Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints
Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints
复制标题
DOI：
10.1287/mnsc.2020.3657
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Mika Sumida;G. Gallego;Paat Rusmevichientong;Huseyin Topaloglu;J. Davis
中科院分区：
文献类型：
--
作者：
Mika Sumida;G. Gallego;Paat Rusmevichientong;Huseyin Topaloglu;J. Davis
我们研究收入-效用分类优化问题，目标是找到一种分类，使公司的预期收入和客户的预期效用的线性组合最大化。该标准捕捉了以公司为中心的最大化预期收入的目标与以客户为中心的最大化预期效用的目标之间的权衡。客户根据多项 Logit 模型进行选择，并且对所提供的类别存在以完全幺模矩阵为特征的约束。我们证明，通过在按相同常数调整每个产品的收入后找到仅最大化预期收入的分类，我们可以解决收入-效用分类优化问题。找到适当的收入调整需要解决非凸优化问题。我们给出一个参数线性程序来生成候选分类的集合，保证包含收入-公用事业分类优化问题的最佳解决方案。候选分类的集合还允许我们构建一个有效的前沿，当我们改变目标函数的权重时，该前沿显示最佳的预期收入-效用对。此外，我们开发了一种近似方案，可以限制候选类别的数量，同时确保预先指定的解决方案质量。最后，我们讨论涉及完全单模约束的实际分类优化问题。在我们的计算实验中，我们证明我们可以获得预期效用的显着改进，而不会导致预期收入的重大损失。这篇论文被收入管理和市场分析部门的 Omar Besbes 接受。
We examine the revenue–utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utility of the customer. This criterion captures the trade-off between the firm-centric objective of maximizing the expected revenue and the customer-centric objective of maximizing the expected utility. The customers choose according to the multinomial logit model, and there is a constraint on the offered assortments characterized by a totally unimodular matrix. We show that we can solve the revenue–utility assortment optimization problem by finding the assortment that maximizes only the expected revenue after adjusting the revenue of each product by the same constant. Finding the appropriate revenue adjustment requires solving a nonconvex optimization problem. We give a parametric linear program to generate a collection of candidate assortments that is guaranteed to include an optimal solution to the revenue–utility assortment optimization problem. This collection of candidate assortments also allows us to construct an efficient frontier that shows the optimal expected revenue–utility pairs as we vary the weights in the objective function. Moreover, we develop an approximation scheme that limits the number of candidate assortments while ensuring a prespecified solution quality. Finally, we discuss practical assortment optimization problems that involve totally unimodular constraints. In our computational experiments, we demonstrate that we can obtain significant improvements in the expected utility without incurring a significant loss in the expected revenue. This paper was accepted by Omar Besbes, revenue management and market analytics.