I recently joined a technology startup company where a key business value-proposition depends on solving certain various problems that no current business competitor solves. There is one particular sub-problem we're looking to offer a commercial solution to - and it has been already solved by an academic team who published a paper describing an algorithmic solution about 15 years ago. To our knowledge, no commercial operation employs their approach. We would like to capitalize on this.
The team-members are still working at the original university and fully contactable.
The problem is the solution as described in the paper is beyond the current academic-ability of the startup's employees - and given time constraints I'm considering the possibility of contacting the team to ask them to implement it for us - as paid professionals, of course.
Is this appropriate? Is there a good way to frame this? Would paying them for their work introduce any kind of conflict-of-interest or other consequences?