I believe it may depend on the context. Typically inventory refers to the value of finished products that are not sold yet (could be also raw materials, partially assembled products, spare parts etc.) This is a position in the balance sheet rather than cost per se.

However, as you noticed, this may incur costs such as storage (rent, insurance, heating/cooling if products are perishable, security and so on). In addition, if the value is significant, the fact that your cash is “frozen” can be the largest cost. You can estimate this cost using interest rates (as if you needed to borrow extra money to compensate for the illiquid assets).