Optimal Dynamic Pricing for Two Perishable and Substitutable Products

This thesis presents a dynamic pricing model where a seller offers two types of a generic product to a random number of customers. Customers show up sequentially. When a customer arrives, he will —depending on the prices—either purchase one unit of type 1 product or one unit of type 2 product, or will leave empty-handed. The sale ends either when the entire stock is sold out, or when the customers are exhausted. The seller’s task is to post the optimal prices for the two product types to each customer to maximize the expected total revenue. We use dynamic programming to formulate this problem, and derive the optimal policy for special cases. For general cases, we develop an algorithm to approximate the optimal policy and use numerical examples to demonstrate the efficiency of the algorithm. Finally, we apply the results to a continuous-time model where customers arrive according to a Poisson process. We develop a heuristic policy and use numerical examples to show the heuristic policy is very effective.