The newsboy problem under progressive multiple discounts

Previous research on the newsboy problem is based on the assumption that excess inventory is either discounted once and sold or disposed of. Real world settings, especially in the apparel industry, involve many cases where multiple discounts are used. Under multiple discounts, a retailer has a series of discounts that are progressively used as the product remains on the shelf. In this paper we formulate and solve a newsboy problem with multiple discounts. The new problem is solved with the objectives of (1) maximizing the expected profit and (2) maximizing the probability of achieving a target profit. We show that multiple discounts, when possible, provide higher expected profit than using a single discount. We verify the analytical results using numerical integration and illustrate the results with numerical examples.