In　this　paper,　we　propose　inventory　lot　sizing　policies　for　a　closed-loop　hybrid　system　over　a　finite　product　life　cycle,　which　consists　of　three　phases:　introduction,　maturity,　and　decline.　Assuming　the　demand　rate　is　a　trapezoidal　type　function　of　time　and　return　rate　increases　linearly　over　the　finite　production　horizon.　New　and　remanufactured　products　are　perfect　substitutes,　which　means　that　customer＇s　demand　can　be　satisfied　by　new　products　or　remanufactured　products.　Different　from　the　previous　literature,　this　paper　proposes　inventory　lot　sizing　models　with　variable　replenishment　intervals　from　the　perspective　of　product　life-cycle.　Firstly,　the　inventory　lot　sizing　models　with　variable　replenishment　intervals　are　established　for　each　phase　of　the　product　life　cycle.　Secondly,　the　optimal　policies　and　algorithms　are　designed　for　the　given　models.　Finally,　sensitivity　analysis　and　comparative　analysis　are　carried　out　through　a　numerical　example.　The　results　show　that　different　inventory　lot　sizing　policies　should　be　adopted　in　different　phases　of　the　product　life　cycle:　(1)　the　optimal　manufacturing　lot　sizes　increase　while　the　replenishment　intervals　decreases　over　time　in　introduction　phase,　(2)　the　optimal　manufacturing/remanufacturing　lot　sizes　and　the　replenishment　intervals　are　constant　in　maturity　phase,　(3)　the　optimal　manufacturing/remanufacturing　lot　sizes　decrease　while　the　replenishment　intervals　increases　over　time　in　decline　phase.　The　higher　the　return　rate,　the　greater　the　advantage　of　the　given　model.　Therefore,　if　return　rate　is　relatively　low,　the　firms　may　choose　the　static　policy　given　by　Hsueh　(2011)　with　fixed　replenishment　intervals　to　simplify　replenishment　operations;　if　the　return　rate　is　relatively　high,　the　firms　may　choose　the　given　policies　with　variable　replenishment　intervals　to　reduce　costs.　©　2020　Elsevier　Ltd