Decentralized multi-product multi-stage systems with backorders

A multi-stage production/inventory system with decentralized two-card kanban control policies producing multiple product types is considered. The system involves one-at-a-time processing at each stage, finite target levels in the buffers and batch transfers between production stages. The demand process for each product is assumed to be Poisson and excess demand is backordered. Products have a priority structure and the processor at each stage is shared according to a switching rule. Our objective is to obtain steady-state performance measures such as the average inventory and service levels for each product type. We propose an approximation algorithm based on: (i) characterization of the delay by a product type before receiving the processor's attention at each stage; and (ii) creation of subsystems for all the storage activity and phase-type modeling of the remaining system's behavior. Numerical examples are presented to show the accuracy of the method and its potential use in system design.