Identical coupled task scheduling: polynomial complexity of the cyclic case

Coupled tasks are two-operation tasks, where the two operations are separated by a time interval of fixed duration. Coupled task scheduling problems refer then to the scheduling of a set of coupled tasks on a single machine. Applications of these problems, reported in the literature, arise in connection with radar systems, robotic cells, and in manufacturing. Most of the complexity issues for scheduling coupled tasks have been settled. However, the complexity status has been unknown for the identical coupled task problem, where multiple copies of a single coupled task are to be processed. The purpose of the article is to solve this open problem in the cyclic case, for which we prove the polynomial complexity.

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