A unified approach for single machine scheduling with position-dependent workloads and positional penalties

• Published in: SN applied sciences Vol. 2; no. 2; p. 214
• Main Author: Mor, Baruch
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2020; Springer Nature B.V
• Subjects: 3. Engineering (general); Algorithms; Applied and Technical Physics; Chemistry/Food Science; Earth Sciences; Engineering; Environment; Fines & penalties; Materials Science; Monotone functions; Research Article; Resource allocation; Resource consumption; Scheduling; Upper bounds; Workload; Workloads; Positional penalties; Position-dependent workloads; Convex resource allocation; Single machine scheduling
• ISSN: 2523-3963; 2523-3971
• DOI: 10.1007/s42452-020-1946-6

In this paper, we provide unified methods for solving scheduling problems with convex resource allocation , concentrating on objective functions that can be expressed as a scalar product of the actual processing times vector and a job-independent and position-dependent penalties vector. We assume general position - dependent workloads , i.e., the workloads are not restricted to be either monotone functions of the job positions or to specific functions. The first unified method focuses on minimizing a scheduling measure subject to a constraint on the resource consumption, whereas the second addresses the complementary problem of minimizing the consumed resource given an upper bound on the scheduling measure. For each unified approach, we provide a methodical analysis and consequently provide a O n 3 solution algorithm. Furthermore, to demonstrate the unified schemes, we solve several scheduling measures that involve earliness and tardiness penalties.