A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work

• Published in: 4OR Vol. 21; no. 3; pp. 421 - 437
• Main Authors: Min, Yunhong, Choi, Byung-Cheon, Park, Myoung-Ju, Kim, Kyung Min
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023; Springer Nature B.V
• Subjects: Algorithms; Approximation; Business and Management; Dynamic programming; Employment; Genetic algorithms; Industrial and Production Engineering; Integer programming; Mathematical models; Maximization; Mixed integer; Operations research; Operations Research/Decision Theory; Optimization; Preempting; Research Paper; Scheduling; 68Q25; Branch and bound; 90C57; 90B35; Scheduling; Early work; Computational complexity
• ISSN: 1619-4500; 1614-2411
• DOI: 10.1007/s10288-022-00517-1

In scheduling with early work, jobs are assigned to a machine by maximizing the parts of non-preemptive jobs executed before their due dates. This paper considers a weighted early work maximization problem on parallel, identical machines with an antithetical property , which holds that w i ≤ w j implies d i ≥ d j for any two jobs i and j where w j and d j are weight and due date of job j , respectively. We show that the problem is weakly NP-hard. Due to the high complexity of dynamic programming, we develop three solution approaches: mixed-integer programming, heuristics, and a branch-and-bound algorithm. Through numerical experiments, we verify their performance.