Map a Problem to Reveal Opportunities for Solution
When a company needs to find a problem’s solution, it is important to consider a comprehensive perspective of the system in question prior to problem solving. Not only must the system boundaries be considered, but also a historic analysis of the decisions that have led to the current predicament. This approach provides a comprehensive framework upon which to base decisions concerning what problem to solve. A powerful technique for achieving these objectives is to create a problemsolution decomposition. The problem solution model is simple to construct and provides a diagrammatic perspective of a system’s problemsolution history.
Diagram the Problem
The diagramming technique is simple. The problem is identified with the “circle p,” a description of the problem used to identify the specifics as shown in Figure 1.

The transition from the problem to a solution is indicated using the “linesegment arrowhead,” seen in Figure 2.

The solution is identified by the “circle s,” a description of the solution used to identify the specifics, shown in Figure 3.

A new problem created by the solution is identified with the “circle p prime,” a description of the secondary problem, seen in Figure 4.

A complete problemsolutionproblem (PSP) model (shown in Figure 5) represents the full cycle – a problem with a solution that generates a secondary problem. The PSP model also indicates contradictions that become inputs to contradiction theory, which is subset of the Theory of Inventive Problem Solving (TRIZ).

“I want a certain S to solve P but I am prohibited by P’.” (It is common for the phrase to need some modification to be completely accurate) The S becomes the improving parameter of a technical contradiction and P’ becomes the degrading parameter. The problem is now ready to be assigned one of the inventive parameters (also from TRIZ) for the S and the P.
The PSP model also provides the opportunity to constrain the system for problem solving at any level. The user needs to select an initiating P and a concluding S (or secondary P). The problem solving then takes place inside the constrained system. The user can move around the limitations and focus problem solving at a higher, more strategic level or a lower, more tactical level.
PSP Model Example
Consider the following:
P = The container’s plastic outer body is too hot to be held.
S = Use an additive in the plastic that reduces thermal conductivity, reducing outer body temperature so that it can be held.
P’= The internal chamber that is used to transfer heat is made from the same material in a blow molding process. A reduction in thermal conductivity, therefore, is detrimental to the container’s primary function of heating the contents quickly.
The problem that needs to be solved in this case is making the container able to be held without the consequential degradation in the thermal conductivity of the plastic. The compromise solution is described in the PSP model above. The innovative solution achieves the solution, S, to the problem, P, without the generation of a secondary problem, P’.
The problem solver could also decide to allow the PSP’ triplet to persist while generating a secondary solution, S’, that resolves the secondary problem, P’. This is an example of constraining the system space to either solve a problem or mitigate its negative effects. The PSP may be integrated into the contradiction syntax as follows: “I want to add a thermal insulator to the plastic to make the outer body able to be held, but I can’t because it will also decrease the thermal conductivity of the internal chamber that is used to heat the contents of the container.”
The ability of the object to be held is the parameter that is improved while heat transfer degrades. The PSP is now prepared to be addressed using TRIZ contradiction theory.
Summary
It is possible to map an entire system of problems and solutions using this technique. This is useful for a number of reasons:
 Identifies a historical perspective for all problems and solutions in a system
 Identifies contradictions in a system (each PSP triplet)
 Identifies the proper contradiction syntax for each PSP triplet
 Identifies strategic and tactical problem solving opportunities
 Constrains problem solving at the required location in the PSP model
With a complete view of a problem and its secondary problems and solution, a company will find moreopportunities for innovative solutions.
About the Author:
Michael S. Slocum, Ph.D., is the principal and chief executive officer of The Inventioneering Company. Contact Michael S. Slocum at michael (at) inventioneeringco.com or visit http://www.inventioneeringco.com.