As a consulting company, we are usually asked to come up with extraordinary solutions to problems. We usually start with using The Harvard Case Study Method. ( sometimes in the military called the Staff Study Method) the procedure is:
1. Define the Central Problem
2. List Relevant Factors
3. List all Alternatives
4. Analyse the Alternatives
5. List your Conclusions
6. Make Recommendations

This process helps the team come up with decisions that have been well thought out and are easier to implement. It works for us. Do you have any other ideas on problem solving?