基于Logit离散选择模型的品类优化问题综述

品类优化问题(Assortment Optimization Problem)是收益管理的经典问题.它研究零售商在满足运营约束的前提下,应如何从给定产品集合中选择一个子集提供给消费者,以最大化预期收益.该问题的核心在于如何准确地刻画消费者在面对细分产品时的选择行为、建立相应的优化模型并设计高效率的求解算法.基于Logit离散选择模型的品类优化问题:首先,介绍了基于Multinomial Logit模型的品类优化问题.然后介绍了两个更复杂的变种:第一个是基于两层以及多层Nested Logit模型的品类优化问题,这类问题可合理刻画细分产品之间的"替代效应";第二个是基于Mixtures of Multinomial Logits模型的品类优化问题,这类问题可充分考虑消费者群体的异质性.随后,介绍了数据驱动的品类优化问题的相关进展.最后,指出该问题未来可能的若干研究方向.

A survey of assortment optimization problems under logit-based discrete choice models

The assortment optimization problem is a classical problem in revenue management. In this problem, the retailer has to determine the subset of products to offer from a much larger set, so as to maximize the expected revenue subject to operational constraints. The core of this problem is how to characterize customers' choice behavior among differentiated products, develop optimization models, and design efficient solution algorithms. In this paper, we review existing studies on assortment optimization problems under logit-based discrete choice models. We first introduce assortment optimization problem based on the multinomial logit model. Next, we cover two advanced variants: (1) The first variant is based on the two-leve or multi-level nested logit models, which are able to take into consideration the substitution effects among differentiated products; and (2) The second variant is based on the mixtures of multinomial logits model, which can capture the heterogeneity among customers. Then, we cover the data-driven assortment optimization problem under rank-based non-parametric model. Finally, we outline possible directions for future research.