A note on scheduling jobs with missing operations in permutation flow shops

Flowshop scheduling problems are usually handled as permutation flowshops because of computational complexity although the technical framework in real-world problems often allows that jobs pass each other. Having a missing operation of a job on a machine, this job passing becomes a natural way to process jobs unless the underlying system is not an inflexible flow-line. However, when scheduling, missing operations are usually handled as zero processing time operations not allowing for any job passing. It is shown that even permitting job passing for missing operations while keeping the permutation constraint improves total completion time only under rather specific circumstances. We propose ‘partial permutation flowshop sequencing’ to overcome these specific formal requirements with respect to the real-world problem setting.