Optimal Control of a Two-Station Tandem Production/Inventory System

A manufacturing facility consisting of two stations in tandem operates in a maketo-stock mode: after production, items are placed in a finished goods inventory that services an exogenous demand. Demand that cannot be met from inventory is backordered. Each station is modelled as a queue with controllable production rate, and the problem is to control these rates to minimize inventory holding and backordering costs. Optimal controls are computed using dynamic programming and compared with kanban and buffer control mechanisms, popular in manufacturing, and with the base stock mechanism popular in inventory/distribution systems. Conditions are found under which certain simple controls are optimal using stochastic coupling arguments. Insights are gained into when to hold work-in-process and finished goods inventory, comparable to previous studies of production lines in make-to-order and unlimited demand ("push") environments.