Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On the complexity of coupled-task scheduling
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Local search algorithms for a single-machine scheduling problem with positive and negative time-lags
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Minimizing Sum of Completion Times and Makespan in Master-Slave Systems
IEEE Transactions on Computers
Scheduling Algorithms
A new neighborhood and tabu search for the Blocking Job Shop
Discrete Applied Mathematics
Note: A note on scheduling identical coupled tasks in logarithmic time
Discrete Applied Mathematics
Scheduling of coupled tasks with unit processing times
Journal of Scheduling
Approximation algorithms for scheduling problems with exact delays
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Approximation algorithms for UET scheduling problems with exact delays
Operations Research Letters
One-machine generalized precedence constrained scheduling problems
Operations Research Letters
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Scheduling coupled-operation jobs with exact time-lags on a single machine has a wide range of applications. In that problem, each job consists of two operations with given processing times, which should be scheduled on a single machine observing a given time-lag. The general case of the problem with arbitrary processing times of operations and arbitrary time lags is known to be NP-hard in the strong sense and the problem remains NP-hard for many special cases. In order to develop a local search algorithm for the problem, we first explore two possible approaches for representing feasible solutions and their neighborhoods based on maintaining a permutation of first operations of the jobs or maintaining a full permutation of all operations. The first representation appears to be unpromising since, as we prove, the problem of finding an optimal sequence of second operations for a fixed sequence of first operations is NP-hard in the strong sense even in the case of unit processing times. We elaborate the second approach by developing a tabu search heuristic based on efficient job re-insertion. Empirical evaluation demonstrates superiority of the developed algorithm in comparison with the earlier published algorithms.