Network Flow Modeling for Flexible Manufacturing Systems with Re-entrant Lines

A relaxed version of the process planning problem for flexible manufacturing systems/cells (FMS/FMC) and processing networks, such as flexible flow shops and general job shops, is formulated using a simple extension of multicommodity network flow problems. Our multistage multicommodity network formulation allows for simultaneous routing and resource allocation and also captures the case of re-entrant lines (recirculation). It can be used to perform rapid, albeit crude, explorations of the combinatorial space of possible configurations and failure scenarios. The technique can also provide bounds on the limits of system performance (eg: throughput, link usage, bottlenecks, etc). This can be used to guide the design of robust FMS architectures with high degree of redundancy in machines and routes, as demonstrated in numerical examples. Being a relaxation to the full discrete problem, our method could potentially be used as an admissible heuristic for pruning Al-based planning methods. We demonstrate our approach on a realistic industrial problem