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Project are the mean to put your organizational strategy into action. So, the matrix must be create for your organization. If not, you will fail. But, at the end, you can split your projects into three main categories: High Risk: those are strategical projects. Low Risk: those are required projects. Medium Risk: those are projects with better ROI or today tendency is with high value delivery.
I can't provide any proprietary examples (there are lots on the web), but I will offer the advice to keep it simple. You will often find that you have variables to compare which aren't easy to quantify in like numbers for comparison such as the lead time of option X vs. customer satisfaction of Y. Using a numerical approach for comparisons can lead to a weighting system that's somewhat meaningless numerical soup. The discussion between stakeholders about where something should fit on the matrix is often far more valuable than finite ranking.
An alternative is to use fuzzy logic which sounds more complicated than it is. Think of those web apps that ask you to answer some simple questions to find out which of the characters of (insert your favorite TV show here) you're most like. It starts with your org developing some sample questions such as "Lead Time 18 months = Bad", "Savings $50k = fair". Then each new project is rated based on a set of simple questions, those answers are compared to the sample, and voila...you're 85% Batman.
I'd suggest you start by finding out what's most important for your leadership team rather than adapting an existing scoring model from the outside. You might come up with a list of 5-10 factors and have the individual leaders (or as a group) rank those to help you understand which are most important to them.
Once you have a draft model defined, score a few existing in-flight projects using the model and see whether the relative priorities match the views of your leadership team and then tune it based on their feedback.
You can find templates on the web to inspire your exercise, but it needs to be made for your organization.
Each industry is different, your decision matrix needs to reflect yours.
April, you might be jumping the gun. There is a bit of groundwork you need to do before even looking at "weighted project priority or effort/impact matrix". Like analyzing what kind of PMO this is going to be, which determines your approach for augmenting the project management function within the organization. Assessing the current project management maturity within the organization, in terms of people's competencies, systems and processes that already exist. Aligning the PMO's responsibilities with the organization's strategic vision, which comes out of discussions with senior management; yes I understand they (or someone) has said go ahead with setting up a PMO, but what is the official document or metrics with which they will asses the success of the PMO? These are just some of the things that should be done when setting up a PMO.
I would also recommend Laura Barnard's blog on this site. She has some great blog posts about PMO's although it appears her last blog post was around 6 months ago.
I'd suggest searching the web for ideas, then leverage when discussing internally to determine specific criteria and thresholds. If possible, have a tie-in into points from the organization's strategy/roadmap to facilitate decision making and priority slotting.
The priorities and weights are generally different in various organization. Even you may need a different list of issues. You better go online and find some samples, however, just get an idea and work on yours.
Another aspect to take into account is what are the painpoints of the organization, and what would senior management like to see improved first. Measuring factors that management does not see as an issue may not bring as much early value as focusing on areas where there is low-hanging fruit to show PMO value to management.
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