A note on “Two-machine flow-shop scheduling with rejection” and its link with flow-shop scheduling and common due date assignment

In a recent paper by Shabtay and Gasper “Two-machine flow-shop scheduling with rejection, Computers and Operations Research”, forthcoming, doi:10.1016/j.cor.2011.05.023, several complexity and approximation results are proposed for a two-criteria two-machine flow-shop scheduling problem with rejection. The two criteria to be minimized are the makespan the total rejection cost. This note positions the contribution of such results with respect to the contributions of the literature on common due date assignment and flow-shop scheduling not considered in the work of Shabtay and Gasper.