A note on a two-agent scheduling problem related to the total weighted late work

• Published in: Journal of combinatorial optimization Vol. 37; no. 3; pp. 989 - 999
• Main Authors: Zhang, Yuan, Yuan, Jinjiang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2019; Springer Nature B.V
• Subjects: Algorithms; Combinatorics; Convex and Discrete Geometry; Employment; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Polynomials; Production scheduling; Scheduling; Theory of Computation; Two-agent; Late work; Scheduling; Single machine
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-018-0337-z

We revisit a two-agent scheduling problem in which a set of jobs belonging to two agents A and B (without common jobs) will be processed on a single machine for minimizing the total weighted late work of agent A subject to the maximum cost of agent B being bounded. Zhang and Wang (J Comb Optim 33:945–955, 2017 ) studied three versions of the problem: (i) the A -jobs having a common due date, (ii) the A -jobs having a common processing time, (iii) the general version. The authors presented polynomial-time algorithms for the first two versions and a pseudo-polynomial-time algorithm for the last one. However, their algorithm for the first version is invalid. Then we show the NP-hardness and provide a pseudo-polynomial-time algorithm for the first version with the cost of agent B being makespan, present a polynomial-time algorithm for an extension of the second version, and show that the third version is solvable in pseudo-polynomial-time by a new technique.