Joint pricing and procurement of fashion products in the existence of clearance markets

This paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets. It is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution. It is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions. Existence of a clearance market increases the profit, price, and the procurement quantity. In order to prove this, the optimal procurement and pricing policy of a price-setting retailer who does not have a clearance market is provided. As opposed to the literature, it is shown that the expected profit function of this problem is unimodal as well. A numerical study demonstrating the magnitude of the increase in profit, procurement quantity, and price is reported.