Categorical models for process planning.

Process plans provide a structure for 1) identifying the tasks involved in a given process, 2) the resources needed to accomplish them, and 3) a variety of relationships and constraints between these. This information guides important operational decisions across various organizational levels, from the factory floor to the global supply chain. Efficient use of this information requires a concrete analytical model that can be easily represented in digital form. In this paper we present a modeling framework for process plans based on a branch of mathematics called category theory (CT). Specifically, string diagrams provide an intuitive yet precise graphical syntax for describing symmetric monoidal categories (SMCs), mathematical structures which support serial and parallel composition. Ideal for process representation, these structures also support a powerful mathematical toolkit. Here we use these tools to analyze the relationship between different levels of abstraction in process planning hierarchy. Our goal in this paper is to provide a precise mathematical account of similarities across levels of process hierarchy; to relate high-level axiomatization of the relationships across levels and to provide sound theoretical foundations for manipulations across levels.