Scheduling Jobs with Piecewise Linear Decreasing Processing Times
We study the problems of scheduling a set of nonpreemptive jobs on a single or multiple machines without idle times where the processing time of a job is a piecewise linear nonincreasing function of its start time. The objectives are the minimization of makespan and minimization of total job completion time. The single machine problems are proved to be NP-hard, and some properties of their optimal solutions are established. A pseudopolynomial time algorithm is constructed for makespan minimization. Several heuristics are derived for both total completion time and makespan minimization. Computational experiments are conducted to evaluate their efficiency. NP-hardness proofs and polynomial time algorithms are presented for some special cases of the parallel machine problems.
Naval Research Logistics
Cheng, T. C. E.; DING, Qing; Kovalyov, M.Y; Bachman, A.; and Janiak, A..
Scheduling Jobs with Piecewise Linear Decreasing Processing Times. (2003). Naval Research Logistics. 50, (6), 531-554. Research Collection Lee Kong Chian School Of Business.
Available at: http://ink.library.smu.edu.sg/lkcsb_research/870