We introduce inventories into a standard New Keynesian Dynamic Stochastic General Equilibrium (DSGE) 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 decoupling 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. We find that in contrast to a model without inventories, Ramsey-optimal monetary policy in a model with inventories deviates from complete inflation stabilization. In the standard model, nominal price rigidity is a deadweight loss on the economy, which an optimizing policymaker attempts to remove. With inventories, a planner can reduce consumption volatility and raise welfare by accumulating inventories and letting prices change as an equilibrating mechanism. We find also find that the application of simple rules comes very close to replicating Ramsey optimal outcomes.