On the Assignment of Optimal Due Dates

In a recent paper, Quaddus presents a linear programming analysis for assigning an optimal due date to n independent jobs. The criterion treated in the model is the minimization of total penalty cost, where, for each job, penalties are assessed on earliness, tardiness and due-date allowance. Quaddus considers job-dependent penalties, thereby generalizing models addressed by other authors, but neglects the sequencing aspect of the problem. As a consequence, the examples are not completely optimized. In this note we offer an alternative proof of the Quaddus result, without relying on duality theory, and we show how Quaddus' examples fall short of optimizing the total penalty.