I'm currently working in a small software firm (~15 employees) as a leader of a two-person (including myself) algorithms team. I'm a big advocate of the "Deep Work" mindset in a workplace, especially when working on tasks requiring thorough research and meticulous development.
The problem is that all the employees sit together in one big open space. Most of the employees work in customer-relations and operations teams, answering a lot of phones during the day and collaborating together (often loudly) on immediate daily tasks.
All this activity in the office produces a lot of noise and distractions to the working flow of my team, since most of the daily tasks aren't our priority. And while there are times when we collaborate with other teams and participate in joint brain-storms, we spend most of the time trying to concentrate on more long-term tasks, using headphones to dissociate from all the fuss around us.
In, addition to that, the other person on my team spends 2+ hours on the daily commute to the office.
Now, adding all this together, a more flexible remote working policy would make a lot of sense in this situation. But all my negotiations concerning this matter were met with a lot of opposition and skepticism.
What would be the best way for me as a team leader to convince the higher management that allowing employees to work remotely some days wouldn't impact their productivity negatively? I am especially interested in the aspect of advocating this for the team members and not for me personally.