动态定价中的跨期价格约束：价格单调性与促销疲劳下的性能保证
Inter-Temporal Price Constraints in Dynamic Pricing: Performance Guarantees Under Price Monotonicity and Promotion Fatigue
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中文总结 AI 辅助
针对跨期价格约束下的动态定价问题，提出基于流体近似的最优解采样价格路径的策略，满足价格单调性和促销疲劳约束，并在大容量下保证至少一半的最优期望收入。
中文摘要 AI 辅助
我们研究在跨期价格约束下的动态定价问题。我们拥有容量有限的资源。在每个时间段，我们决定提供哪些产品以及为这些产品设定什么价格。产品的销售概率取决于其价格。如果我们售出某个产品，我们获得反映价格的收入，并消耗一组资源的容量。我们处理两种类型的跨期约束。在价格单调性中，产品在不同时间段收取的价格必须是单调的。在促销疲劳中，我们可以在每个固定长度的时间间隔内最多对产品打折一次。计算最优策略是难以处理的。我们使用流体近似来构造策略。传统上，来自流体近似的策略在每个时间段通过遵循流体近似的最优解做出随机决策，但这种随机决策容易违反价格单调性或促销疲劳约束。我们开发了根据流体近似的最优解对价格路径进行采样，同时满足跨期约束的策略。设$c_{\min}$为资源的最小初始容量，$L$为产品使用的最大资源数量，我们的策略具有性能保证$\max\Big\{ \frac{1}{8L}, \\, \frac{1}{2} - \sqrt{\frac{\log c_{\min}}{2 \\,c_{\min}}} - \frac{L}{c_{\min}}\Big\}$。因此，在资源容量较大的情况下，我们的策略保证至少获得最优总期望收入的一半。后者的性能保证是紧的，因为即使资源容量较大，任何策略通常也无法获得超过流体近似最优目标值的一半。我们统一了我们的方法，为扩展到其他跨期价格约束开辟了道路。
英文摘要
We study dynamic pricing problems under inter-temporal price constraints. We have resources with limited capacities. At each time period, we decide which products to make available and what prices to charge for the available products. The sale probability for a product depends on its price. If we make a sale for a product, then we collect a revenue reflecting the price and consume the capacities of a combination of resources. We work with two types of inter-temporal constraints. In price monotonicity, the prices charged for a product at different time periods have to be monotone. In promotion fatigue, we can discount a product at most once over each time interval of a fixed length. Computing the optimal policy is intractable. We use fluid approximations to construct policies. Traditionally, policies from fluid approximations make randomized decisions at each time period by following an optimal solution to the fluid approximation, but such randomized decisions easily violate price monotonicity or promotion fatigue constraints. We develop policies that sample price paths according to an optimal solution to the fluid approximation, while satisfying the inter-temporal constraints. Letting $c_{\min}$ be the smallest initial capacity of a resource and $L$ be the maximum number of resources used by a product, our policies have a performance guarantee of $\max\Big\{ \frac{1}{8L}, \, \frac{1}{2} - \sqrt{\frac{\log c_{\min}}{2 \,c_{\min}}} - \frac{L}{c_{\min}}\Big\}$. Thus, under large resource capacities, our policies are guaranteed to obtain at least half of the optimal total expected revenue. The latter performance guarantee is tight in the sense that no policy can, in general, obtain more than half of the optimal objective value of the fluid approximation even under large resource capacities. We unify our approach to open the path for extensions to other inter-temporal price constraints.
发表机构
- School of Operations Research and Information Engineering, Cornell Tech（康奈尔科技学校运营研究与信息工程学院）
- Marshall School of Business, University of Southern California（南加州大学马歇尔商学院）
机构由 AI 辅助整理，请以论文原文为准。
