A Generalized Framework for Scheduling of Printed Circuit Boards

这项研究致力于开发一种方法论，以解决电子制造中一个具有重大工业意义的问题。最重要的是认识到在两级和三级印刷电路板(PCB)组装系统中需要解决复杂的分组调度问题。它考虑了外部设置(套件)时间和内部(机器)设置时间之间的相互作用，以及机器运行(放置)时间与进位顺序相关性。为了满足不同印刷电路板制造商的运营需要，将考虑各种性能指标，即最大限度地减少完工时间、流动次数/加权流动次数之和和加权拖期之和。重点是开发真正反映实际运营约束的调度模型。将开发一种新的线性数学建模框架，该框架侧重于混合两种不同的建模范例：每组中电路板类型顺序的传统优先关系，以及？插槽？用于将每个插槽分配给一个板组。该模型虽然紧凑，但可能涉及大量的二元变量。为了克服这一困难，将使用基于分支和价格方法的机制来确定原始研究问题的有效下限，并将其用于搜索算法，以百分比偏差(PD)的形式评估其有效性。这项研究不仅将通过对复杂群体调度问题的研究来促进知识的进步，使整个行业受益，而且还将为各种印刷电路板制造商提供一种方法框架，以快速生成具有保证可量化性能的调度。寻求3%或更低的PD。除了方法论上的贡献，这项研究还将通过让研究生参与日程安排研究来培训和教育他们。这项研究的富有洞察力的研究成果将丰富生产计划与控制以及调度方面的研究生课程。

This research focuses on developing a methodology for solving a problem of significant industrial relevance in electronics manufacturing. Foremost is the realization of the need to solve complex group scheduling problems in two- and three-stage printed circuit board (PCB) assembly systems. It considers the interaction between external setup (kitting) times and internal (machine) setup times with carryover sequence dependency, along with machine run (placement) times. A variety of performance measures, namely the minimization of makespan, sum of the flow times/weighted flow times, and sum of the weighted tardiness will be considered to meet the operational needs of various PCB manufacturers. The emphasis is on the development of scheduling models that truly reflect real operational constraints. A novel, linear mathematical modeling framework that focuses on blending two different modeling paradigms will be developed: conventional precedence relationships for the sequence of board types in each group, and ?slots? for assigning each slot to a board group. The model, although compact, could involve a huge number of binary variables. To combat this difficulty, mechanisms based on branch and price methods will be used to identify an effective lower bound for the original research problem, which in turn will be used in the search algorithm to evaluate its effectiveness as a percentage deviation (PD). This research will not only advance the knowledge through research on complex group scheduling problems, benefiting industry at large, but will also provide various PCB manufacturers with a methodological framework for rapidly generating schedules with guaranteed quantifiable performance. A PD of 3 percent or below is sought. Apart from methodological contributions, this research will train and educate graduate students by engaging them in scheduling research. The insightful research findings from this research will enrich the graduate courses on production planning and control, and scheduling.