The goal is to determine multiple common durations for all jobs as well as an optimal scheduling sequence for the jobs that minimizes the weighted sum of the earliness penalties, lateness penalties, and common due date assignments. The matching process of position weight and processing time is used to obtain the optimal solution. This problem can be solved when the number of jobs assigned to the common due date is given a constant. The problem is polynomially solvable and a specific solution algorithm is given.