The convergence of the Internet of Things (IoT) and Business Process Management (BPM) in cyber-physical systems highlights a critical limitation in current standards: the inability to effectively model and manage the operational lifecycle of physical resources. Standard BPMN lacks native constructs to differentiate between consumable materials, reusable tools, and generic data in the form of DataObjects, creating a digital-physical divide that hinders execution support and process transparency. This paper addresses this gap by presenting PRiME, a comprehensive and executable BPMN extension developed following the Design Science Research methodology. PRiME provides explicit constructs to model passive resource requirements, inventories, and physical flows while distinguishing between fungible materials and specific tool instances. The extension is validated through a prototype, demonstrating two key capabilities: providing runtime operational support through automated resource checklists and shortage alerts, and enabling analysis through a design-time visualization of material flows. This concept helps bridge the gap between digital process models and physical resource orchestration, fostering a more holistic BPM that enables the support of manual tasks in cyber-physical environments.