Assortment Optimization under the Generalized Markov Chain Choice Model

Abstract

This paper addresses the assortment optimization problem under the Generalized Markov Chain (GMC) choice model, which captures complex customer choice behaviors through an exogenous and flexible stopping probability function. The GMC model extends the traditional Markov Chain (MC) model by allowing customers to probabilistically choose whether to make a purchase or continue browsing after viewing an item, providing a more realistic framework for assortment decisions. We investigate both the unconstrained and cardinality-constrained assortment optimization problems, proposing exact and approximation algorithms tailored to the GMC setting. For the unconstrained problem, we develop an improved value iteration algorithm and an adjusted-price algorithm, both demonstrating superior computational efficiency and reduced iteration counts compared to existing methods. For the cardinality-constrained problem, we adapt a constant-factor approximation algorithm and introduce a bidirectional greedy algorithm that leverages the complementary strengths of forward and backward iterations. Numerical experiments validate the practical effectiveness of the proposed algorithms, showing significant improvements in solution quality and running time compared to baseline methods. Our work contributes to the theoretical and methodological advancement of assortment optimization, with applications in e-commerce, retail, and resource-constrained decision-making scenarios.

Keywords: assortment optimization, generalized Markov chain choice model, discrete choice model