We consider a network in which field stocking locations (FSLs) manage multiple parts according to an (S-1,S) policy. Demand processes for the parts are assumed to be independent stuttering Poisson processes. Regular replenishments to an FSL occur from a regional stocking location (RSL) that has an unlimited supply of each part type. Demand in excess of supply at an FSL is routed to an emergency stocking location (ESL), which also employs an (S-1,S) policy to manage its inventory. Demand in excess of supply at the ESL is backordered. Lead time from the ESL to each FSL is assumed to be negligible compared to the RSL-ESL resupply time. In companion papers we have shown how to approximate the joint probability distributions of units on hand, units in regular resupply, and units in emergency resupply. In this paper, we focus on the problem of determining the stock levels at the FSLs and ESL across all part numbers that minimize backorder, and emergency resupply costs subject to an inventory investment budget constraint. The problem is shown to be a nonconvex integer programming problem, and we explore a collection of heuristics for solving the optimization problem.