relationships to a class of bicriteria models are demonstrated.

90B35 Deterministic scheduling theory in operations research
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