双模内容平台中的品类与采购设计

中文摘要 AI 辅助

我们研究提供广告支持访问和订阅访问的数字内容平台的品类与采购设计问题。用户在内容偏好和广告容忍度方面存在异质性，会在两种访问模式或外部选项中自主选择。对于固定的统一订阅价格和广告负载，平台需选择针对每种用户类型和访问模式的特定品类分布，并做出内容家族层面的购买或租赁决策以最大化利润。租赁成本随实际消费量变化，而购买则提供可重复使用的内容库，其成本取决于所有用户类型和模式中产生的最大需求。我们证明该问题是NP难的。随后，我们开发了一种可扩展的近似框架，基于候选购买集、采购耦合的松弛，以及分解为带有单个等式约束的线性规划。这些子问题通过带基数约束的品类优化的对偶二分法求解，之后采用受限主处理恢复原始可行性。该方法可计算最优性间隙边界、可解释的基于阈值的采购启发式算法，且在市场规模和网格分辨率增加时，在比例市场缩放条件下具有渐近最优性。数值实验表明，其在中等市场规模和网格尺寸下表现优异。

英文摘要

We study assortment and procurement design for a digital content platform offering both ad-supported and subscription access. Users are heterogeneous in content preferences and ad tolerance and self-select between the two modes or an outside option. For a fixed common subscription price and ad load, the platform chooses assortment distributions specific to each user type and access mode, together with content-family-level buy-versus-rent decisions to maximize profit. Rental costs scale with realized consumption, whereas buying provides a reusable pool of titles whose cost depends on the largest induced requirement across user types and modes. We show that the resulting problem is NP-hard. We then develop a scalable approximation framework based on a candidate buy set, a relaxation of the procurement coupling, and a decomposition into linear programs with a single equality constraint. These subproblems are solved by dual bisection with cardinality-constrained assortment optimization, followed by restricted-master postprocessing to recover primal feasibility. The method yields computable optimality-gap bounds, an interpretable threshold-based procurement heuristic, and asymptotic optimality under proportional market scaling as market size and grid resolution increase. Numerical experiments show strong performance at moderate market scales and grid sizes.

发表机构

• IEOR Department, Columbia University（哥伦比亚大学工业工程与运筹学系）

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