The recent notable focus on distributed production management in academic and industrial contexts has underscored the importance of scheduling across multiple factories. Accordingly, this study investigates a new multi-factory configuration in which non-identical factories produce different components of a final product in the first stage. Each factory is considered as a classical flow-shop, which can manufacture a unique component. These components are assembled into final products in the assembly factory, which is located in the second stage. Unlike other distributed scheduling problems, to determine a united production sequence in such a system, there is no need to find a suitable factory to assign a job since each factory is qualified for a particular task. In real-world applications, these systems encounter challenges that span from information architectures and negotiation mechanisms to the development of scheduling algorithms. The objective of this research is to schedule the jobs in each factory to minimize the makespan of the entire process. For this purpose, a mixed-integer programming model is developed to deal with small-size instances. Then, the lower bound is derived and incorporated to develop a branch and bound method. Furthermore, to deal with larger instances, five heuristic methods are developed, and the worst-case analysis is carried out. Computational experiments are conducted for different test classes to compare and to highlight the performance of the proposed solution procedures.

最近学术和工业领域对分布式生产管理的关注凸显了跨多个工厂调度的重要性。因此，本研究研究了一种新的多工厂配置，其中不同的工厂在第一阶段生产最终产品的不同组件。每个工厂都被视为经典的流水车间，可以制造独特的组件。这些部件在位于第二阶段的装配工厂组装成最终产品。与其他分布式调度问题不同，在这样的系统中确定统一的生产顺序，不需要找到合适的工厂来分配作业，因为每个工厂都有资格完成特定的任务。在实际应用中，这些系统遇到了从信息架构、协商机制到调度算法开发的挑战。这项研究的目的是安排每个工厂的工作，以尽量减少整个流程的完工时间。为此，开发了混合整数编程模型来处理小规模实例。然后，导出并合并下限以开发分支定界方法。此外，为了处理更大的情况，开发了五种启发式方法，并进行了最坏情况分析。针对不同的测试类别进行计算实验，以比较和突出所提出的解决方案程序的性能。