We consider a supply chain in which two suppliers compete for supply to a customer. Pricing and delivery-frequency decisions in the system are analyzed by two three-stage noncooperative games with different decision rights designated to the parties involved. The customer first sets the price (or delivery frequency) for each supplier. Then, the suppliers offer the delivery frequencies (or prices) simultaneously and independently. Finally, the customer determines how much demand to allocate to each of the suppliers. We show that delivery frequency, similar to delivery speed in time-based competition, can be a source of competitive advantage. It also allows firms that sell identical products to offer complementary services to the customer because she can lower her inventory with deliveries from more suppliers. In general, higher delivery frequencies lower the value of getting deliveries from the second supplier and therefore intensify price competition. Assuming the cost structures do not change and the suppliers are identical, we show that when the customer controls deliveries, she would strategically increase delivery frequencies to lower prices. The distortion in delivery frequencies is larger and the overall performance of the supply chain is lower when the customer, not the suppliers, controls deliveries. Moreover, the customer is better off under delivery competition, while the suppliers are better off under price competition.