FPTAS for the non-resumable two-machine open-shop problem

Determine whether the two-machine open-shop scheduling problem with a single fixed machine-unavailability interval in the non-resumable setting admits a fully polynomial-time approximation scheme (FPTAS).

Background

The paper establishes the first FPTAS for the resumable two-machine open-shop scheduling problem with a single fixed unavailability interval, where an operation interrupted by the interval may resume without penalty. The non-resumable variant instead requires an interrupted operation to restart from the beginning. Although approximation results, including a PTAS, are known for the non-resumable setting, the paper leaves unresolved whether an FPTAS exists for that problem.

This question is identified as a direction for future work after the paper’s seven-dimensional pseudo-polynomial dynamic program and FPTAS construction for the resumable variant.