Abstract: This study is mainly to cope with the problems when a firm faces time-varying demand and receives product from a single supplier who faces random supply. The supplier`s availability may be affected by events such as natural disasters, labor strikes, manufacturing defects, machine breakdowns, or other events. A model is proposed in this research that considers a dynamic production-inventory environment: the exponential distribution of disruption, as well as the demand can be time dependent. The model explains production-inventory as a NP-hard problem, which using genetic algorithms is developed to minimize the average total cost to determinate the production cycles under various ordering policies. To evaluate the performance of the proposed algorithm, a numerical study has been conducted to compare the ordering policies under various demands in an extensive order. Based on the computational result, it can be seen that the optimal ordering policy not only should strike a balance between protecting against stockouts during disruptions but also maintaining low inventory levels of finished products and raw materials.