# On the complexity of open shop scheduling with time lags

@article{Kubiak2021OnTC, title={On the complexity of open shop scheduling with time lags}, author={Wieslaw Kubiak}, journal={ArXiv}, year={2021}, volume={abs/2107.08102} }

The minimization of makespan in open shop with time lags has been shown NP-hard in the strong sense even for the case of two machines and unit-time operations. The minimization of total completion time however has remained open for that case though it has been shown NP-hard in the strong sense for weighted total completion time or for jobs with release dates. This note shows that the minimization of total completion time for two machines and unit-time operations is NP-hard in the strong sense… Expand

#### References

SHOWING 1-8 OF 8 REFERENCES

Minimizing Makespan in a Two-Machine Flow Shop with Delays and Unit-Time Operations is NP-Hard

- Mathematics, Computer Science
- J. Sched.
- 2004

It is shown that the problem of minimizing the makespan in a two-machine flow shop can be solved in O(n log n) time and that this is even the case if all processing times are equal to one. Expand

Two-machine open shop scheduling with special transportation times

- Computer Science
- J. Oper. Res. Soc.
- 1999

A linear time algorithm is presented that finds an optimal schedule if no transportation time exceeds the smallest of the processing times, and an algorithm is described that creates a heuristic solution to the problem with job-independent transportation times. Expand

Complexity Results for Flow-Shop and Open-Shop Scheduling Problems with Transportation Delays

- Computer Science
- Ann. Oper. Res.
- 2004

We consider shop problems with transportation delays where not only the jobs on the machines have to be scheduled, but also transportation of the jobs between the machines has to be taken into… Expand

A Heuristic for the Two-machine Open-shop Scheduling Problem with Transportation Times

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1999

This paper considers a problem of scheduling n jobs in a two-machine open shop to minimize the makespan and presents an algorithm that requires O (n log n) time and provides a worst-case performance ratio of 3 2. Expand

Scheduling with Time Lags

- Computer Science
- 2003

This thesis designs and analyzes algorithms for various on-line and off-line scheduling problems with time lags and shows that Polynomial-Time Approximation Schemes (PTAS) can be constructed under certain mild conditions and the fixed interval scheduling problem is solvable in polynomial time. Expand

The two-machine flow shop problem with delays and the one-machine total tardiness problem

- Computer Science
- 1996

This paper proves that the answer to the question whether the proper augmentation of a consistent partial order always results in a partial order which is also consistent is affirmative for the normal procedure, i.e., the procedure of proper augmentations beginning from "null". Expand

Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

- Computer Science, Mathematics
- 1977

The state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory are surveyed. Expand