Setting Base Stock Levels Using Product-Form Queueing Networks

A manufacturing facility produces multiple products in a make-to-stock manner, and unsatisfied demand is backordered. A simple production control policy is analyzed: When the amount of work-in-process inventory plus finished goods inventory for a particular product falls below a base stock level, then release another unit of that product onto the shop floor. Assuming that the work-in-process inventory has a steady state distribution and that there are different costs incurred for carrying in-process, completed and backordered units, we show that the cost minimizing base stock level for each product is a critical fractile of the steady state distribution of the product's total work-in-process inventory. By exploiting the relationship between the make-to-stock system and an open queueing network, we identify specific formulas for the base stock levels under standard product-form assumptions. For the lost sales case, a similar relation to a closed queueing network can be used to characterize the optimal control parameters.