The research endeavors to harness the benefits stemming from the integration of constraint theory into construction project management, with the primary goal of mitigating project completion delays. Additionally, it employs fuzzy analysis to determine the relative significance of fundamental constraints within projects by assigning them appropriate weights. The research problem primarily revolves around two key issues. Firstly, the persistent utilization of outdated methodologies and a heavy reliance on workforce experience without embracing modern computerized technologies. Secondly, the recurring problem of project delivery delays. Construction projects typically encompass five fundamental constraint types: cost restrictions, time constraints, administrative and legal limitations, technical and design constraints, and environmental constraints. To address these issues, a field study was conducted, focusing on the development of a housing complex in Qa'imaqamiya, Al-Mada'in district, Bismayah. The researchers propose a three-stage methodology to tackle these challenges. In the initial stage, the theory of accelerated activities is applied to all concurrent implementable tasks. Subsequently, the second stage introduces a hierarchical analysis process, known as FAHP, to quantify the importance of each constraint. Finally, in the third phase, fuzzy logic is employed to calculate the projected duration and associated costs for each activity, ensuring project execution and delivery within agreed-upon timeframes. After applying the proposed methodology, there is a reduction in completion time by up to (23%). Research Type: Research Paper