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Project managers strive to reduce the capital project execution times. Project owners typically insists on quick delivery for financial benefits of early occupation of the built facility (commercial projects), or for reducing public dissatisfaction caused by the works (public projects like road repairs). Construction and civil projects are notorious for delays due to both external and internal factors. The delays require action to be taken to make the project “back on tracks” and finish on time. Given a limited budget and the need for efficient use of resources, the problem of scheduling projects with short completion times is being addressed by a variety of ideas, such as letting non-critical construction processes to be suspended to free resources to more crucial ones, switching to faster but costly construction methods, or allowing changes in the process sequence. This paper presents a new idea on how to accelerate a construction project by relocating some of the workers from non-critical processes to support crews performing critical ones, and possibly by employing additional resources. The authors describe their idea in the form of a mixed-integer linear problem. The model facilitates finding an optimal schedule of processes allowing the relocation of some non-critical or subcontractor resources to support critical crews and meet the baseline execution deadline. A numerical example illustrates the merits of the proposed approach. In practice, the method presented can constitute a valuable tool used in the management of construction projects.