[论文解读] Asymptotic optimality of Tailored Base-Surge policies in dual-sourcing inventory systems

Linwei Xin, David A. Goldberg|arXiv (Cornell University)|Mar 3, 2015

Supply Chain and Inventory Management参考文献 61被引用 26

一句话总结

本文证明了当常规（慢，便宜）供应商的提前期趋于无穷大，而快速（快，昂贵）供应商的提前期保持固定时，定制化基量-追加（TBS）策略在双源采购库存系统中渐近最优。作者通过新颖的凸性论证、消失折扣因子法以及排队论，建立了这一结论的理论基础，为TBS策略在实践中表现出的优异性能提供了理论支持。

ABSTRACT

Dual-sourcing inventory systems, in which one supplier is faster (i.e. express) and more costly, while the other is slower (i.e. regular) and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize due to the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for over 40 years. Recently, so-called Tailored Base-Surge (TBS) policies have been proposed as a heuristic for the dual-sourcing problem. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the express source follows a simple order-up-to rule. Numerical experiments by several authors have suggested that such policies perform well as the lead time difference between the two sources grows large, which is exactly the setting in which the curse of dimensionality leads to the problem becoming intractable. However, providing a theoretical foundation for this phenomenon has remained a major open problem. In this paper, we provide such a theoretical foundation by proving that a simple TBS policy is indeed asymptotically optimal as the lead time of the regular source grows large, with the lead time of the express source held fixed. Our main proof technique combines novel convexity and lower-bounding arguments, an explicit implementation of the vanishing discount factor approach to analyzing infinite-horizon Markov decision processes, and ideas from the theory of random walks and queues, significantly extending the methodology and applicability of a novel framework for analyzing inventory models with large lead times recently introduced by Goldberg and co-authors in the context of lost-sales models with positive lead times.

研究动机与目标

• 为定制化基量-追加（TBS）策略在双源采购库存系统中表现出的优异经验性能提供理论依据。
• 解决长期悬而未决的开放问题：为何当双源之间提前期差异较大时，TBS策略表现良好？
• 将大提前期分析方法从缺货模型扩展至双源采购模型，克服维度灾难问题。
• 证明当常规供应商的提前期趋于无穷大时，一种简单的TBS策略渐近最优。
• 为适用于其他具有大延迟的复杂库存系统的新型分析框架奠定基础。

提出的方法

• 作者采用新颖的凸性论证，通过单源采购问题对最优成本进行下界估计。
• 应用消失折扣因子方法，分析大提前期下的无限时域马尔可夫决策过程（MDP）。
• 证明过程结合了随机游走和排队论工具，以刻画提前期增加时系统的行为。
• 关键步骤是显式构造一个最优成本的下界，该下界在极限情况下与TBS策略的性能一致。
• 分析聚焦于渐近情形：常规供应商的提前期趋于无穷大，而快速供应商的提前期保持固定。
• 该方法将先前在缺货模型上的研究扩展至双源采购系统，调整技术以处理双源采购和基量-追加机制。

实验结果

研究问题

• RQ1 为何当提前期差异较大时，TBS策略在双源采购系统中表现如此出色？
• RQ2 是否存在理论基础，说明TBS策略在常规提前期增长时渐近最优？
• RQ3 消失折扣因子方法能否扩展至具有复杂提前期结构的双源采购模型？
• RQ4 如何结合凸性与排队论，对大提前期库存系统中的最优成本进行界定？
• RQ5 在高维库存MDP中，简单启发式策略如TBS在多大程度上可实现近似最优性能？

主要发现

• 当常规供应商的提前期趋于无穷大，而快速供应商的提前期保持固定时，TBS策略渐近最优。
• TBS策略与真实最优策略之间的最优性差距在常规提前期极大时趋于零。
• 证明建立了最优成本的下界，该下界在渐近情形下与TBS策略的成本一致。
• 该方法成功地将大提前期分析框架从缺货模型扩展至双源采购模型。
• 研究结果为工业界广泛采用TBS策略提供了理论依据。
• 该方法为分析其他具有大延迟和高维性的复杂库存系统开辟了新路径。