Constrained Assortment Optimization with Satisficers Consumers

A growing body of research suggests that an abundance of choices can lead to decision-making difficulties for consumers. Rather than maximizing utility, many consumers employ a satisficing decision-making approach, whereby they search for products sequentially until they find one that is satisfactory. In this study, we explore assortment optimization with cardinality constraints for satisficers consumers and compare it to traditional assortment optimization methods. Our findings indicate that, in general, this type of optimization is APX-hard. However, we propose a dependence-relaxation approximation that utilizes last-choice probabilities and guarantees a worst-case approximation ratio of $(1-1/e)$ in $O(nk)$ times. Furthermore, we demonstrate that assortment optimization is NP-hard for satisficers consumers in the context of latent class MNL models. Nevertheless, we provide a fully polynomial time approximation for this scenario. We introduce the concept of last-choice regularity and demonstrate that the seller prefers facing satisficers consumers over maximizers in choice models with this property. Our study also reveals that satisficing decision-making can be a rational strategy within a game-theoretic framework. Additionally, we investigate assortment optimization with impatient satisficers and develop a quasi-polynomial time approximation for the latent class MNL model