TY - JOUR

T1 - Scheduling two agents on a single machine

T2 - A parameterized analysis of NP-hard problems

AU - Hermelin, Danny

AU - Kubitza, Judith Madeleine

AU - Shabtay, Dvir

AU - Talmon, Nimrod

AU - Woeginger, Gerhard J.

N1 - Funding Information:
Danny Hermelin and Dvir Shabtay were supported by Grant no. 2016049 from the United States-Israel Binational Science Foundation (BSF). Danny Hermelin is also supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number 631163.11 and by the Israel Science Foundation (Grant no. 551145/14). Nimrod Talmon was supported by a postdoctoral fellowship from I-CORE ALGO. We would also like to thank both reviewers for their insightful comments on this paper, as these comments helped us to improve our work.
Publisher Copyright:
© 2018

PY - 2019/3/1

Y1 - 2019/3/1

N2 - Scheduling theory is a well-established area in combinatorial optimization, whereas the much younger area of parameterized complexity has only recently gained the attention of the scheduling community. Our aim is to bring these two fields closer together by studying the parameterized complexity of a class of two-agent single-machine scheduling problems. Our analysis focuses on the case where the number of jobs belonging to the second agent is considerably smaller than the number of jobs belonging to the first agent and thus can be considered as a fixed parameter k. We study a variety of combinations of scheduling criteria for the two agents and for each such combination we determine its parameterized complexity with respect to the parameter k. The scheduling criteria that we analyze include the total weighted completion time, the total weighted number of tardy jobs, and the total weighted number of just-in-time jobs. Our analysis determines the border between tractable and intractable variants of these problems.

AB - Scheduling theory is a well-established area in combinatorial optimization, whereas the much younger area of parameterized complexity has only recently gained the attention of the scheduling community. Our aim is to bring these two fields closer together by studying the parameterized complexity of a class of two-agent single-machine scheduling problems. Our analysis focuses on the case where the number of jobs belonging to the second agent is considerably smaller than the number of jobs belonging to the first agent and thus can be considered as a fixed parameter k. We study a variety of combinations of scheduling criteria for the two agents and for each such combination we determine its parameterized complexity with respect to the parameter k. The scheduling criteria that we analyze include the total weighted completion time, the total weighted number of tardy jobs, and the total weighted number of just-in-time jobs. Our analysis determines the border between tractable and intractable variants of these problems.

UR - http://www.scopus.com/inward/record.url?scp=85051056240&partnerID=8YFLogxK

U2 - 10.1016/j.omega.2018.08.001

DO - 10.1016/j.omega.2018.08.001

M3 - Article

AN - SCOPUS:85051056240

VL - 83

SP - 275

EP - 286

JO - Omega

JF - Omega

SN - 0305-0483

ER -