In this article, a stochastic model is presented to schedule the maintenance tasks and control the inventory simultaneously in an unreliable deteriorating production system. The optimal planning of these aspects improves the productivity of the production system and reduces the costs. The shift time of the states follows a general continuous distribution. The time of maintenance is also considered as a random variable, and a buffer stock is maintained to avoid possible shortage and satisfy the demand during the performance of maintenance. The purpose of this study is to integrate the decisions of safety stock determination and maintenance scheduling to minimize the expected total cost of the system. Due to the complexity of the equations of the model, at first, a genetic algorithm (GA) is employed for optimization. To validate the GA solutions, they are compared with those obtained by a grid search algorithm. It is found that the differences between the optimal values of the objective function (ECT) in GA and grid search are almost small and, in some cases, only 5.58% and 2.03%. This result indicates the validity of the solutions obtained by the GA. In the next step, to speed up the run time of the proposed GA, a Monte Carlo simulation approach is developed, and the GA is combined with the simulation approach. In particular, the fitness function of each chromosome is obtained using the proposed simulation approach. In order to examine the performance of the proposed simulation approach, the results of simulation are compared with the findings on optimization by the GA. This comparison indicates that the difference between the values of ECT calculated through the GA and simulation is averagely 4.55%, which is negligible. The results denote the appropriate performance of the model and the efficiency of the proposed hybrid approach. Finally, comprehensive sensitivity analyses are performed regarding the parameters of the model.
