In　this　paper,　a　new　scheduling　problem　is　investigated　in　order　to　optimise　a　more　generalised　Job　Shop　Scheduling　system　with　a　Combination　of　four　Buffering　constraints　(i.e.　no-wait,　no-buffer,　limited-buffer　and　infinite-buffer)　called　CBJSS.　In　practice,　the　CBJSS　is　significant　in　modelling　and　analysing　many　real-world　scheduling　systems　in　chemical,　food,　manufacturing,　railway,　health　care　and　aviation　industries.　Critical　problem　properties　are　thoroughly　analysed　in　terms　of　the　Gantt　charts.　Based　on　these　properties,　an　applicable　mixed　integer　programming　model　is　formulated　and　an　efficient　heuristic　algorithm　is　developed.　Computational　experiments　show　that　the　proposed　heuristic　algorithm　is　satisfactory　for　solving　the　CBJSS　in　real　time.　©　2017　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.