The　clothes　inventory　balancing　scheduling　problem　(CIBSP)　among　branch　stores　with　the　allowance　of　lateral　transshipments　has　gained　increasing　attentions　in　fast-fashion　apparel　industry,　especially　for　the　trial　sale　of　new　products.　To　solve　the　CIBSP　faced　by　a　leading　apparel　company　in　China,　a　mixed　integer　linear　programming　(MILP)　model　is　first　formulated,　based　on　which　a　relax-and-fix　(R&F)　method　is　developed.　Several　heuristic　cuts　based　on　practical　experience　and　observations　are　further　integrated　into　the　R&F　method　to　speed　up　the　searching.　The　effectiveness　of　the　method　is　demonstrated　through　extensive　computational　experiments:　it　is　able　to　provide　near-optimal　solutions　with　average　optimality　gap　1.15%　with　less　computation　time,　compared　to　solving　the　MILP　model　directly　in　a　commercial　solver.　Case　studies　also　demonstrate　that　the　developed　R&F　method　can　obtain　high-quality　solutions　with　average　optimality　gap　0.09%　with　much　less　computation　time.