Single-machine scheduling with deteriorating jobs

Abstract

In this article, we study a single-machine scheduling problem in which the processing time of a job is a nonlinear function of its basic processing time and starting time. The objectives are to minimise the makespan, the sum of weighted completion times and the sum of the kth powers of completion times. We show that the makespan minimisation problem can be solved in polynomial time. However, the total completion time and the sum of the kth powers of completion times minimisation problems can be solved in polynomial time in some cases. Besides, some useful properties are also provided for the sum of weighted completion times problem under certain conditions.

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

“…And extensive surveys of research related to scheduling deteriorating jobs were provided by Alidaee and Womer (1999), and Cheng, Ding, and Lin (2004). More recent papers which have considered scheduling with deteriorating jobs include He (2009), Li, Li, Sun, andXu (2009), Lee, Shiau, Chen, and Wu (2010), Kuo and Yang (2010) and Zhao and Tang (2010). We refer the reader to book Gawiejnowicz's (2008) book for more details on scheduling problems with time-dependent processing times.…”