Timed weighted marked graphs are a mathematical formalism suitable to model automated manufacturing systems in which synchronization and bulk services and arrivals appear, such as assembly lines and kanban systems. In this paper, we aim to develop practically efficient methods for the marking optimization of timed weighted marked graphs, a problem which consists in finding an initial resource assignment to minimize the cost of resources under a given requirement on the cycle time. Starting with a live initial marking, we first compute the critical places of a timed weighted marked graph by exploring an equivalent model called timed marked graph. Then, we develop an analytical method to identify the critical circuit of the system to which tokens will be iteratively added. Application to a real manufacturing system is finally provided, which shows that the developed approach is significantly more efficient than the existing ones.

中文翻译：

---

一种改进的时间加权标记图标记优化方法

定时加权标记图是一种数学形式，适用于对出现同步和批量服务和到达的自动化制造系统进行建模，例如装配线和看板系统。在本文中，我们的目标是开发用于时间加权标记图的标记优化的实用有效的方法，该问题包括寻找初始资源分配以在给定的循环时间要求下最小化资源成本。从实时初始标记开始，我们首先通过探索称为定时标记图的等效模型来计算定时加权标记图的关键位置。然后，我们开发了一种分析方法来识别将迭代添加令牌的系统的关键电路。最终提供了对实际制造系统的应用，