Modeling the Impact of Merging Capacity in Production-Inventory Systems

We model two separate, decentralized systems, each consisting of a warehouse and a production capacity. The demand processes experienced by the systems have different variabilities. The two decentralized systems consider an agreement to pool their production capacities. We examine the impact of the pooling of capacity on inventory costs under two operating rules: (i) the orders from the two warehouses are treated in a first-come--first-served manner, and (ii) the orders from the lower-variability warehouse are given nonpreemptive priority. We examine this issue using an analytical model that integrates base-stock inventory models with queuing models for the production capacity. The higher-variability demand is modeled as a hyperexponential renewal process, and the lower-variability demand is modeled as a Poisson process. In case of pooled capacity, the arrival process at the production queue is the superposition of the two processes. We prove conditions under which the first-come--first-served operating rule will fail to achieve a Pareto improvement over the separate systems because it would increase inventory cost at the lower-variability warehouse. We then show cases under which the high-variability warehouse will see a reduction in inventory cost over the split system even if it accepts lower priority.