MySQL : Get critical path time - mysql

Question

I have to manage a gantt like interface where we can have multiple project (project_id). And need to get the minimum time to accomplish a project
My tables are the following :
Task
+---------+-------+----------------+
| id_task | name | days_allocated |
+---------+-------+----------------+
| 1 | task1 | 2 |
| 2 | task2 | 3 |
| 3 | task3 | 0.5 |
| 4 | task4 | 4 |
+---------+-------+----------------+
Task_predecessor (both field are linked to Task.id_task)
+------+-------------+
| task | predecessor |
+------+-------------+
| 2 | 1 |
| 3 | 1 |
| 4 | 2 |
| 4 | 3 |
+------+-------------+
Progress
+-------------+---------+------------+---------+
| id_progress | task_id | project_id | current |
+-------------+---------+------------+---------+
| 1 | 1 | 1 | 0 |
| 2 | 2 | 1 | 1 |
| 3 | 3 | 1 | 1 |
| 4 | 4 | 1 | 1 |
| 5 | 1 | 2 | 0 |
| 6 | 2 | 2 | 0 |
+-------------+---------+------------+---------+
So the Task table is our "template" and we track the advancment in the Progress table.
In this case, for project_id = 1, the id_task 1 is already done (progress.current is 0 where project_id = 1 AND task_id = 1)
So it's either tasks id_task 2 + id_task 4 or id_task 3 + id_task 4.
id_task 2 take more time than id_task 3 so the critical path is id_task 2 --> id_task 4 , 7 days
I have 2 options :
Option n°1
I can add a minimal_days column in my Task table because I know the predecessors. So the table will be
+---------+-------+----------------+--------------+
| id_task | name | days_allocated | minimal_days |
+---------+-------+----------------+--------------+
| 1 | task1 | 2 | 9 |
| 2 | task2 | 3 | 7 |
| 3 | task3 | 0.5 | 4.5 |
| 4 | task4 | 4 | 4 |
+---------+-------+----------------+--------------+
And I can retrieve the minimal days with this kind of query :
SELECT MAX(minimal_days) FROM progress
LEFT JOIN task ON task.id_task = progress.task_id
WHERE project_id = 1 AND current = 1
Option n°2
I rewrite the logic in a MySQL query ? But honestly, I dont know how ...
Option n°1 can be easily implemented, the result will be nearly instantaneous but the system is pretty limited, if a task is added or removed, all days_allocated must be recalculed and updated.
Option n°2 is in my opinion most difficult to write in MySQL. The request may be slower. Especially if we have to retrieve it for several projects at once. Once agin is a suposition... But the system will be more modular.
I prefear the option n°2, what about you ? Should I prefear another option ? Is there any other way to proceed ? Can you help me to write this logic in MySQL ?
PS : We can work with a total of 50 - 100 project at a time. A project can have 30 tasks max and the task_predecessor thing is pretty linear. We don't have very complex schema. So I think the result can be displayed in "real-time"