Instead of implementing a -h or --help, consider using some code like "if nothing else matches, display the help". The asterisk is for this purpose.

  while getopts :hvr:e: opt
  do
      case $opt in
          v)
              verbose=true
              ;;
          e)
              option_e="$OPTARG"
              ;;
          r)
              option_r="$option_r $OPTARG"
              ;;
          h)
              usage
              exit 1
              ;;
          \*)
              echo "Invalid option: -$OPTARG" >&2
              usage # call some echos to display docs or something...
              exit 2
              ;;
      esac
  done