While digital twins (DTs) have recently gained prominence as a viable option for creating reliable asset representations, many existing frameworks and architectures in the literature involve the integration of different technologies and paradigms, including the Internet of Things (IoTs), data modeling, and machine learning (ML). This complexity requires the orchestration of these different technologies, often resulting in subsystems and composition frameworks that are difficult to seamlessly align. In this paper, we present a scalable compositional framework designed for the development of a DT-based production management system (PMS) with advanced production monitoring capabilities. The conducted approach used to design the compositional framework utilizes the Factory Design and Improvement (FDI) methodology. Furthermore, the validation of our proposed framework is illustrated through a case study conducted in a phosphate screening station within the context of the mining industry.