The optimal and near-optimal enterprise-wide networks are designed, that,is synthesized, for supplying feedstocks and-distributing multiple products manufactured from these feedstocks in the process industry by resorting to the graph-theoretic method based on process graphs (P-graphs). Such feedstocks and products, conveyed through supply networks, are invariably materials for which the law of mass conservation is universally valid. Moreover, any of the actions applied to or exerted on a given feedstock or product, transiting through the supply networks, will induce a change in at least one of its attributes, thereby transforming the feedstock or product. Examples of the actions are loading, blending, pumping, tracking, unloading, subdividing, and/or wrapping; and those of the attributes are chemical composition, physical state, flow characteristics, external appearance, and/or location. Thus, in the broadest sense, any supply network can be regarded as a process network. The feedstocks and the products manufactured from them serve as the raw materials for and the products from the supply network at its entrance and exit, respectively. An operating, that is functional, unit can be unequivocally identified where any action is exerted on these raw materials or products. Naturally, the networks can be represented graph-theoretically as P-graphs. The proposed method is illustrated with an example involving three process plants, three markets, and three products under the three scenarios of coordination, cooperation, and competition. It has given rise simultaneously to the optimal as well as near-optimal supply networks in the ranked order. The example, formulated as the mixed integer linear programming problem, yields the same optimal solutions only, but not the near-optimal solutions in the ranked order.