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

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 33:94...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-018-0337-z