Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.
翻译:在过去几十年里,由于最佳分配办法的实际重要性,最佳分配办法得到了积极的探索。尽管有大量文献涉及优化算法和潜在分数估计,但最佳分配办法的不确定性量化仍需要探讨,而且具有巨大的实际意义。决策者可能只有兴趣测试某一财产是否对最佳分配办法具有真实性,例如它们是否应包括一些对最佳分配办法感兴趣的产品,或最佳分配办法应包括多少类产品。本文提出了测试这类属性的新颖的推断框架。我们考虑了广泛采用的多数值记录模式,我们假设每个客户将在所提供的产品中购买一项物品,其概率与产品的相关基本优惠分数成正比。我们减少一般的最佳分类属性,以量化与标志改变点检测边际收入差距有关的不确定性。我们显示了边际收入差距估计办法的正常性,并通过差距估计办法建立最高统计办法,通过差距估计办法进行最大程度的统计,以检测与产品相关的基本优惠分数;我们减少一般的最佳分配办法,以量化与迹象改变差值有关的不确定性差值;我们还表明边际收入差距估计办法的正常性,并通过差距统计方法进行最大程度的估测算。