Optimization for Due-Date Assignment Single-Machine Scheduling under Group Technology

Abstract

In this paper, the single-machine scheduling problem is studied by simultaneously considering due-date assignment and group technology (GT). The objective is to determine the optimal sequence of groups and jobs within groups and optimal due-date assignment to minimize the weighted sum of the absolute value in lateness and due-date assignment cost, where the weights are position dependent. For the common (CON) due-date assignment, slack (SLK) due-date assignment, and different (DIF) due-date assignment, an $O\left(n\log n\right)$ time algorithm is proposed, respectively, to solve the problem, where $n$ is the number of jobs.