TY - JOUR
T1 - On the parameterized tractability of single machine scheduling with rejection
AU - Hermelin, Danny
AU - Pinedo, Michael
AU - Shabtay, Dvir
AU - Talmon, Nimrod
N1 - Funding Information:
This research was supported by Grant no. 2016049 from the United States-Israel Binational Science Foundation. The first author 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).
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/2/16
Y1 - 2019/2/16
N2 - In this paper we study a single machine scheduling problem with rejection. In such a scheduling problem, the scheduler can reject to process a job in the shop at a certain cost. Our objective is to minimize the total completion time of the jobs to be processed in the shop, given that the total rejection cost will not exceed a certain predefined threshold. The problem is known to be NP-hard, and to better investigate its hardness our objective is to study whether the problem becomes tractable when some specific natural parameters are of a limited size. The analysis is done by using the theory of parameterized complexity and includes the following parameters: the cardinality of the set of accepted jobs, the number of different processing times, the number of different rejection costs, the maximal processing time, and the maximal rejection cost. We show that the problem is W[1]-hard for the first parameter, while it is fixed-parameterized tractable for all other parameters.
AB - In this paper we study a single machine scheduling problem with rejection. In such a scheduling problem, the scheduler can reject to process a job in the shop at a certain cost. Our objective is to minimize the total completion time of the jobs to be processed in the shop, given that the total rejection cost will not exceed a certain predefined threshold. The problem is known to be NP-hard, and to better investigate its hardness our objective is to study whether the problem becomes tractable when some specific natural parameters are of a limited size. The analysis is done by using the theory of parameterized complexity and includes the following parameters: the cardinality of the set of accepted jobs, the number of different processing times, the number of different rejection costs, the maximal processing time, and the maximal rejection cost. We show that the problem is W[1]-hard for the first parameter, while it is fixed-parameterized tractable for all other parameters.
KW - Fixed-parameter tractability
KW - Parameterized complexity
KW - Scheduling with rejection
KW - Single machine scheduling
UR - http://www.scopus.com/inward/record.url?scp=85051501730&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2018.07.038
DO - 10.1016/j.ejor.2018.07.038
M3 - Article
AN - SCOPUS:85051501730
SN - 0377-2217
VL - 273
SP - 67
EP - 73
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 1
ER -