There is an enormous amount of Problem solving methods. A rather new method is the CLEAR method. Clear stands for:
- Clarify and break down the problem
- Learn about the problem and the reasons for it
- Experiment with countermeasures
- Assess the results of the experiment and adjust as needed
- Roll out the new way of operating
The basics of this CLEAR method are about learning and applying a system approach for implementing change. A short manifest on this CLEAR method is published can be found at: http://changethis.com/manifesto/162.05.ClarityFirst/pdf/162.05.ClarityFirst.pdf
The author of this CLEAR manifest has however a rather narrow view on what a problem is: ‘Problems are simply gaps between how an organization is performing now and how it wants to or needs to perform.’ So since problems are never simple and certainly most of the time not about performance improvements only, maybe you should take care applying and trying this method.