A contribution is sought in the time–cost trade-off problem (TCTP) to determine a minimum project duration at minimum additional costs per acceleration. To achieve the objective, a model that minimizes the deadline of the linear time–cost trade-off problem (LTCTC) with generalized precedence relations (GPR) is proposed. The optimization model corresponds to a mixed integer linear program and is solved using GNU Linear Programming Kit (GLPK), validating, and contrasting the results of an artificial case adapted from the literature and a larger case corresponding to a road infrastructure project developed in Chile. The results guarantee the fulfillment of the objectives of minimizing the project duration, increasing the profitability without exceeding the available budget, without violating the precedence and lag time restrictions. It is concluded that the proposed model allows us to address the time–cost trade-off of a generalized project efficiently.