On the complexity of coupled-task scheduling
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Interleaving two-phased jobs on a single machine
Discrete Optimization
Minimizing Total Completion Time in Two-Machine Flow Shops with Exact Delays
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Minimizing total completion time in two-machine flow shops with exact delays
Computers and Operations Research
A 3/2-approximation for the proportionate two-machine flow shop scheduling with minimum delays
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Coupled-task scheduling on a single machine subject to a fixed-job-sequence
Computers and Industrial Engineering
Scheduling coupled-operation jobs with exact time-lags
Discrete Applied Mathematics
| Hi-index | 0.00 |
We give first constant-factor approximations for various cases of the coupled-task single machine and two-machine flow shop scheduling problems with exact delays and makespan as the objective function. In particular, we design 3.5- and 3-approximation algorithms for the general cases of the single-machine and the two-machine problems, respectively. We also prove that the existence of a (2−ε)-approximation algorithm for the single-machine problem as well as the existence of a (1.5−ε)-approximation algorithm for the two-machine problem implies P=NP. The inapproximability results are valid for the cases when the operations of each job have equal processing times and for these cases the approximation ratios achieved by our algorithms are very close to best possible: we prove that the single machine problem is approximable within a factor of 2.5 and the two-machine problem is approximable within a factor of 2.