Critical Demand in a Stochastic Model of Flows in Supply Networks

Supply networks are essential for modern production, yet their critical properties remain understudied. We present a stochastic model with random production capacities to analyze material flow to a root node, focusing on topology and buffer stocks. The critical demand, where unsatisfied demand diverges, is examined mostly through numerical simulations. Without stocks, minimal production dictates behavior, making topology irrelevant. With stocks, memory effects arise, making topology crucial. Increased local connectivity is beneficial: firms should favor broad, short supply chains over long, narrow ones.