Stochastic　scheduling　optimisation　is　a　hot　and　challenging　research　topic　with　wide　applications.　Most　existing　works　on　stochastic　parallel　machine　scheduling　address　uncertain　processing　time,　and　assume　that　its　probability　distribution　is　known　or　can　be　correctly　estimated.　This　paper　investigates　a　stochastic　parallel　machine　scheduling　problem,　and　assumes　that　only　the　mean　and　covariance　matrix　of　the　processing　times　are　known,　due　to　the　lack　of　historical　data.　The　objective　is　to　maximise　the　service　level,　which　measures　the　probability　of　all　jobs　jointly　completed　before　or　at　their　due　dates.　For　the　problem,　a　new　distributionally　robust　formulation　is　proposed,　and　two　model-based　approaches　are　developed:　(1)　a　sample　average　approximation　method　is　adapted,　(2)　a　hierarchical　approach　based　on　mixed　integer　second-order　cone　programming　(MI-SOCP)　formulation　is　designed.　To　evaluate　and　compare　the　performance　of　the　two　approaches,　randomly　generated　instances　are　tested.　Computational　results　show　that　our　proposed　MI-SOCP-based　hierarchical　approach　can　obtain　higher　solution　quality　with　less　computational　effect.　©　2018,　©　2018　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.