Stochastic single machine scheduling with quadratic early-tardy penalties

Stochastic single machine scheduling with quadratic early-tardy penalties

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Article ID: iaor19941449
Country: United States
Volume: 41
Issue: 4
Start Page Number: 786
End Page Number: 795
Publication Date: Jul 1993
Journal: Operations Research
Authors: ,
Abstract:

The authors 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.

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