Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties

John Mittenthal and M. Raghavachari
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John Mittenthal: Rensselaer Polytechnic Institute, Troy, New York
M. Raghavachari: Rensselaer Polytechnic Institute, Troy, New York

Operations Research, 1993, vol. 41, issue 4, 786-796

Abstract: 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.

Keywords: production/scheduling; sequencing: early/tardy; quadratic penalty functions; production/scheduling; stochastic: random breakdown (search for similar items in EconPapers)
Date: 1993
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