An FPTAS for Minimizing the Weighted Number of Tardy Jobs with Group Due Date Assignment, Resource Allocation and Distribution planning in Supply Chain

In this paper, an integrated due date assignment, resource allocation (controllable processing times) and production and batch delivery scheduling problem for single customer in a "make to order" production system in supply chain has been surveyed. One manufacture received orders from one customer. The due date of orders is common and manufacture can assign the due dates with a related cost. The processing times of orders can be changed by amount of resource that is assigned to them. Orders must be process by one machine and send to customers by vehicles. Sending several jobs with one vehicle lead to less transportation cost but may increase the number of tardy jobs. The objective is determining the due dates, resource allocation and production and delivery scheduling so that the related costs is minimized. The problem is NP-hard. We present a dynamic programming (DP), an integer programming (IP) and a fully polynomial time approximation scheme (FPTAS) for this problem.