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In this paper, we introduce a random time-dependent project -scheduling problem (RTPSP), in which activity duration times are represented as randomness as well as time dependence. Under these circumstances, the resulting RTPSP is far more complex when compared with existing project-scheduling problems. The complexity stems identifying the critical path, a core issue when dealing with project-scheduling problems. Considering the critical path, we first show that using “standard” path algorithms (e.g., the well-known Dijkstra method) are not able to arrive at solutions. Subsequently, we propose an approach of handling the critical path of RTPSP. Next, we formulate the RTPSP and present three stochastic-programming models to address various requirements arising within this framework. The proposed models are handled through techniques that combine mechanisms of stochastic simulation and genetic optimization. Stochastic simulation is exploited here to estimate the value of uncertain functions that do not exist in the general project-scheduling problems. Numerical experiments are used to illustrate the effectiveness of the algorithm.