Resource allocation via project scheduling plays an important role to balance project time and cost. In this paper, we are designing a framework to handle scheduling problems using neutrosophic activity duration times. We consider important aspects of time-cost tradeoffs while taking into account the real and uncertain situation surrounded by the projects. In real situations, there are many considerable aspects which should be considered by managers, for instance, the tradeoffs between the project completion time and cost and the uncertain conditions of the environment. Since the concept of the deterministic project scheduling and time-cost tradeoffs conflict with the real situation, where in many cases, some data on the activities durations of the project changes during the implementation process. Fuzzy scheduling and time-cost tradeoffs models assume only truth-membership functions dealing with uncertainties surrounded by the projects and their activities duration which are unable to handle indeterminacy and inconsistency. Therefore, neutrosophic theory is a better framework that takes into account the dynamic features of all parameters. Trapezoidal neutrosophic numbers are used to estimate the activities durations in this paper. The crisp model for activities time obtained by applying score and accuracy functions. The goal here is to minimize the cost of projects under uncertain environmental conditions.