Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties

• Published in: Operations research Vol. 41; no. 4; pp. 786 - 796
• Main Authors: Mittenthal, John, Raghavachari, M
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.07.1993; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; Determinism; Exact sciences and technology; Functions; Job shops; Machinery; Mathematical models; Objective functions; Operational research and scientific management; Operational research. Management science; Operations research; Penalty function; Poisson process; Production scheduling; quadratic penalty functions; Random variables; Scheduling; Scheduling, sequencing; Sequencing; sequencing: early/tardy; Stochastic models; stochastic: random breakdown; Studies; Inhomogeneous process; Penalty function; Breakdown; Scheduling; Stochastic process; Poisson process; Machine
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.41.4.786

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.