Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
Sequencing with earliness and tardiness penalties: a review
Operations Research
An efficient algorithm for finding a maximum weight 2-independent set on interval graphs
Information Processing Letters
On the k-coloring of intervals
Discrete Applied Mathematics
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs
Computers and Operations Research
Maximizing Weighted number of Just-in-Time Jobs on Unrelated Parallel Machines
Journal of Scheduling
Maximizing the weighted number of just-in-time jobs in flow shop scheduling
Journal of Scheduling
Computers and Operations Research - Articles presented at the conference on routing and location (CORAL)
| Hi-index | 0.00 |
The problem of maximizing the weighted number of just-in-time jobs in a two-machine flow shop scheduling system is known to be $\mathcal {NP}$ -hard (Choi and Yoon in J. Shed. 10:237---243, 2007). However, the question of whether this problem is strongly or ordinarily $\mathcal{NP}$ -hard remains an open question. We provide a pseudo-polynomial time algorithm to solve this problem, proving that it is $\mathcal{NP}$ -hard in the ordinary sense. Moreover, we show how the pseudo-polynomial algorithm can be converted to a fully polynomial time approximation scheme (FPTAS). In addition, we prove that the same problem is strongly $\mathcal{NP}$ -hard for both a two-machine job shop scheduling system and a two-machine open shop scheduling system.