据MS官网显示，来自东南大学的张恺人、香港中文大学的高翔宇和周翔、南开大学的王湛越，合作的论文“Sampling-Based Approximation for Series Inventory Systems”在国际管理学顶刊《Management Science》线上正式发表。
Title: Sampling-Based Approximation for Series Inventory Systems
基于抽样的多级库存系统近似算法
张恺人
东南大学
高翔宇
香港中文大学
王湛越
南开大学
周翔
香港中文大学
We study inventory management of an infinite-horizon, series system with multiple stages. Each stage orders from its immediate upstream stage, and the most upstream stage orders from an external supplier. Random demand with unknown distribution occurs at the most downstream stage. Each stage incurs inventory holding cost while the most downstream stage also incurs demand backlogging cost when it experiences inventory shortage. The objective is to minimize the expected total discounted cost over the planning horizon. We apply the sample average approximation (SAA) method to obtain a heuristic policy (SAA policy) using the empirical distribution function constructed from a demand sample (of the underlying demand distribution). We derive an upper bound of sample size (viz., distribution-free bound) that guarantees that the performance of the SAA policy be close (i.e., with arbitrarily small relative error) to the optimal policy under known demand distribution with high probability. This result is obtained by first deriving a separable and tight cost upper bound of the whole system that depends on (given) echelon base-stock levels and then showing that the cost difference between the SAA and optimal policies can be measured by the distance between the empirical and the underlying demand distribution functions. We also provide a lower bound of sample size that matches the upper bound (in the order of relative error). Furthermore, when the demand distribution is continuous and has an increasing failure rate (IFR), we derive a tighter sample size upper bound (viz., distribution-dependent bound). Both distribution-free and distribution-dependent bounds for the newsvendor problem, a special case of our series system, improve the previous results. In addition, we show that both bounds increase polynomially as the number of stages increases. The performance of SAA policy and the sample size bounds are illustrated numerically. Finally, we extend the results to finite-horizon series systems.
本文研究具有多个阶段的无限期多级库存系统的库存管理问题。每个阶段从其直接上游阶段订货，而最上游阶段从外部供应商订货。在最下游阶段会出现分布未知的随机需求。每个阶段都会产生库存持有成本，而当最下游阶段出现库存短缺时，还会产生缺货积压成本。目标是在规划期内使期望总折扣成本最小化。本文应用样本平均近似（SAA）方法，利用从（潜在需求分布的）需求样本构建的经验分布函数来获得一种启发式策略（SAA 策略）。本文推导出样本量的一个上限（即无分布界限），该上限保证在已知需求分布的情况下，SAA 策略的性能以高概率接近（即相对误差可任意小）最优策略。这一结果的得出，首先是通过推导整个系统的一个可分离且紧密的成本上限，该上限取决于（给定的）层级基本库存水平，然后表明 SAA 策略与最优策略之间的成本差异可以通过经验需求分布函数与潜在需求分布函数之间的距离来衡量。本文还给出了样本量的下限，该下限与上限在相对误差量级上相匹配。此外，当需求分布是连续的且具有递增失效率（IFR）时，本文推导出一个更紧的样本量上限（即依赖分布的界限）。对于报童问题（本文多级库存系统的一个特殊情况），无分布界限和依赖分布的界限都改进了先前的结果。另外，本文表明这两个界限都随着阶段数的增加呈多项式增长。通过数值示例说明了 SAA 策略的性能以及样本量界限。最后，本文将结果扩展到有限期多级库存系统。
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