历史依赖效应下的品类优化
Assortment Optimization Under History-Dependent Effects
AI总结：
本文研究历史品类影响顾客效用时的多期品类优化问题，提出混合整数指数锥规划重构方法和序贯收入排序策略，并给出渐近最优循环策略，通过餐饮数据验证模型能平衡多样性与收入。
摘要：
本文研究当顾客效用依赖于历史品类时如何规划多期品类。我们将该问题建模为一个非线性整数规划模型，并证明在存在负向历史依赖效应（如饱和效应）时该问题是NP难的。我们构建了在历史依赖效应可能为正负混合的一般设定下获得全局最优解的求解方法。我们提出使用基于提升的框架将该问题重构为混合整数指数锥规划，从而可由最先进的求解器直接求解。我们还设计了一种序贯收入排序策略，并证明当历史品类对顾客效用产生正向影响（如成瘾效应）时，该策略可在多项式时间内求得最优解。此外，我们针对渐近情形识别出一种最优循环策略，并将其周期长度与顾客的记忆长度联系起来。最后，我们利用一个餐饮服务数据集进行了案例研究，结果表明我们的模型具有良好的拟合性，并能有效平衡多样性与收入。
英文摘要：
This paper examines how to plan multi-period assortments when customer utility depends on historical assortments. We formulate this problem as a nonlinear integer programming model and show it is NP-hard in the presence of a negative history-dependent effect (such as a satiation effect). We build solution methodologies for obtaining global optimal solutions under a general setting that the history-dependent effects could be a mixture of positive and negative. We propose using a lifting-based framework to reformulate the problem as a mixed-integer exponential cone program that state-of-the-art solvers can solve. We also design a sequential revenue-ordered policy and show that it solves our problem to optimality in polynomial time when historical assortments positively affect customer utility (such as an addiction effect). Additionally, we identify an optimal cyclic policy for an asymptotic regime, and we also relate its length to the customer's memory length. Finally, we present a case study using a catering service dataset, showing that our model demonstrates good fitness and can effectively balance variety and revenue.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
