Managing capacity and inventory jointly for multi-server make-to-stock queues

Motivated by practices in modern supply chains, we consider capacity-inventory joint management for a make-to-stock manufacturing system operating under a base stock policy. The production facility is modeled as multiple servers operating in parallel. The number of servers corresponds to the capacity decision and the base stock level is the inventory decision. The main problem which we consider is the joint optimization of the capacity and inventory decisions to minimize a combination of capacity, inventory, and backordering costs. We develop a square-root rule for the joint decision and justify the rule analytically in a many-server queue asymptotic framework. We also provide operational insights into the tradeoffs involved in such joint management problems, through various analysis based on the square-root rule as well as a comparison with analogous results for single-server make-to-stock queues.