解决有限混合Logit模型下的受限定价问题，可高效求解多客户群体场景。
Constrained Pricing under Finite Mixtures of Logit
- 将受限定价重构成指数锥双线性规划，提升求解效率。
- 当客户群体数固定时，可获得任意精度的近似最优解。
- 适合需要考虑价格约束的实际商业定价场景。
混合Logit模型是定价与收益管理中灵活且广泛应用的需求模型。然而，现有研究大多关注无约束情形，限制了其在实际业务或监管约束下的应用。本文研究了多类别Logit及有限混合Logit需求下的受限定价问题。对于单客户群体的多项式Logit模型，通过指数锥规划重构，证明存在多项式时间近似方案（PTAS），可在多项式时间内获得ε-最优解。对于包含T个客户群体的有限混合Logit模型，将问题重构为含O(T)个双线性项的指数锥双线性规划，进而设计分支定界算法，其复杂度仅在T上指数增长。因此，当客户群体数有界时，该问题同样具有PTAS。数值实验表明，该方法性能优于当前主流基线。
原文摘要 · Abstract (English)
The mixed logit model is a flexible and widely used demand model in pricing and revenue management. However, existing work on mixed-logit pricing largely focuses on unconstrained settings, limiting its applicability in practice where prices are subject to business or regulatory constraints. We study the constrained pricing problem under multinomial and mixed logit demand models. For the multinomial logit model, corresponding to a single customer segment, we show that the constrained pricing problem admits a polynomial-time approximation scheme (PTAS) via a reformulation based on exponential cone programming, yielding an $\varepsilon$-optimal solution in polynomial time. For finite mixed logit models with $T$ customer segments, we reformulate the problem as a bilinear exponential cone program with $O(T)$ bilinear terms. This structure enables a Branch-and-Bound algorithm whose complexity is exponential only in $T$. Consequently, constrained pricing under finite mixtures of logit admits a PTAS when the number of customer segments is bounded. Numerical experiments demonstrate strong performance relative to state-of-the-art baselines.
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