In this paper, we consider due-window assignment scheduling in the proportionate flow shop setting with position-dependent weights where the weights depend on the position in which a job is scheduled. Under the common due-window (CONW) and slack due-window (SLKW) assignment methods, the location of the window and its properties are established. The objective is to determine the sequence of all jobs to minimize the total weighted cost function where the total weighted cost function must also consider the window start time and size. Based on these considerations, the corresponding algorithm and algorithm complexity are proposed.

中文翻译：

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比例流水车间设置中的到期窗口分配调度

在本文中，我们考虑在具有位置相关权重的成比例流水车间设置中的到期窗口分配调度，其中权重取决于调度作业的位置。在常见的到期窗口（CONW）和松弛到期窗口（SLKW）分配方法下，窗口的位置及其属性被建立。目标是确定所有作业的顺序以最小化总加权成本函数，其中总加权成本函数还必须考虑窗口开始时间和大小。基于这些考虑，提出了相应的算法和算法复杂度。