Finding the end date from asynchronous starting but consecutive running date ranges - postgresql

Question

I need to help with a database model and and efficient calculation method of the last end date.
The ranges have a start date but will wait to start until the currently active ranges have ended. Changing the length or start of one range should cascade to the waiting ranges and push them back. But they can never start before their start date.
The database mock here is just to explain the problem and doesn't need to be followed as long as it works properly.
| id | start | length | 01 02 03 04 05 06 07 08 09 10 11 12 |
| 1 | 03 | 2 | ------ |
| 2 | 06 | 2 | ------ |
I am aware that I can brute force the answer to get the last date. But I'm looking for a more efficient solution as there are many ranges and the end date needs to read often.
Also is this something that's possible to calculate in a PostgreSQL query? Or maybe keep end date fields up to date with triggers?
Examples
Here range 2 starts on 04 but can't be used until after range 1 finishes.
| id | start | length | 01 02 03 04 05 06 07 08 09 10 11 12 |
| 1 | 02 | 5 | ------------------ |
| 2 | 04 | 5 | ------------------ |
If we update the range 1, range 2 should move up with it.
| id | start | length | 01 02 03 04 05 06 07 08 09 10 11 12 |
| 1 | 02 | 4 | -------------- |
| 2 | 04 | 5 | ------------------ |
But range 2 shouldn't move past its start date.
| id | start | length | 01 02 03 04 05 06 07 08 09 10 11 12 |
| 1 | 02 | 1 | -- |
| 2 | 04 | 5 | ------------------ |
If you just take the latest start date and add its duration you will get the wrong answer.
| id | start | length | 01 02 03 04 05 06 07 08 09 10 11 12 |
| 1 | 04 | 5 | ------------------ |
| 2 | 05 | 2 | ------ |
Get: 7
Expected: 10