论文标题
切换的最高线性双偶双不平等：应用多产品处理网络的调度
Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks
论文作者
论文摘要
P时间事件图是离散的事件系统，适用于建模过程，其中必须在预定义的时间窗口中执行任务。它们的动力学可以由最大代数中的线性动力学不平等系统及其双重二元代数（最低代数）表示表示，称为最大 - 加上线性双重不平等（LDIS）。我们定义了一种称为Switched LDI（SLDIS）的新型模型，该模型允许在不同的操作模式之间切换每个模式，每种操作模式与LDI相对应，该模式的序列称为Schedule。在本文中，我们将重点放在时间表固定且周期性时对SLDIS的分析。我们表明，SLDIS可以对单重型多产品处理网络进行建模，其中每个产品都有不同的处理要求，并且对应于特定的操作方式。基于对SLDIS的分析，我们提出了一种算法来计算这些过程的最小周期时间和最大周期时间，以改善其他现有方法的时间复杂性。
P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by systems of linear dynamical inequalities in the max-plus algebra and its dual, the min-plus algebra, referred to as max-plus linear-dual inequalities (LDIs). We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operations, each corresponding to an LDI, according to an infinite sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the schedule is fixed and periodic. We show that SLDIs can model single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose an algorithm to compute minimum and maximum cycle times for these processes that improves the time complexity of other existing approaches.
