Joint Replenishment of spare parts is a common practice in several industries, mainly where logistic difficulties exist, such as mining, petroleum and military missions. In addition, quantity discounts have been considered in many operations and production scenarios, as a useful practice to promote substantial savings to the actors of a supply chain. The model presented corresponds to the Joint Replenishment Problem in a system operating with quantity discounts. This work presents the definition and the solution of the optimization model using techniques based on the Particle Swarm Optimization (PSO) and a Genetic Algorithm (GA). Extensive computational experiments were performed and several performance comparisons are included. Results clearly show that the PSO algorithm achieved better repeatability and the GA presented better performance in terms of minimization capability getting lower fitness values.