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

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.