The objective of markdown optimization is to find a monotonically decreasing sequence of merchandise prices that maximizes the revenue subject to inventory constraint and demand dependence on time, price and inventory level. This article examines the adverse effect of inventory depletion on the consumer demand also known as broken-assortment effect. Using certain popular demand models, we derive a closed-form analytical solution for optimal price as a function of time. On the basis of this solution, we propose an open-loop discrete time price policy with prices selected from a predefined set. The policy is evaluated with real-life sales data by computing associated regret measures.