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A formal modeling system intended for modeling the flow of parts, tools, information, and material on the factory floor is developed. The models are to be used as part of a generic control system for the factory floor, that is, a control system capable of controlling an arbitrary factory floor making an arbitrary mix of parts. The basic approach is to model a factory floor and process plans as "games" in which 1) there are pieces or, as they will be referred to, entities, 2) entities can be in contact with one aniother, and 3) the moves of the game correspond to changing the pattern of contacts. The game also allows an entity to be designated as a substructure of another entity. This allows a hierarchical decomposition of a model. The approach of the paper is in the spirit of first-order logic in the sense that a formal model is viewed as a structure or instantiation of a quasi first-order logical system.