A note on "common due window scheduling"

Kramer and Lee recently addressed a common due window scheduling problem with earliness and tardiness penalties, where earliness and tardiness penalty factors are constant and the common window size is given. They showed that the problem is polynomial when the location of the due window is a decision variable. For the case where the location of the due window is given, the problem is also polynomial when the latest due date is greater than or equal to the makespan, and they proposed a pseudopolynomial dynamic programming algorithm to find an optimal schedule when the latest due date is less than the makespan. In this note we address the problem for the case where the location of the due window is given. Specifically, we show that the problem is polynomial if the window location is unrestricted, and present a more efficient dynamic program algorithm to optimally solve the problem if the window location is restricted. The concepts of unrestricted and restricted window locations are defined in this note.