Single Machine Scheduling with Step-Deteriorating Processing Times
We study in this paper a scheduling model in which each task has a normal processing time which deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on problems with identical task deteriorating dates. We show that the flow time problem is NP-complete and suggest a pseudo-polynomial algorithm for the makespan problem. We also introduce a general method of solution, which facilitates the identification of solvable cases for some related problems. Finally, we provide a counter-example that invalidates the conjecture of optimality of a switching algorithm reported in the literature. Thus, we solve several unexplored or open problems and obtain a sharp boundary delineating the complexity of the considered problems.
European Journal of Operational Research
Cheng, T. C. E. and DING, Qing.
Single Machine Scheduling with Step-Deteriorating Processing Times. (2001). European Journal of Operational Research. 134, (3), 623-630. Research Collection Lee Kong Chian School Of Business.
Available at: http://ink.library.smu.edu.sg/lkcsb_research/872