Actually, yes, I think you would need an entire engineering team to write, maintain, scale, and run a system that solves this problem. For example, my employer

Actually, yes, I think you would need an entire engineering team to write, maintain, scale, and run a system that solves this problem. For example, my employer has a whole team working on internal tools for booking/managing/re-allocating conference rooms. It's almost exactly the same problem, it's non-trivial, it's complex, and it takes an entire team.