In this paper, we investigate a two-echelon, two-product Supply Chain (SC) inspired by a real-world production/distribution firm, in which the product change-over time, necessary to switch from a product to another, induces a variable capacity in the factory. Such a varying production capacity is further exacerbated by the machine breakdowns that may occur in the manufacturing system. Since the two products share the same production system, a production planning rule has to be executed to decide the change-over, i.e. to select the product to be manufactured over time. An extended experimental campaign has been performed to investigate how the fill rate and the standard deviation of inventories vary as a series of operational and tactical parameters changes. Several ANOVA analyses revealed a strong interaction between the production planning model and the adopted smoothing replenishment strategy, which remarkably affects the performance of the SC. Interestingly, a higher value of the proportional controller negatively affects the service levels since the adopted production planning policy, under these circumstances, tends to encourage longer production runs for a certain product and, consequently, persistent stock outs for the other one.