Common due window assignment in parallel processor scheduling problem with nonlinear penalty functions

In this paper we study a scheduling problem with earliness and tardiness penalties. The objective is to find a sequence of jobs on parallel identical processors and a common due window. The beginning and the end of the due window are decision variables but the size of the due window is constrained from above and below. A job incurs penalty if it completes before or after the due window. A penalty function is nonlinear and identical for all the jobs. In the considered problem we minimize the sum of earliness and tardiness penalties, due window location penalty and due window size penalty. We proved some properties of an optimal solution and constructed a pseudopolynomial time algorithm based on the dynamic programming method. We also established the computational complexity of the problem.