Two due date assignment problems with position-dependent processing time on a single-machine

The focus of this study is to analyze single-machine scheduling and due date assignment problems with position-dependent processing time. Two generally positional deterioration models and two frequent due date assignment methods are investigated. The objective functions include the cost of changing the due dates, the total cost of positional weight earliness, and the total cost of the discarded jobs that cannot be completed by their due dates. We conclude that the problems are polynomial time solvable. Significantly enough, after assessing the special case of each problem, this research found out that they can be optimally solved by lower order algorithms.