Production planning and inventory control in supply chain are of prime importance for companies which aim to produce high quality Finished products at lowest costs and right on time. For this reason, planners must reduce average stock levels and determine optimal safety lead times. This study deals with a multi-period production planning problem with a known dynamic demand. The lead times of demands are independent, discrete random variables with known and bounded probability distributions. A general probabilistic model, including a recursive procedure to calculate the expected total cost, is derived. A Genetic Algorithm is developed for this model to determine planned lead times and safety stock level which minimize the total expected cost. The latter is equal to the sum of the backlogging and inventory holding costs. This approach is compared to three other ones to illustrate its performance. The results prove that, under certain assumptions, it could be advantageous to optimizing planned lead times rather than implementing safety stocks. To understand the effect of dispersion on the robustness of the solution, different levels of variance and different shapes of lead time distributions are studied. Different analysis proves that the variability of the lead time affects slightly the expected total cost when the unit inventory holding cost is close to the unit backlogging cost.