Analysis of cross-price effects on markdown policies by using function approximation techniques

Keywords: Approximate dynamic programming Artificial neural networks Cross-price elasticity Markdown optimization Dynamic pricing Aggregation a b s t r a c t Markdown policies for product groups having significant cross-price elasticity among each other should be jointly determined. However, finding optimal policies for product groups becomes computationally intractable as the number of products increases. Therefore, we formulate the problem as a Markov decision process and use approximate dynamic programming approach to solve it. Since the state space is multidimensional and very large, the number of iterations required to learn the state values is enormous. Therefore, we use aggregation and neural networks in order to approximate the value function and to determine the optimal markdown policies approximately. In a numerical study, we provide insights on the behavior of markdown policies when one product is expensive, the other is cheap and both have the same price. We also provide insights and compare the markdown policies for the cases in which there is a substitution effect between products and the products are independent. One important aspect of revenue management or yield management is dynamic pricing of perishable products. The ''perishability'' of the products means that the product has short selling periods (seasonality of the product), during which inventory management and pricing strategies are central while the replenishment of inventory is not allowed. This is a realistic trend since most products such as medicine, dairy products, fast fashion products and chemicals start to deteriorate once they are produced. The inventory of seats on a particular flight, the inventory of rooms at a hotel at a particular night, the tables at the restaurant all perish at certain times. Retailers and service providers have the opportunity to enhance their revenues through optimal pricing of their perishable products that must be sold within a fixed period of time. Therefore, the seller has fixed inventory on hand and must decide on how to price the product over the remaining selling horizon. Ever increasingly shortening selling seasons for apparel products and increasingly more demanding customers who buy them pressure the retail chains to minimize distress inventories and maximize revenues. One of the most commonly used tools to achieve this goal is markdowns. Markdowns are permanent price reductions such that once the price of a product is marked down, it may not be brought up to the same price level again in the same selling season. Existing academic research on …