多产品个性化定价的界限与启发式算法
Bounds and Heuristics for Multi-Product Personalized Pricing
摘要：
我们提出了个性化的，多产品定价问题的紧边界和算法。在温和的条件下，我们表明，在一个积极的向量的方向上的最佳价格的利润，保证至少是大的一小部分，从最佳个性化定价的利润。对于无约束问题，分数取决于因素和不同客户类型的最优价格向量。对于约束问题，因子取决于因子和约束的比率。使用具有相等分量的因子向量会导致一致定价，并且具有非常温和的充分条件来保持界限。一个强大的因素，实现了最佳的性能保证。作为一个应用程序，我们的模型产生了一个严格的下限的线性定价相对于最佳个性化的非线性定价的性能，并建议有效的非线性价格策略相对于个性化的解决方案。此外，我们的模型提供了简单的策略，如最佳个性化的混合捆绑定价的尺寸定价和组件定价的保证。启发式集群客户类型也开发了提高性能的目标，允许每个集群价格沿自己的因素。数值结果的各种需求模型，说明使用的经济因素和强大的因素为每个集群之间的权衡，以及使用聚类启发式与最坏情况下的性能为2和机器学习聚类算法之间的权衡。在我们的实验中，经济动机因素加上机器学习聚类算法表现最好。
英文摘要：
We present tight bounds and heuristics for personalized, multi-product pricing problems. Under mild conditions we show that the best price in the direction of a positive vector results in profits that are guaranteed to be at least as large as a fraction of the profits from optimal personalized pricing. For unconstrained problems, the fraction depends on the factor and on optimal price vectors for the different customer types. For constrained problems the factor depends on the factor and a ratio of the constraints. Using a factor vector with equal components results in uniform pricing and has exceedingly mild sufficient conditions for the bound to hold. A robust factor is presented that achieves the best possible performance guarantee. As an application, our model yields a tight lower-bound on the performance of linear pricing relative to optimal personalized non-linear pricing, and suggests effective non-linear price heuristics relative to personalized solutions. Additionally, our model provides guarantees for simple strategies such as bundle-size pricing and component-pricing with respect to optimal personalized mixed bundle pricing. Heuristics to cluster customer types are also developed with the goal of improving performance by allowing each cluster to price along its own factor. Numerical results are presented for a variety of demand models that illustrate the tradeoffs between using the economic factor and the robust factor for each cluster, as well as the tradeoffs between using a clustering heuristic with a worst case performance of two and a machine learning clustering algorithm. In our experiments economically motivated factors coupled with machine learning clustering heuristics performed best.
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