Application of the cumulative flow graph to the case of a parallel flow system based on stock quantity

In the area of materials stock-flow analysis, the cumulative graph is an effective method to visualize and analyze flow patterns and embedded problems, leading to identifying ways to improve material flows in production and service systems. However, since the conventional approach of cumulative flow graphs assumes a tandem flow shoptype one-way flow, the graph cannot be used in complicated flow patterns where each stage is comprised of parallel processes and materials flow back-and-forth between these stages. This paper proposes a method to apply a cumulative flow graph to the case of such parallel flow pattern, where a single stage is comprised of a main system and a subsystem, and materials repeatedly flow between these systems before finally flowing out from the process. For the purpose of identifying fundamental problems in the material flow, the method proposed focuses on depicting stock quantity in each system on the cumulative flow graph. The paper finally applies the method proposed to the actual case of a physical distribution system comprised of the main and secondary warehouses, and the validity of the method proposed is discussed and clarified using practical examples.