The　inventory　routing　problem　(IRP)　arises　in　a　broad　spectrum　of　real-life　applications　related　to　joint　decisions　of　inventory　and　routing.　In　the　basic　IRP,　a　supplier　has　to　make　decisions　about　the　delivery　timing,　delivered　quantity　of　a　single　product　and　routing　with　a　single　vehicle　to　a　set　of　retailers　without　backlog.　It　poses　computational　challenge　due　to　its　natural　complexity.　To　tackle　this　problem,　we　propose　a　two-phase　decomposition-based　heuristic　method.　In　Phase　1,　a　logic-based　Benders　like　decomposition　method　is　employed　to　first　determine　the　retailers＇　replenishments,　followed　by　the　routing　decisions　individually　for　each　period.　Valid　cuts,　inequalities　for　diversification　constraints　and　for　greedy　search　are　employed.　Then,　the　solutions　obtained　in　Phase　1　are　improved　with　a　restricted　mixed　integer　linear　programming　(MILP)　model　in　Phase　2.　Computational　experiments　are　conducted　on　220　benchmark　problem　instances　with　up　to　200　retailers　and　6　periods.　The　results　show　the　high　performance　of　the　proposed　method　and　it　is　comparable　to　the　state-of-the-art　heuristics　in　terms　of　both　efficiency　and　effectiveness.