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It is an established fact that projects are almost always behind schedule. Consequently, there is a great need for the allocation of additional resources with a view to accelerating projects, so as to ensure delivery on the planned date. These resources are obtained from project budget contingency, whose purpose is to foresee and budget for delays arising from disruptions, inaccurate activity time and cost estimates, and resource nonavailability when required for the execution of project activities. This type of problem arises both in the planning phase of a project, particularly in the context of bidding, as well as in ongoing projects, including new product development projects. The research reported in this paper provides a mixed-integer nonlinear programming model for the acceleration of projects, employing the simultaneous crashing, overlapping, and substitution of project activities. In order to ensure convergence, this model is transformed exactly into a mixed-integer linear programming model. The assumptions of the model are presented and discussed with engineering project management practice in mind. Application of the model to four examples of different sizes and nature, three of which are practical cases, demonstrates the efficiency of the model, implemented in commercial optimization software, in solving practical project acceleration problems.