Open shop problems with unit time operations

@article{Brucker1993OpenSP,
  title={Open shop problems with unit time operations},
  author={Peter Brucker and Bernd Jurisch and Marion Jurisch},
  journal={Zeitschrift f{\"u}r Operations Research},
  year={1993},
  volume={37},
  pages={59-73}
}
We show that them-machine open shop problem in which all operations have unit processing times can be polynomially transformed to a special preemptive scheduling problem onm identical parallel machines. Many results published recently as well as some new results are derived by using this transformation. The new results include solutions of open problems mentioned in a recent paper by Kubiak et al. p]A similar relationship is derived between no-wait open shop problems with unit time operations… 
On unit time open shops with additional restrictions
We consider open shop problems with unit processing times,n jobs have to be processed onm machines. The order in which a given job is processed on the machines is not fixed. For each job a release
Polynomial time algorithms for special open shop problems with precedence constraints and unit processing times
TLDR
A polynomial time algorithm is given for the minimization of the makespan with a better worst case complexity than a previous algorithm known from the literature if the number of arcs is of linear order.
Scheduling Unit-Time Open Shops with Deadlines
TLDR
This work will give a polynomial algorithm to minimize the completion time of all jobs where a deadline is imposed for each job and apply this solution to give improved algorithms to minimizing the number of tardy jobs and the maximum lateness.
The complexity of mean flow time scheduling problems with release times
TLDR
This paper shows that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming, and shows that the problem is unary NP-hard.
Identical Parallel Machines Vs. Unit-Time Shops, Preemptions Vs. Chains, And Other Offsets In Schedu
This paper studies the complexity variations of scheduling problems in di erent machine environments when replacing operations with arbitrary processing times by the chains of operations with unit
On the Solution Region for Certain Scheduling Problems with Preemption *
The paper deals with parallel-machine and open-shop scheduling problems with preemptions and arbitrary nondecreasing objective function. An approach to describe the solution region for these problems
...
...

References

SHOWING 1-10 OF 31 REFERENCES
Unit Execution Time Shop Problems
TLDR
It is shown that the problem of constructing optimal mean finishing time preemptive and nonpreemptive schedules is NP-hard, even when all nonzero tasks have identical execution time requirements.
Scheduling Open Shops with Unit Execution Times to Minimize Functions of Due Dates
TLDR
This work develops polynomial algorithms to minimize the total tardiness and the number of tardy jobs in an open shop with identical processing time jobs.
A Fast Algorithm for Multiprocessor Scheduling of Unit-Length Jobs
An efficient polynomial time algorithm for the problem of scheduling n unit length jobs with rational release times and deadlines on m identical parallel machines is presented. By using
NP-Complete Scheduling Problems
Preemptive Scheduling of. Precedence-Constrained Jobs on Parallel Machines
Polynomial time-bounded algorithms are presented for solving three problems involving the preemptive scheduling of precedence-constrained jobs on parallel machines: the “intree problem”, the
Some simple scheduling algorithms
This paper considers situations in which jobs require only one operation on a single machine, or on one of a set of identical machines. Penalty‐free interruption is allowed. Some simple algorithms
A Note On The Complexity Of Openshop Scheduling Problems
AbstractWe investigate the complexity of openshop scheduling problems. A number of variations of the shop with different objective functions have been surveyed. The problem of minimizing mean flow
Parallel Sequencing and Assembly Line Problems
TLDR
This paper deals with a new sequencing problem in which n jobs with ordering restrictions have to be done by men of equal ability, and how to arrange a schedule that requires the minimum number of men to complete all jobs within a prescribed time T.
...
...