Scheduling Start Time Dependent Tasks with Deadlines and Identical Initial Processing Times on a Single Machine

• Main Authors: Cheng, T. C. E., DING, Qing
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: Sequencing; Time dependence scheduling; Computational complexity; Business
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/871; https://doi.org/10.1016/s0305-0548(01)00077-6
• Institution: Singapore Management University

In this paper, we study the feasibility problem of scheduling a set of start time dependent tasks on a single machine with deadlines, processing rates and identical initial processing times. First, we show that the cases with arbitrary deadlines are strongly NP-complete. Second, we show that the cases with two distinct deadlines are NP-complete in the ordinary sense. Finally, we give an optimal polynomial algorithm for the makespan problem with two distinct processing rates. We solve a series of open problems in the literature and give a sharp boundary delineating the complexity of the problems.