Many variations of this triangle exist and today its basic concept is getting more and more muddled.
In the early 1990s, the concept of scope started to become more and more important and was seen as the area of the triangle, again varying against cost, time and quality. And value was still very much focused on quality. Good value was when the highest quality was achieved for the least expenditure of resources.
Today, stakeholder satisfaction, which can include quality, but also scope and other issues have replaced the concept of quality.
In project management, value could be represented as scope and quality (satisfaction) on one side of the scale and cost and time (resources) on the other side: the more scope and quality for the least cost and time yielding the most value.
Although this is an interesting concept, it is usually not the project manager's role to define these elements. They are usually imposed as parameters in the project charter.
It is the role of the sponsor to define the value that the project will generate by setting the scope and quality that will satisfy the stakeholders and define the cost and time that will be acceptable and achievable.
There is a simple equation that can be represented graphically to represent this:
If offered benefits are greater or equal than expected benefits, satisfaction is achieved. If available resources are greater or equal than required resources, value can be realized.
Typically projects are measured against their capability to fulfill strategic objectives and business benefits, including increased operational capabilities.
Estimated resources (time, cost and human resources) are measured against resources available at the time the project is scheduled to take place. If both ratios are positive, then value will be achieved. If many projects are competing against each other, those that provide the highest benefits to resource ratio will be chosen.
But is this truly the norm? Is this how things work at your organization?