In　this　paper,　we　propose　a　so-called　capacitated　min-max　correlation　clustering　model,　a　natural　variant　of　the　min-max　correlation　clustering　problem.　As　our　main　contribution,　we　present　an　integer　programming　and　its　integrality　gap　analysis　for　the　proposed　model.　Furthermore,　we　provide　two　approximation　algorithms　for　the　model,　one　of　which　is　a　bi-criteria　approximation　algorithm　and　the　other　is　based　on　LP-rounding　technique.