Dynamic pricing of durable products with heterogeneous customers and demand interactions over time

• Dynamic pricing model with heterogeneous customers and demand interactions over time.
• Four different heuristics are proposed for the solution of the dynamic program.
• A decomposition based heuristic (DH) that relaxes a constraint performs the best.
• DH provides more than 25% better results than a myopic pricing strategy.
• Optimal prices converge to a fixed price as the population gets larger.

In this study, we analyze a dynamic pricing problem in which the demand is interdependent over time and the customers are heterogeneous in their purchasing decisions. The customers are grouped into different classes depending on their purchase probabilities and the customer classes evolve over time depending on the demand realizations at every period, which are a function of the prices set by the company. To decide on the optimal prices at every period, we model this problem using a stochastic dynamic program (SDP) and we develop several approximation algorithms to solve this SDP since the size of the state space of the SDP makes the optimal solution almost impossible to find. We present the efficiencies of the heuristics and provide managerial insights through a computational study in which we compare the revenues obtained with each heuristic with an upper bound value that we find on the optimal revenues.