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.
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 : The International Journal of Management Science
JF - Omega : The International Journal of Management Science
SN - 0305-0483
ER -