This paper considers a single-machine due-window assignment scheduling problem with position-dependent weights, where the weights only depend on their position in a sequence. The objective is to minimise the total weighted penalty of earliness, tardiness, due-window starting time, and due-window size of all jobs. Optimal properties of the problem are given, and then, a polynomial-time algorithm is provided to solve the problem. An extension to the problem is offered by assuming general position-dependent processing time.

中文翻译：

---

具有位置相关权重的适当窗口分配计划的优化

本文考虑具有位置相关权重的单机到期窗口分配调度问题，其中权重仅取决于其在序列中的位置。目的是最大程度地减少所有工作的早期性，拖延性，到期窗口开始时间和到期窗口大小的总加权损失。给出了问题的最佳性质，然后提供了多项式时间算法来解决该问题。通过假定一般的位置相关处理时间，可以扩展该问题。