On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization
On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization
复制标题
顾客选择模型的（重新调整的）多重尝试逼近及其在品类优化中的应用
DOI：
10.2139/ssrn.2791127
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Stefanus Jasin
中科院分区：
文献类型：
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作者：
Hakjin Chung;Hyun;Stefanus Jasin
受经典的外生需求模型和最近开发的马尔可夫链模型的启发，我们提出了一种基于随机效用的一般客户选择模型的新近似，称为多次尝试模型，其中客户在最终决定不购买任何东西之前可能会考虑几种替代品。我们表明，多次尝试模型的近似误差随着尝试次数呈指数下降。然而，尽管多尝试模型的理论性能很强，但其实证性能却并不令人满意。这促使我们构建多尝试模型的修改，称为重新缩放的多尝试模型。我们证明，当底层真实选择模型是多项式 Logit (MNL) 时，重新调整的 2 次尝试模型是精确的；然而，如果底层的真实选择模型不是 MNL，我们在数值上表明，重新缩放的 2 次尝试模型的近似质量非常接近马尔可夫链模型的近似质量。我们提出的方法的关键特征是可以明确地写出结果的近似选择概率。从实践的角度来看，这允许决策者使用现成的求解器，或借用文献中的现有算法，来解决具有各种现实世界约束的一般分类优化问题。
Motivated by the classic exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the general customer choice model based on random utility called multi-attempt model, in which a customer may consider several substitutes before finally deciding to not purchase anything. We show that the approximation error of multi-attempt model decreases exponentially in the number of attempts. However, despite its strong theoretical performance, the empirical performance of multi-attempt model is not satisfactory. This motivates us to construct a modification of multi-attempt model called re-scaled multi-attempt model. We show that re-scaled 2-attempt model is exact when the underlying true choice model is Multinomial Logit (MNL); if, however, the underlying true choice model is not MNL, we show numerically that the approximation quality of re-scaled 2-attempt model is very close to that of Markov chain model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use off-the-shelf solvers, or borrow existing algorithms from literature, to solve a general assortment optimization problem with a variety of real-world constraints.