I ran into this article recently:
The advice in it is interesting, but it also caused me to reflect on the dual nature of problem solving, and how the two aspects need to be handled almost separately. The article above more or less discusses the stakeholder aspect of problem solving with the original raiser. In fact managing the stakeholders of a problem goes further than this, as there may be a whole set of people involved with any given problem that need to be considered in solving a problem. An example is the person who is in the role “at fault”. If they are not engaged in the solution then they might consider your “problem solving” to be a threat to them, and so block progress of your solution.
The other major aspect of the solution of problems will tend to be technical. I have proivided advice on a technical process for considering solutions previously. In that article I didn’t consider the stakeholder management aspects of solving problems. It is likely, however, that at each step of resolving the technical issue it will be necessary to engage the different stakeholders to the problem, to make sure that they are bought in to the solution. A failure to do this will result in blocking behaviour, which will hamper the progress of the solution.