Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint
Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint
复制标题
库存约束下非参数动态定价的近最优二分搜索
DOI：
10.2139/ssrn.2509425
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Amitabh Sinha
中科院分区：
文献类型：
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作者：
Y. Lei;Stefanus Jasin;Amitabh Sinha
本文研究了一类具有库存约束和未知噪声需求函数的单产品收益管理问题。公司的目标是动态调整价格，以最大限度地提高总预期收益。我们限制我们的范围，以非参数的方法，我们只假设一些常见的规律性条件的需求函数，而不是一个特定的功能形式。我们提出了一个家庭的定价策略，成功地平衡勘探和开发之间的权衡。我们的想法是推广经典的二分法搜索方法的问题，同时受到随机噪声和库存约束。我们的算法扩展了二分法，以产生一个序列的定价区间，收敛到最优静态价格的高概率。使用遗憾（收入损失相比，确定性定价问题的千里眼）作为性能指标，我们表明，我们的一个appropriatics完全匹配的理论渐近下限，已被证明为任何可行的定价启发式。虽然研究结果是在收入管理问题的背景下提出的，但我们对学习随机优化的二分法的分析可以潜在地应用于其他应用领域。
We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the firm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a specific functional form. We propose a family of pricing heuristics that successfully balance the tradeoff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is affected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.