Yii, CGridView: filtering and sorting count column from related tables - yii

Question

I have 3 tables: productions, chunks (production may have a lot of chunks, so chunks contains production_id column) and chunk_designers (chunk may have a lot of designers, so chunk_designers has a column chunk_id).
I have to render data from productions in CGridView and add a column: count of chunks (for every production item in table), which are not assigned to any chunk. In other words:
SELECT COUNT(*) FROM `chunks`
left JOIN `chunk_designers`
ON chunks.id = chunk_designers.chunk_id
WHERE production_id = 520 AND chunk_id IS null
...where 520 - dynamic value for every row, productions.id.
ChunkController action:
function actionProductionList() {
$model = new Productions('search');
$model->unsetAttributes(); // clear any default values
$dataProvider = $model->search($_GET);
$dataProvider->criteria->order = 'start_time DESC';
$this->render('production_list', array(
'provider' => $dataProvider,
'model' => $model,
));
}
Model Productions:
class Productions extends AppModel {
....
public $unassignedBlocksCount;
....
public function rules() {
return array(
array('unassignedBlocksCount, id, ...', 'safe'),
array('unassignedBlocksCount, id, ...', 'safe', 'on'=>'search'),
);
}
//in search() I added:
$criteria->compare('unassignedBlocksCount', $this->unassignedBlocksCount, true);
}
And in view:
$this->widget('zii.widgets.grid.CGridView', array(
'id' => 'menu-grid',
'dataProvider' => $provider,
'filter' => $model,
'enablePagination' => true,
'columns' => array(
array(
'name' => 'unassignedBlocksCount',
'value' => 'Chunks::getUnassignedBlocksCount($data->id)'
),
...
Column data is rendered fine, but when I try to filter it, I get the following error: unknown column unassignedBlocksCount in where clause.
I tried to write in search() method in Productions model:
// subquery to retrieve the count of posts
$count_sql = "(SELECT COUNT(*) FROM `chunks` "
. "LEFT JOIN `chunk_designers` "
. "ON chunks.id = chunk_designers.chunk_id "
. "WHERE production_id = 520 AND chunk_id IS NULL)";
// select
$criteria->select = array(
'*',
$count_sql . " as unassignedBlocksCount",
);
And just added unassignedBlocksCount element in columns in view.
But I still get the same error, when filter, and also problem is that I don't know, how to get production_id in $count_sql dynamically, depending on every table row (that's why in every row for that column value is 1, because it's correct value for production_id = 520).
So, my question is: how to get sortable and filterable column in CGridView, which is calculated (by COUNT()) from data in other tables? Thanks in advance.