We introduce inventories into a standard New Keynesian Dynamic Stochastic General Equilibrium model to study the effect on the design of optimal monetary policy. The possibility of inventory investment changes the transmission mechanism in the model by de-coupling production from final consumption. This allows for a higher degree of consumption smoothing since firms can add excess production to their inventory holdings. We consider both Ramsey-optimal monetary policy and a monetary policy that maximizes consumer welfare over a set of simple interest rate feedback rules. Surprisingly, we find that in contrast to a model without inventories, Ramsey-optimal monetary policy in a model with inventories slightly deviates from complete inflation stabilization, but the welfare differences are minor. Moreover, we also find in line with the existing literature that the application of simple rules comes very close to replicating Ramsey-optimal outcomes.