双源库存系统中定制的基本波动策略的渐近最优性
Asymptotic optimality of Tailored Base-Surge policies in dual-sourcing inventory systems
摘要：
双源库存系统，其中一个供应商速度更快（即快递），成本更高，而另一个供应商速度更慢（即常规），成本更低，在许多现实世界的供应链中自然出现。由于最优解的复结构和维数灾难，这些系统非常难以优化，已经抵抗了40多年的解决方案。最近，所谓的定制基地浪涌（TBS）政策已被提出作为一种启发式的双源问题。在这样的策略下，在每个时段中，在常规源处放置恒定订单，而在快速源处放置的订单遵循简单的订单最多规则。几位作者的数值实验表明，这样的政策表现良好的两个源之间的前置时间差变大，这正是设置中的维数灾难导致问题变得棘手。然而，为这种现象提供理论基础仍然是一个重大的开放问题。在本文中，我们提供了这样一个理论基础，证明了一个简单的TBS政策确实是渐近最优的定期源的提前期增长大，与表达源的提前期固定。我们的主要证明技术结合了新的凸性和下界参数，一个明确的实现消失折扣因子的方法来分析无限时域马尔可夫决策过程，和思想理论的随机游动和队列，显着扩展的方法和适用性的一个新的框架，分析库存模型与大的提前期最近介绍了戈德堡和共同作者的背景下，失去了，销售模式与积极的前置时间。
英文摘要：
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.
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