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; determining whether a reorganization flag indicates a pending uncompleted reorganization state, wherein the data set is in the pending uncompleted reorganization state if the reorganization started against the data set and was interrupted and did not complete; and in response to an access request for the data set and determining that the reorganization flag indicates the pending uncompleted reorganization state and that no other process is currently accessing the data set, initiating to complete the reorganization of the data set in the storage device.