Customer　credit　risk　or　payment　probability,　influenced　by　factors　such　as　financial　conditions　and　bank　policies,　has　hindered　fast　Asia-Pacific　economic　growth.　Besides,　the　working　time　is　usually　limited　due　to　regulations　and　limited　resources.　Driven　by　profit,　some　jobs　may　be　rejected　on　tactical　level　and　the　accepted　jobs　are　scheduled　on　operational　level,　respecting　the　allowed　working　time.　This　paper　studies　a　stochastic　flowshop　scheduling　problem,　assuming　that　only　the　mean　and　covariance　matrix　of　uncertain　payment　probabilities　and　processing　times　are　known.　The　objective　is　to　maximise　the　profit　level,　i.e.　the　probability　of　the　profit　no　less　than　the　planned　one,　while　controlling　the　risk　of　surpassing　the　limited　working　time.　A　new　distributionally　robust　chance　constrained　model　is　proposed.　The　sample　average　approximation　(SAA)　method,　the　robust　SAA　method　and　a　hierarchical　approach,　based　on　an　approximated　mixed　integer　second-order　conic　program,　are　developed.　Numerical　experiments　show　that　the　hierarchical　approach　is　more　efficient.　Moreover,　some　managerial　insights　are　drawn.　©　2020,　©　2020　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.