In　this　paper,　we　consider　a　three-machine　permutation　flow　shop　scheduling　problem　under　simple　linear　deterioration.　By　a　simple　linear　deterioration　function,　we　mean　that　the　processing　time　of　a　job　is　a　simple　linear　function　of　its　execution　start　time.　The　objective　is　to　find　a　sequence　that　minimizes　makespan.　This　problem　is　well　known　NP-hard.　Optimal　schedules　are　obtained　for　some　special　cases.　For　the　general　case,　several　dominance　properties　and　two　lower　bounds　are　derived　to　speed　up　the　elimination　process　of　a　branch-and-bound　algorithm.　Moreover,　a　heuristic　algorithm　is　proposed　to　overcome　the　inefficiency　of　the　branch-and-bound　algorithm.　Computational　experiments　on　randomly　generated　problems　is　conducted　to　evaluate　the　branch-and-bound　algorithm　and　heuristic　algorithm.　The　analysis　shows　that　the　proposed　heuristic　algorithm　performs　effectively　and　efficiently.　(C)　2010　Elsevier　B.V.　All　rights　reserved.