Determination of common due window location in a single machine scheduling problem

We consider the static deterministic single machine scheduling problem in which all jobs have a common due window. Jobs that are completed within the window incur no penalty. The objective is to find the optimal sequence and the optimal common due window location given that the due window size is a problem parameter such that the weighted sum of earliness. tardiness, and due window location penalties is minimized. We propose an O(n log n) algorithm to solve the problem. Me also consider two special cases For which simple solutions can be obtained.