This paper investigates common (slack) due-date assignment single-machine scheduling with controllable processing times within a group technology environment. Under linear and convex resource allocation functions, the cost function minimizes scheduling (including the weighted sum of earliness, tardiness, and due-date assignment, where the weights are position-dependent) and resource-allocation costs. Given some optimal properties of the problem, if the size of jobs in each group is identical, the optimal group sequence can be obtained via an assignment problem. We then illustrate that the problem is polynomially solvable in $O\left({\wp }^3\right)$ time, where ℘ is the number of jobs.

This paper investigates the single-machine due-window assignment scheduling with truncated learning effects and past-sequence-dependent setup times simultaneously. The scheduler has the option of job-rejection, i.e., some jobs are processed and the other jobs are rejected. Under three (i.e., common, slack and different) due-window assignment methods, our goal is to minimize the sum of a general earliness-tardiness cost (i.e., the weighted sum of earliness-tardiness, number of early and tardy jobs, starting time and size of due-window) and a total rejection cost. Some optimal properties of the problem are provided, and we demonstrate that the problem is polynomially solvable.

This article investigates the due-window assignment scheduling problem with setup times on a single machine, where setup times of jobs are past-sequence-dependent. Under common, slack and unrestricted due-window assignment methods, the goal is to determine the optimal job sequence and due-window such that the cost function (i.e., the weighted sum of earliness and tardiness, number of early and tardy jobs, due-window starting time and size) is minimized. We solve the problem optimally by introducing a polynomial time algorithm. An extension to the problem with learning and deterioration effects is also studied.