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 de-cision 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. Keywords: make-to-stock queue; capacity-inventory joint management; multi-server queue; many-server asymptotics; square-root rule; diffusion approximation 1