Single machine scheduling with two competing agents and equal job processing times

• Published in: European journal of operational research Vol. 244; no. 1; pp. 86 - 99
• Main Authors: Oron, Daniel, Shabtay, Dvir, Steiner, George
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2015; Elsevier Sequoia S.A
• Subjects: Agency theory; Algorithms; Completion time; Complexity; Computation; Equal processing times; Job shops; Mathematical analysis; Mathematical models; Mathematical problems; Operational research; Operations research; Optimization; Optimization algorithms; Polynomials; Production scheduling; Scheduling; Single machine scheduling; Studies; Two competing agents; Equal processing times; Two competing agents; Single machine scheduling; Complexity
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2015.01.003

•The paper studies two agent scheduling models with unit processing times.•We provide comprehensive complexity results for many min-max and min-sum type scheduling objectives.•We provide polynomial and pseudo-polynomial time algorithms for the problems under consideration. We study various two-agent scheduling problems on a single machine with equal job processing times. The equal processing time assumption enables us to design new polynomial-time or faster-than-known optimization algorithms for many problems. We prove, however, that there exists a subset of problems for which the computational complexity remains NP-hard. The set of hard problems includes different variations where the objective functions of the two agents are either minimizing the weighted sum of completion times or the weighted number of tardy jobs. For these problems, we present pseudo-polynomial time algorithms.