Maximum Flow of Complex Manufacturing Networks

Abstract With the advent of Industry 4.0, manufacturing lines have evolved from processing goods in a serial manner to doing so by means of cellular manufacturing. Furthermore, the use of ubiquitous radio-frequency identification tags and cyber-physical systems allow to seamlessly follow goods through the manufacturing plant. The data collected from these can easily be used to abstract manufacturing networks as a directed graph with workstations as nodes and material flows as edges. It is also possible to analyze manufacturing networks in the sense of "flow networks" in order to answer questions about material flows. In a flow network, materials with different levels of processing move through the system from a source (the raw materials storage room, for example) to a sink (like a warehouse for finished goods). Raw materials leave the source at some steady rate, and finished goods arrive to the sink at the same rate. Directed edges act as conduits for material with a stated capacity and vertices (workstations) act as junctions where material flows without accumulating. The present work aims at solving the following optimization problem: given a manufacturing flow network of known edge capacities, determine the theoretical maximum production rate that the network can attain under the assumptions of steady state flow and zero intermediate inventory levels. To accomplish this, the manufacturing network must be analyzed in terms of complex networks and graph theory and the results subsequently interpreted in terms of Operations Research. Finally, the method is illustrated with the analysis of the manufacturing network of an appliances manufacturer by determining the maximum theoretical production rate and the network bottleneck.