The increasing complexity of globalized manufacturing networks has led to the adoption of Computer-Integrated Manufacturing (CIM) as a strategic enabler of flexibility, responsiveness, and integration. However, the collaborative and distributed nature of multi-vendor environments introduces supervisory challenges related to interoperability, control heterogeneity, and real-time coordination. This study conceptualises a systems-oriented supervisory control model that addresses these challenges by integrating computational methods, including discrete-event modelling, multi-agent coordination, and knowledge-based supervisory frameworks. The model combines systems theory with computational abstractions to enable interoperability across heterogeneous vendor systems while ensuring robustness, scalability, and resilience. Validation is outlined through a hybrid simulation methodology combining discrete-event system simulation (DESS), Petri nets, and system dynamics for reflective analysis. The conceptual model provides a foundation for computational frameworks that support adaptive decision-making in collaborative CIM environments.