Due to the emergence of the Internet of Things, supply chain control can increasingly be based on virtual objects instead of on the direct observation of physical objects. Object virtualization allows the decoupling of control activities from the handling and observing of physical products and resources. Moreover, virtual objects can be enriched with information that goes beyond human observation. This will allow for more advanced control capabilities, e.g. concerning tracking and tracing, quality monitoring and supply chain (re)planning. This paper proposes a control model for object virtualization in supply chain management, which is based on a multiple case study in the Dutch floriculture. It includes a typology of distinct mechanisms for object virtualization, which discerns reference objects and future projections next to the representation of real physical objects. The control model helps to define feasible redesign options for the virtualization of supply chain control. It is also of value as a basis to define the requirements for information systems that enable these redesign options.