On the multiple-machine extension to a common due-date assignment and scheduling problem

In a recent paper, Cheng considers the multiple-machine extension to a due-date assignment and scheduling problem. The paper implicitly assumes zero start times for all schedules (which does not ensure optimality), and overlooks the critical V-shape property for an optimal schedule (which leads to over-estimation of the effort needed to solve the problem). In this note, the authors correct these flaws, and also discuss the complexity of the problem and its special cases.