Abstract
AbstractWe study two $$\mathcal {NP}$$
NP
-hard single-machine scheduling problems with generalized due-dates. In such problems, due-dates are associated with positions in the job sequence rather than with jobs. Accordingly, the job that is assigned to position j in the job processing order (job sequence), is assigned with a predefined due-date, $$\delta _{j}$$
δ
j
. In the first problem, the objective consists of finding a job schedule that minimizes the maximal absolute lateness, while in the second problem, we aim to maximize the weighted number of jobs completed exactly at their due-date. Both problems are known to be strongly $$\mathcal {NP}$$
NP
-hard when the instance includes an arbitrary number of different due-dates. Our objective is to study the tractability of both problems with respect to the number of different due-dates in the instance, $$\nu _{d}$$
ν
d
. We show that both problems remain $$ \mathcal {NP}$$
NP
-hard even when $$\nu _{d}=2$$
ν
d
=
2
, and are solvable in pseudo-polynomial time when the value of $$\nu _{d}$$
ν
d
is upper bounded by a constant. To complement our results, we show that both problems are fixed parameterized tractable (FPT) when we combine the two parameters of number of different due-dates ($$\nu _{d}$$
ν
d
) and number of different processing times ($$\nu _{p}$$
ν
p
).
Publisher
Springer Science and Business Media LLC
Subject
Artificial Intelligence,Management Science and Operations Research,General Engineering,Software
Reference19 articles.
1. Browne, J., Dubois, D., Rathmill, K., Sethi, S. P., & Stecke, K. (1984). Classification of flexible manufacturing systems. The FMS Magazine, 2, 114–117.
2. Cheng, T. C. E. (1987). Minimizing the maximum deviation of job completion time about a common due-date. Computers and Mathematics with Applications, 14, 279–283.
3. Downey, R., & Fellows, M. (1999). Parameterized complexity. Springer.
4. Du, J., & Leung, J. Y. T. (1990). Minimizing total tardiness on one machine is NP-hard. Mathematics of Operations Research, 15, 483–495.
5. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability - a guide to the theory of NP completeness. Freeman.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献