Group scheduling and due date assignment on a single machine

We consider a single‐machine scheduling problem involving both the due date assignment and job scheduling under a group technology environment. The jobs (orders) of customers are classified into groups according to their production similarities in advance. To achieve production efficiency and save time/money resource, all jobs of the same group are required to be processed contiguously on the machine. A sequence‐independent setup time precedes the processing of each group. The due dates are assignable according to one of the following three due date assignment methods: FML‐CON, FML‐SLK and DIF, where FML‐CON means that all jobs within the same group are assigned a common due date, FML‐SLK means that all jobs within the same group are assigned an equal flow allowance, and DIF means that each job can be assigned a different due date with no restrictions. The goal is to determine an optimal combination of the due date assignment strategy and job schedule so as to minimize an objective function that includes earliness, tardiness, due date assignment and flow time costs. An $O(n\log n)$ time unified optimization algorithm is provided for all of the above three due date assignment methods.