Stochastic single machine scheduling with proportional job weights to minimize deviations of completion times from a common due date

• Published in: 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) Vol. 5; pp. 5124 - 5127 Vol.5
• Main Author: Chunfu Jia
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2003
• Subjects: Costs; Educational institutions; Electric breakdown; Information technology; Job shop scheduling; Manufacturing processes; Random variables; Single machine scheduling; Stochastic processes; Virtual manufacturing
• ISBN: 9780780379244; 0780379241
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2003.1272449

Deterministic single machine scheduling to minimize total weighted absolute deviations of job completion times from a common due date (abbreviated by TWD) is a typical scheduling model in just-in-time manufacturing environment, and it is NP-hard. However, LPT (largest processing time) job schedule is optimal for the case where jobs' weights are proportional to their processing times. In this paper, we consider the stochastic counterpart of the TWD problem with proportional weights, where the processing times are arbitrary positive random variables, while the common due date is an exponentially distributed random variable. The optimal solution of the problem is derived. Moreover, the case where the machine is subject to stochastic breakdowns is also discussed. It is shown that the results can be extended to the situation where the machine is subject to stochastic breakdowns when the counting process describing machine breakdowns is characterized by a Poisson process and the down times are independent identically distributed.