We address the lead time quotation problem of a manufacturer serving multiple customer classes. Customers are sensitive to the quoted lead times and the manufacturer has the flexibility to keep inventory to improve responsiveness. We model the problem as a Markov decision process and characterize the optimal lead time quotation, rationing, and production policies. We then define internal and external service level measures and analyze the impact of inventory keeping decision on these measures. Before analyzing the impact, we first derive the relation between inventory level and lead time quotes. We then show that the effect of inventory level on the service levels may not follow the intuition. We also study alternative lead time quotation and production schemes. We contrast the performance of these alternative policies with that of the optimal policy. Specifically, through a numerical study, we quantify the value of controlled arrivals and customer rejection, the value of information on customer status, and the value of a far-sighted policy. Through the numerical study, we also identify the effect of revenue mix and demand mix on the inventory keeping decisions and the performance measures. Finally, we measure the impact of lead time quotation on resource pooling (i.e., inventory and capacity pooling). We show that the value of resource pooling is limited under the optimal policy, since lead time quotation is already effective in balancing the demand with capacity, and in allocating the resources among different customer classes.