Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties

Operations Research · 1993 · Volume 41 · Issue 4

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

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