A Unified Analysis for Assortment Planning with Marginal Distributions

We study assortment problems under the marginal distribution model (MDM), a semiparametric choice model that only requires marginal error information without assuming independence. It is known that the multinomial logit (MNL) model belongs to MDM. In this paper, we further show that some multi-purchase choice models, such as the multiple-discrete-choice (MDC) model, and threshold utility model (TUM), also fall into the framework of MDM, although MDM does not explicitly model multi-purchase behavior. For the assortment problem under MDM, we characterize a general condition for the marginal distributions under which a strictly profit-nested assortment is optimal. Moreover, though the problem is shown to be NP-hard, we prove that the best strictly profit-nested assortment is a 1/2-approximate solution for all MDMs. We further construct a simple case of MDM such that the 1/2-approximate bound is tight. These results either generalize or improve existing results on assortment optimization under MNL, MDC, and TUM