A mesoscopic approach to the simulation of semiconductor supply chains

Production flows through factories are modeled through conservation laws leading to nonlinear hyperbolic partial differential equations (PDEs). For a linear production line, models based on conservation laws can be derived from first principles, using methods from gas dynamics. For reentrant manufacturing, a heuristic model is presented merging a nonlocal state equation relating throughput time to work in progress through Little's law to produce a nonlinear, nonlocal hyperbolic PDE. These two models can serve as the building blocks of fast simulations of the dynamics of capacity-limited supply chains. The authors present simulations for a chain consisting of a reentrant module, followed and preceded by a linear module. The response of the system to various production scenarios is discussed.