Pseudo-polynomial dynamic programming for an integrated due date assignment, resource allocation, production, and distribution scheduling model in supply chain scheduling

In this study, we consider an integrated due date assignment, production, and batch delivery scheduling problem with controllable processing times for multiple customers in a supply chain. The objective is to minimize the sum of the weighted number of tardy jobs as well as the due date assignment, resource allocation, and batch delivery costs. This model can also be applied when some parts of the jobs are outsourced. The problem is NP-hard. We propose a pseudo-polynomial dynamic programming algorithm to solve this problem, which shows that the problem is ordinary NP-hard. We performed computational tests to evaluate the proposed method.