The best open source alternative to Priority Matrix is Redmine, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 100 alternatives to Priority Matrix and 14 is open source so hopefully you can find a suitable replacement. Other interesting open source alternatives to Priority Matrix are TreeSheets (Free, Open Source), GanttProject (Free, Open Source), fluxday (Free, Open Source) and ZenTao (Freemium, Open Source).
GanttProject is a cross-platform desktop tool for project scheduling and management. It runs on Windows, Linux and MacOSX, it is free and its code is opensource. What can it do? * Gantt chart. - Create work breakdown structure, draw dependencies, define milestones.
ZenTao is an open source project management tool, supporting Scrum. It integrates product management, project management, bug management and QA management, etc., covering all lifecycle of software development.
Leantime is a project management system for small teams and startups. Designed to help you manage your projects from ideation to delivery. Leantime's Idea Manager allows you to store ideas, communicate them with team members, discuss and move them from idea to validation.