Block stacking, which involves the storage of unit loads in stacks within storage rows, is typically used in traditional warehouses to achieve a high space utilization at a low investment cost. In this paper, assuming that the demand size from a customer is an i.i.d. random variable, we develop a probabilistic block stacking storage model and its algorithm for a singles product, which minimizes the time-overage floor space requirement under an (s, S) inventory policy and the violation of the FIFO lot rotation rule only in a single partially-occupied row.