Dear Hudson...
The Balanced Scorecard framework typically has three major elements - Objectives, Measures, and Initiatives.
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example from: http://www.site-optimiser.com.au/wp-content/uploads/UX_Figure_4.jpg
Initiatives are analogous to projects. They are a tangible group of actions that are expected to fix or change something about the organization and should generally improve one or more strategy measures (also called key performance indicators (KPIs)). They are not day-to-day activities, but classically designed projects complete with a scope, schedule, and budget.
Balanced Scorecards and the PMI's method of project management are both effective techniques (and trending management buzz words) but they are not the same tool and should not be used on the same problem.
Balanced Scorecards should be developed the leadership team as a guide on what the organization should be broadly working towards - and is generally managed by a Chief Strategy Officer. Project Management should be used on one or more specific projects (also called initiatives) that support the strategy.
Integration of the two methods relates to budget setting, fitting individual time lines into the broader vision, and ensuring that the scope also aligns with the strategic plan.
Once this alignment is set, the project manager should report progress as it relates to the Balanced Scorecard and continue remind those actually completing the project about the projects charter and the vision of what it's expected to deliver.
One other note: Most medium sized organizations and every large organization uses some sort of project management software to manage this reporting and alignment process. If you are looking for a directory of project management software - but sure to visit this site: Project Management Software Directory
Cheers mate -CB