This　paper　considers　the　problem　of　scheduling　a　group　of　jobs　with　arbitrary　release　times,　non-identical　sizes,　and　different　processing　times　on　non-identical　parallel　batch　processing　machines　to　minimize　the　total　completion　time.　A　mixed-integer　programming　(MIP)　model　is　firstly　constructed　in　this　paper　to　solve　this　problem.　Then　since　the　studied　problem　is　strongly　NP-hard,　a　modified　elite　ant　system　algorithm　with　the　local　search　(MEASL)　is　also　proposed　to　solve　it,　which　is　compared　with　several　meta-heuristic　algorithms　and　the　commercial　optimization　solver　(Gurobi)　through　extensive　simulation　experiments.　Finally,　the　experimental　results　verify　the　effectiveness　of　the　proposed　algorithm.　©　2023　Elsevier　B.V.