In　electronics　industry,　aircraft　manufacturing,　distributed　computer　systems　and　supply　chains,　it　is　common　that　many　jobs　are　divisible　and　can　be　considered　as　a　batch　of　potentially　infinitely　small　and　independent　items.　Subcontracting　divisible　jobs　means　that　a　job　can　be　partially　processed　by　an　in-house　machine　and　the　remaining　of　it　can　be　processed　by　a　subcontractor＇s　machine.　Considering　three　subcontracting　pricing　strategies:　non-increasing,　non-decreasing　and　constant　over　time,　this　paper　studies　a　scheduling　problem　with　divisible　jobs　and　subcontracting　option　in　which　both　the　manufacturer　and　the　subcontractor　are　in　single-machine　environment.　The　objective　is　to　minimize　the　sum　of　total　weighted　tardiness　and　total　subcontracting　costs.　A　mixed　integer　programming　(MIP)　model　is　formulated.　Then　a　Lagrangian-based　Benders　Dual　Decomposition　(denoted　by　LB-BDD)　method　is　developed　based　on　the　MIP　formulation.　Extensive　computational　experiments　are　conducted　on　five　groups　of　randomly　generated　problem　instances,　and　the　results　show　that　the　proposed　LB-BDD　method　outperforms　the　basic　Benders　Decomposition　(denoted　by　BD)　method　and　solving　the　MIP　model　directly　in　Gurobi　solver.　©　2022　Elsevier　Ltd