While the question asks for a single source, the variety of problem solving processes out there are similar enough that they can be synthesized together relatively easily. The process below is a result of the works cited at the end, which range from 5 to 8 total steps.
1. Identify/define the problem
The aim of this step is to take careful stock of the issues faced and the problem to be resolved, for only by knowing the problem can we begin to solve it. This involves understanding both how the problem is affecting us, and any desired outcome we may have. Usually, the affects of the problem and the desired outcome will be rather obvious, but it is always good to take some time to evaluate these items in a systematic manner to ensure that they are clearly understood and correct. Often, this step helps us also determine if a problem is "too big" or if it needs to be redefined (or refined) into a set of smaller issues in order to ensure that it is manageable.
2. Understand root causes
The aim with this step is to understand why the problem occurred in the first place. There are many reasons that we may wish to know and understand these causes, including: A) knowing that the problem may recur, we would like to find a reliable way out of the issue; B) in order to prevent the problem from recurring, we are likely to need to address the root causes of the issue as a part of our solution, or as part of a longer term plan to mitigate those root factors; or C) to simply explain why we are in the current situation to a superior or to a committee.
3. Examine potential solutions
This step usually begins with a brainstorming session, in which many ideas are presented and placed upon the table all at once. Each idea is then evaluated based on its merits and how easily and efficiently it brings the problem to resolution. Additionally, all solutions should be noted and recorded, without prejudice, to ensure that the best solutions remain on the table and eventually are used to resolve the issue. Before ending this section of the process, ensure that all who have presented ideas have fully explained their thoughts on the solution, to ensure that their solution can be adequately weighed against the others.
4. Choose a plan
It is during this step that discussion of the potential solutions are now weighted based on resources required, circumstances faced, time needed, and aspects of realistic implementation are brought to the fore. Here, solutions are eliminated based on the factors that matter most to the people implementing the solutions, usually starting with the most restrictive factor and moving to the least restrictive: for example, if funds are restricted but time is not, a project that takes a long time but is cheap is more likely to be chosen than one that takes a short amount of time but is more expensive.
5. Implement the plan
Once a plan is chosen, it is then implemented: resources are allocated, people are given tasks, and reporting times are set up to ensure that milestones are met and tracked correctly. It is important that implementation be done according to the original plan as much as possible, to ensure that the planning phase was not time ill-spent. Generally, the best plans to implement are ones that involve the changing of systems or processes, not ones that involve someone "working harder" at a current process. A single person should usually be put in charge of a project and made responsible for its completion.
6. Review the plan
As mentioned above, reporting on milestones and tracking of completion is important. Additionally, however, the plan should be reviewed at specific stages to ensure that it is on track, and once it is determined that the plan is "completed," a full review should be done at that time as well. Doing this ensures that the plan addressed the issue it was supposed to address, that it addressed it correctly, and that the outcome achieved was the same one that was desired back at the beginning of the process. If the problem is not solved, then it is time to return to the top and re-examine the problem and seek a new solution, after determining why the initial solution did not work as planned.
Works Cited
Problem Solving Process. http://www.c-pal.net/course/module3/pdf/Week3_Lesson21.pdf. Accessed 11/28/09.
Basadur, Min. Simplex: A Powerful Problem Solving Process. http://www.mindtools.com/pages/article/newCT_10.htm. Accessed 11/28/09.
The Problem Solving Process. http://www.gdrc.org/decision/problem-solve.html. Accessed 11/28/09.
McNamara, Carter. Basic Guidelines to Problem Sovling and Decision Making. http://managementhelp.org/prsn_prd/prb_bsc.htm. Accessed 11/28/09.
UBUYACAR. Problem Solving Process. http://www.mcli.dist.maricopa.edu/pbl/ubuystudent/process.html. Accessed 11/28/09.
