In recent years, we have witnessed an increased adoption of existing dynamic pricing strategies and their further development. We analyze the optimal design of a markdown pricing mechanism, a form of dynamic pricing, in which the price decreases over time according to a pre-announced schedule. In the presence of limited supply, buyers who choose to purchase at a lower price may face a scarcity in supply. Our focus is on the structure of the optimal markdown mechanisms in the presence of rational or "strategic" buyers. We first examine a complete information setting where each customer demands multiple units. We then generalize our analysis to incomplete information settings where each customer's own valuation/demand is private information to that customer. Under complete and incomplete information settings, we compare the seller's profits resulting from the optimal markdown prices and the optimal single price.