Looking Upstream: Optimal Policies for a Class of Capacitated Multi‐Stage Inventory Systems
Looking Upstream: Optimal Policies for a Class of Capacitated Multi‐Stage Inventory Systems
复制标题
向上游看：一类能力多级库存系统的最优策略
DOI：
10.1111/poms.12742
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发表时间：
2017
影响因子：
5
通讯作者：
Wanshan Zhu
中科院分区：
文献类型：
--
作者：
Alexandar Angelus;Wanshan Zhu
我们考虑一个多阶段库存系统，每个阶段都有随机需求和处理能力约束，适用于有限范围和无限范围、贴现成本设置。对于一类以最下游阶段容量最小且系统利用率高于某个阈值为特征的此类系统，我们确定了最优策略的结构，它代表了 order-up-to 策略的一种新颖变体。我们找到了最佳订单级别的显式函数形式，并表明它们（仅）依赖于上游梯队库存。我们确定，在阈值利用率之上，该最优策略实现了系统的多维目标成本函数分解为单维凸函数之和。这种分解消除了维数灾难，使我们能够用数值方法解决问题。我们提供了一种快速算法来确定任意阶段数量的容量受限库存问题的阈值利用率的（严格）上限。我们利用该算法来量化一系列模型参数上的三级、四级和五级容量系统的阈值利用率上限，并讨论出现的见解。
We consider a multi‐stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite‐horizon and infinite‐horizon, discounted‐cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order‐up‐to policy. We find the explicit functional form of the optimal order‐up‐to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single‐dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity‐constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three‐, four‐, and five‐stage capacitated systems over a range of model parameters, and discuss insights that emerge.
DOI：
10.1287/opre.1090.0716
发表时间：
2010-03
期刊：
Oper. Res.
影响因子：
--
作者：
W. T. Huh;G. Janakiraman
通讯作者：
W. T. Huh;G. Janakiraman