In this study, we model a stochastic scheduling problem for a robotic cell with two unreliable machines susceptible to breakdowns and subject to the probability of machine failure and machine repair. A single gripper robot facilitates the loading/unloading of parts and cell-internal movement. Since it is more complicated than the other cycles, the focus has been on the S_2 cycle as the most frequently employed robot movement cycle. Therefore, a multi-objective mathematical formulation is proposed to minimize cycle time and operational costs. The -constraint method is used to solve small-sized problems. Non-dominated sorting genetic algorithm II (NSGA-II), is used to solve large-sized instances based on a set of randomly generated test problems. The results of several Test problems were compared with those of the GAMS software to evaluate the algorithm's performance. The computational results indicate that the proposed algorithm performs well. Compared to GAMS software, the average results for maximum spread (D) and non-dominated solutions (NDS) are 0.02 and 0.04, respectively.