单机家族调度问题最优控制策略确定的基本引理
Fundamental lemmas for the determination of optimal control strategies for a class of single machine family scheduling problems
AI总结：
本文提出四个引理，为单机家族调度问题的最优控制策略确定提供理论基础，结合动态规划方法，通过两个实例展示引理的应用。
摘要：
本文技术报告提出了四个引理，这些引理构成了确定单机家族调度问题最优控制策略所需的理论基础。该调度问题具有序列依赖的批量设置和可调节的加工时间，并采用广义截止期模型。这些引理被应用于一种构造性过程中（由作者提出，基于动态规划的应用），允许根据系统状态确定最优解决调度问题的决策。技术报告包含两个完整的单机家族调度问题实例，旨在展示所提出方法中基本引理的应用。
英文摘要：
Four lemmas, which constitute the theoretical foundation necessary to determine optimal control strategies for a class of single machine family scheduling problems, are presented in this technical report. The scheduling problem is characterized by the presence of sequence-dependent batch setup and controllable processing times; moreover, the generalized due-date model is adopted in the problem. The lemmas are employed within a constructive procedure (proposed by the Author and based on the application of dynamic programming) that allows determining the decisions which optimally solve the scheduling problem as functions of the system state. Two complete examples of single machine family scheduling problem are included in the technical report with the aim of illustrating the application of the fundamental lemmas in the proposed approach.
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