Review of the P-graph Framework and its Applications

Abstract The P-graph framework was originally developed for solving Process Network Synthesis (PNS) problems in chemical plant design. Using axioms-based combinatorial tools, it reduces the optimization search space by orders of magnitude compared with direct superstructure optimization of the problem topology. P-graph tools also systematically generate maximal network structures, which eliminates human error in problem formulation. A key feature is the generation of a family of strategically n-best solutions, enabling engineers and managers to make informed decisions. During the five decades of development, the P-graph framework has been extended to solving PNS-like problems, i.e., network optimization problems beyond traditional industrial manufacturing that can be found in other domains, including energy networks, supply chains, regional resource planning, risk management, process scheduling, and business operations. This review paper provides a comprehensive analysis of developments in the P-graph framework since its inception. The benefits to researchers, engineers, and managers are evaluated, revealing the necessary improvements to provide effective tools for contemporary PNS and PNS-like problems. The important directions of future research are also discussed.