On the viability of partial inventory pooling

When demands are uncertain, complete inventory pooling is known to be a better strategy than no pooling if the trans-shipment cost is low enough; otherwise, pooling is undesirable. But are there situations where pooling some inventories, but not the rest, in a central warehouse, are the best strategy? We show that such is indeed the case for certain demand distributions and cost parameter values. We show it for a symmetric discrete demand scenario, as well as for a symmetric continuous demand scenario.