1. A computer program product for managing data sets in a storage device, the computer program product comprising a computer readable storage medium including hardware having computer readable program code embodied therein that executes to perform operations, the operations comprising: performing a reorganization of a data set in the storage device; and in response to an access of the data set, initiating to complete the reorganization the data set in the storage device in response to the data set being in a pending uncompleted reorganization state and no other process currently accessing the data set.