Optimal Due Date Assignment Without Restriction and Convex Resource Allocation in Group Technology Scheduling

Abstract

We consider a single machine group scheduling problem with convex resource allocation in which the scheduler decides optimal due dates for different jobs under a group technology environment. The jobs are classified into groups in advance due to their production similarities, and jobs in the same group are required to be processed consecutively, to achieve efficiency of high-volume production. The goal is to determine the optimal group sequence and job sequence within each group, together with a due date assignment strategy and resource allocation to minimize an objective function, which includes earliness, tardiness, due date assignment and resource allocation costs. The actual job processing times are resource dependent, and the due date assignment is without restriction, that is, it is allowed to assign different due dates to jobs within one group. We present structural results that characterize the optimal schedule in the case where the number of jobs in each group is identical and the cost $\psi _{ij}$ (the minimum of the due date assignment cost and the tardiness cost) for each job $J_{ij}$ is also identical, and present an $O(n\log n)$ time algorithm to solve this problem optimally.