An Efficient Algorithm for Scheduling Problem with Batching and Common Due Window

Jobs share a common due window and belong to distinct families with sequence-independent setup tasks on a single machine. The window location and size are decision variables with linear penalties. Our objective is to find a schedule minimizing the sum of the weighted number of early and tardy jobs, together with the determination cost of the due window. Following several properties of an optimal schedule, a polynomial algorithm is firstly proposed and range it to P-problem.