The Focal Multinomial Logit Model: Threshold Effects on Consumer Choice, Assortment, Pricing and Estimation

Problem definition: This paper considers the operations management problems under a newly proposed choice model referred to as a focal multinomial logit (FMNL) model. It generalizes the famous multinomial logit (MNL) model and various well-studied consideration-set choice models and can effectively capture irrational choice behaviors such as the context effect, halo effect, and choice overload, as well as the effect of focality. Methodology/results: We focus on the threshold focal set and various focal parameter settings, including the constant, cardinality, and linear threshold FMNL models, as well as a broader model that satisfies certain regularity conditions and subsumes the above models. We analyze the computational complexity and propose polynomial-time exact or approximation algorithms for assortment optimization problems under different focal parameters. We then characterize the optimal strategy for the joint price and assortment optimization problem. Our investigation into the statistical properties of maximum-likelihood estimators addresses identifiability, consistency, and convergence rates, as well as their implications on operations decisions. We also present a convex mixed-integer nonlinear programming reformulation method that achieves a global optimal estimator for model calibration. Managerial implications: Through extensive numerical experiments on synthetic and real data sets, we demonstrate the efficiency of the proposed algorithms, highlight the issues of model misspecification, and reveal revenue improvement under the family of FMNL models. Our analyses suggest that retailers should consider the impact of focality to potentially improve demand estimation accuracy and operations performance. Funding: L. Guan acknowledges financial support from the Fundamental Research Funds for the Central Universities [Grant 2025CX13014]. K. Nip acknowledges financial support from the National Natural Science Foundation of China [Grant 72571183]. L. Zhang acknowledges financial support from the National Natural Science Foundation of China [Grant 72471156] and the Hong Kong Research Grant Council [Grant GRF 16209923]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0381 .