New approximation algorithms for machine scheduling with rejection on single and parallel machine

• Published in: Journal of combinatorial optimization Vol. 40; no. 4; pp. 929 - 952
• Main Authors: Liu, Peihai, Lu, Xiwen
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2020; Springer Nature B.V
• Subjects: Algorithms; Approximation; Combinatorics; Completion time; Convex and Discrete Geometry; Fines & penalties; Job shops; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Rejection; Release dates; Scheduling; Theory of Computation; Rejection; Release date; Scheduling; Approximation algorithm; Worst-case ratio
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-020-00642-9

In this paper we consider three machine scheduling problems with the special feature that jobs may be rejected at a certain penalty. There are n jobs which are characterized by a release date, a processing time and a penalty. Each job is either accepted and then processed by one machine, or rejected and then a rejection penalty is paid. The objective is to minimize the maximum completion time of all accepted job plus the total penalties of all rejected jobs. When jobs have identical release dates, we present a ( 3 2 - 1 2 m )-approximation algorithm for the parallel machine problem. When jobs have general release dates, we propose a 4 3 -approximation algorithm for the single machine problem and a ( 1 + max { 0.618 , 1 - 1 m } )-approximation algorithm for the parallel machine problem, respectively.