In　this　paper,　an　unrelated　parallel　machine　scheduling　problem　is　studied,　where　order　acceptance,　sequence　and　machine-dependent　setup　times　and　the　maximum　available　times　of　machines　are　additionally　considered.　The　objective　is　to　maximize　the　profit,　which　is　the　difference　between　the　total　revenues　of　accepted　jobs　and　the　cost　associated　with　makespan.　A　mixed　integer　programming　(MIP)　model　is　formulated.　To　tackle　this　problem　efficiently,　an　exact　decomposition　method,　which　is　a　two-layer　logic-based　Benders　decomposition　(LBBD)　based　(denoted　by　TL-LBBD)　method,　is　developed,　where　an　inner　LBBD　is　embedded　into　an　outer　LBBD.　Specifically,　in　the　outer　LBBD　method,　the　master　problem　is　used　to　determine　the　acceptance　of　jobs,　whereas　the　subproblem　examines　the　schedule　given　the　accepted　jobs　from　the　master　problem.　The　subproblem　could　be　further　decomposed　into　an　assignment　master　problem　and　a　sequencing　subproblem　by　the　inner　LBBD　method　as　well.　Extensive　computational　experiments　are　conducted　and　the　results　show　that　the　developed　TL-LBBD　method　produce　better　quality　solutions　in　significantly　less　computation　time　than　solving　the　MIP　model　directly　and　the　classic　LBBD　method.　Moreover,　the　maximum　scales　of　the　problem　instances　that　could　be　solved　to　optimality　by　the　developed　TL-LBBD　method　within　30　min　are　also　evaluated.　©　2022　Elsevier　Ltd