In an Industry 4.0 Factory, physical entities such as humans, machines and materials are digitized into digital twins (DT) with smart IoT (Internet of Things) devices resulting in Cyber-Physical Production Systems (CPPS). Real-time data analytics builds up traceability and visibility, not only in the physical domain but also cyber space. This paper adds a new concept of cyber-physical inventory or simply meta-inventory to Industry 4.0 CPPS. In addition to physical items, their digital twins are considered as part of production inventory. Traceability and visibility enabled by digital twin can significantly reduce complexity and uncertainties (e.g. lead times and variability) while achieving resilience in case of major disturbances. The CPPS factory hedges the risks through meta-inventory without incurring cost for holding inventory digitally. After reflecting upon the developments of production inventory management corresponding to the evolutionary history of manufacturing systems to Industry 4.0, the paper presents the meta-inventory paradigm within a simple Industry 4.0 compliant supply chain. The factory, the supplier, and the transport implement a VMI (vendor-managed inventory) strategy. Two well-known basic EOQ (Economic Order Quantity) and EPQ (Economic Production Quantity or production Lot Sizing) problems are extended to demonstrate and quantify the impacts of using meta-inventory on the supply chain and the member enterprise. The analyses allow us to unfold key perspectives in more complex production and supply chain systems for further research.

在工业 4.0 工厂中，人、机器和材料等物理实体通过智能 IoT（物联网）设备数字化为数字孪生体 (DT)，从而形成网络物理生产系统 (CPPS)。实时数据分析不仅在物理领域而且在网络空间中都建立了可追溯性和可见性。本文为工业 4.0 CPPS 添加了网络物理库存或简单元库存的新概念。除了物理项目外，他们的数字双胞胎也被视为生产库存的一部分。数字孪生实现的可追溯性和可见性可以显着降低复杂性和不确定性（例如交货时间和可变性），同时在发生重大干扰时实现弹性。CPPS 工厂通过元库存对冲风险，而不会产生以数字方式持有库存的成本。在反思与制造系统向工业 4.0 的演化历史相对应的生产库存管理的发展之后，本文提出了一个简单的工业 4.0 兼容供应链中的元库存范例。工厂、供应商和运输部门实施 VMI（供应商管理库存）策略。扩展了两个著名的基本 EOQ（经济订单数量）和 EPQ（经济生产数量或生产批量）问题，以证明和量化使用元库存对供应链和成员企业的影响。这些分析使我们能够在更复杂的生产和供应链系统中展现关键观点，以供进一步研究。