Steps towards scalability - Introducing a flow-based view on the scheduling problem

Recent developments in automation, digital twins, and artificial intelligence chal-lenge our understanding of efficient process design. However, modern automa-tion technology remains constrained by computational limits of existing schedulingmethods, which lack algorithms that scale while preserving acceptable accuracy.This work addresses that challenge by reframing the scheduling problem from a tra-ditional job-based perspective to a flow-based formulation. The proposed approachmodels the movement of resources rather than discrete, matrix-based job assign-ments, reducing computational complexity and enabling continuous-time schedul-ing. In addition, the work outlines adaptions of contemporary metaheuristic op-timization techniques - such as swarm search or genetic algorithms - to improveconvergence and scalability. Together, these contributions offer a foundation forfuture work on flow-based scheduling approaches , supporting next-generation au-tomated systems and the integration of digital twin systems.