MySql: sum orders in an efficient way (OR too slow)

Question

I want to sum up orders. There are products p and ordered items i like:

DROP TABLE IF EXISTS p;
CREATE TABLE p (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `combine` int(10) unsigned DEFAULT NULL,
  PRIMARY KEY (`id`),
  INDEX `combine`(`combine`)
) ENGINE=InnoDB;

DROP TABLE IF EXISTS i;
CREATE TABLE i (
  `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `p` int(10) unsigned DEFAULT NULL,
  `quantity` decimal(15,2) NOT NULL,
  PRIMARY KEY (`id`),
  INDEX `p`(`p`)
) ENGINE=InnoDB;


INSERT INTO p SET id=1, combine=NULL;
INSERT INTO p SET id=2, combine=1;
INSERT INTO p SET id=3, combine=1;
INSERT INTO p SET id=4, combine=NULL;

INSERT INTO i SET id=1, p=1, quantity=5;
INSERT INTO i SET id=2, p=1, quantity=2;
INSERT INTO i SET id=3, p=2, quantity=1;
INSERT INTO i SET id=4, p=3, quantity=4;
INSERT INTO i SET id=5, p=4, quantity=2;
INSERT INTO i SET id=6, p=4, quantity=1;

The idea is that products may be combined which means all sales are combined for these products. This means for example that products 1, 2 and 3 should have the same result: All sales of these products summed up. So I do:

SELECT p.id, SUM(i.quantity) 
FROM p 
LEFT JOIN p AS p_all ON (p_all.id = p.id OR p_all.combine=p.combine OR p_all.id = p.combine OR p_all.combine = p.id)
LEFT JOIN i ON i.p = p_all.id
GROUP BY p.id;

which gives the required result:

p=1:    12 (i: 1, 2, 3, 4 added)
p=2:    12 (i: 1, 2, 3, 4 added)
p=3:    12 (i: 1, 2, 3, 4 added)
p=4:    3 (i: 5, 6 added)

My problem is that on the real data the OR in the JOIN of the products for p_combine make the query very slow. Just querying without the combination takes 0.2 sec, while the OR makes it last for more than 30 sec.

How could I make this query more efficient in MySql?

Added: There are some more constraints on the real query like:

SELECT p.id, SUM(i.quantity) 
FROM p 
LEFT JOIN p AS p_all ON (p_all.id = p.id OR p_all.combine=p.combine OR p_all.id = p.combine OR p_all.combine = p.id)
LEFT JOIN i ON i.p = p_all.id
LEFT JOIN orders o ON o.id = i.order
WHERE o.ordered <= '2018-05-10'
AND i.flag=false
AND ...
GROUP BY p.id;

Added: EXPLAIN on real data:

+----+-------------+------------------+------------+-------+-----------------------------+---------+---------+--------------+------+----------+-------------------------------------------------+
| id | select_type | table            | partitions | type  | possible_keys               | key     | key_len | ref          | rows | filtered | Extra                                           |
+----+-------------+------------------+------------+-------+-----------------------------+---------+---------+--------------+------+----------+-------------------------------------------------+
|  1 | SIMPLE      | p                | NULL       | index | PRIMARY,...combine...       | PRIMARY | 4       | NULL         | 6556 |   100.00 | NULL                                            |
|  1 | SIMPLE      | p_all            | NULL       | ALL   | PRIMARY,combine             | NULL    | NULL    | NULL         | 6556 |   100.00 | Range checked for each record (index map: 0x41) |
|  1 | SIMPLE      | p                | NULL       | ref   | p                           | p       | 5       | p_all.id     |   43 |   100.00 | NULL                                            |
+----+-------------+------------------+------------+-------+-----------------------------+---------+---------+--------------+------+----------+-------------------------------------------------+

Answer 1

I don't know if you have the flexibility to do this, but you could speed it up by changing the combine field in p:

UPDATE p SET combine=id WHERE combine IS NULL;

Then you can massively simplify the ON condition to:

ON p_all.combine = p.combine

making the query ( SQLFiddle ):

SELECT p.id, SUM(i.quantity) AS qty
FROM p
JOIN p AS p_all 
ON p_all.combine = p.combine
JOIN i 
ON i.p = p_all.id
GROUP BY p.id

Output:

id  qty
1   12
2   12
3   12
4   3

Answer 2

Using subqueries can sometimes be faster than joins.

eg

Select p.id, (Select sum(quantity) from i where p in  
        (Select id from p as p2 where 
            p2.id = p.id or
            p2.combine=p.id or 
            p2.id = p.combine or
            p2.combine = p.combine)
    ) as orders
from p 

You could add all of your constraints on i inside the 'orders' subquery