Comments on “Flow shop and open shop scheduling with a critical machine and two operations per job”

A recent paper addresses a flow-shop scheduling problem, where (i) each of the n jobs is limited to at most two operations, and (ii) one of these operations is common for all the jobs. The paper introduces a polynomial time solution algorithm for the problem, which appears to be surprisingly simple. Our short note contains several comments related to the correctness of the algorithm, to its complexity, to the proof of optimality and to a possible extension.