There is a rather trivial situation. We have a development team with known rates of each of them, PM/PO and sprint backlog. Each member evaluates every task in hours with planning poker. Finally we potentially know evaluation time of every task by every developer. Here the question is: how can we efficiently distribute the tasks between all the team members from the point of the busyness' view? Are there tools to do that in automatic or semi-automatic mode? Are there plugins for Jira/Redmine to do that? Thanks in advance for the answer.
I am one of the developers of https://pollunit.com
We build a feature to automatic distribute tasks according to personal preferences. You can read more about this here: https://pollunit.com/en/tutorials/distribute_tasks
This function is rather intended to avoid quarrels when choosing tasks. Maybe it will help you anyway and could be a semi-automatic solution for you ;)
If you click on "Create PollUnit" > "Voting" you see the question "What do you want to do?" If you choose "Distribute" + "Something else" you can later enter free text (task names) as options. On the next page you can open the "Further settings for advanced users" and can choose star rating (or maybe dot voting) to let your teams rate the tasks. The stars can be a abstract symbol for how unbusy they are. Or you choose "lowest resistance" as target. Then your team can make negative votes and can tell how unwilling they are to do this task.
For small teams our tool is free. So you can try it.