Optimal Inventory Policies when Purchase Price and Demand Are Stochastic
Optimal Inventory Policies when Purchase Price and Demand Are Stochastic
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DOI：
10.1287/opre.1100.0862
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Berling;Víctor Martínez-de-Albéniz
中科院分区：
文献类型：
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作者：
P. Berling;Víctor Martínez-de-Albéniz
在本文中，我们考虑一个公司面临随机（泊松）需求并且必须从价格波动的市场（例如商品市场）进行补充的问题。我们将价格演化描述为一个连续的随机过程，并重点关注金融文献中提出的常用过程，例如几何布朗运动和奥恩斯坦-乌伦贝克过程。众所周知，在可变购买价格下，价格依赖的基础油政策是最优的。使用单单位分解方法，我们使用一系列阈值价格明确描述最佳基础库存水平。我们发现，在当前采购价格中，基础油水平先上升后下降。我们提供了计算阈值的过程，当价格遵循几何布朗运动时，该过程会产生封闭式解，并在 Ornstein-Uhlenbeck 价格模型下产生隐式解。此外，我们的数值研究表明，最优策略的表现比忽略未来价格演变的库存策略要好得多，因为当预计价格上涨时，它往往会下更大的订单。
In this paper we consider the problem of a firm that faces a stochastic (Poisson) demand and must replenish from a market in which prices fluctuate, such as a commodity market. We describe the price evolution as a continuous stochastic process and we focus on commonly used processes suggested by the financial literature, such as the geometric Brownian motion and the Ornstein-Uhlenbeck process. It is well known that under variable purchase price, a price-dependent base-stock policy is optimal. Using the single-unit decomposition approach, we explicitly characterize the optimal base-stock level using a series of threshold prices. We show that the base-stock level is first increasing and then decreasing in the current purchase price. We provide a procedure for calculating the thresholds, which yields closed-form solutions when price follows a geometric Brownian motion and implicit solutions under the Ornstein-Uhlenbeck price model. In addition, our numerical study shows that the optimal policy performs much better than inventory policies that ignore future price evolution, because it tends to place larger orders when prices are expected to increase.