A note on the single machine CON and CONW problems with lot scheduling

We study extensions of the classical single machine common due-date (CON) and common due-window (CONW) assignment problems to the setting of lot scheduling. In the CON problem, all the jobs share a common due-date, and jobs completed prior to or after the due-date are penalized according to their earliness/tardiness. In CONW, there exists a time interval, such that jobs completed within this interval are not penalized. In both cases the due-date/due-window are decision variables. In lot scheduling, a number of customer orders of different sizes may be processed in the same lot. We allow order splitting between consecutive lots. The objective is to find the order allocation to lots, such that the total cost of earliness, tardiness and due-date/due-window is minimized. Given n orders, and under the very realistic assumption that the lot capacity is of the order of n, we introduce polynomial time dynamic programming algorithms for both extensions. Our numerical tests indicate that both algorithms can easily solve medium-size problems.