<abstract><p>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.</p></abstract>
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(℘3) time, where ℘ is the number of jobs.
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