Natural disasters have been adversely affecting human societies for many centuries. One effective strategy in preparation for a timely response to such disasters is inventory prepositioning. Holding the right amount of inventory is critical in minimizing the social and economic impact and cost. Scholars usually model such problems assuming common Probability Density Functions (PDFs) like Normal, Poisson, and Exponential to simplify calculations. Following Gumbel’s studies regarding “the nature of nature” and exploring the nature of extreme events, in this research, we address the following research questions: first, do the magnitude and timing of natural disasters follow specific PDFs? Second, how can unrealistic assumptions affect such disasters’ economic and social costs of such disasters? Third, how should researchers and practitioners correct their assumptions when modeling inventory prepositioning? To answer these questions, we design a semi-Markovian model for an (S,s) inventory system that considers the magnitude and the timing of disasters for general PDFs. The model is an inventory system that considers the magnitude and the timing of disasters for general PDFs. The model is analytically solved and tested with real data from 1996 to 2019 regarding typhoons in Florida and earthquakes in California. Our findings show that correct assumptions about the time between disasters are far more critical than the disaster’s magnitude regarding the resulting social and economic costs. In this respect, we can summarize our findings as follows: (1) if the maximum inventory level (S) depends only on the average demand, the impact of assumed PDFs is insignificant; (2) if S depends on both the average and standard deviation (STD) of demand, the impact of the employed PDFs is significant; and (3) the STD is the main factor influenced by the type of the PDF.

中文翻译：

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自然灾害的频率和规模对库存预置的影响


几个世纪以来，自然灾害一直对人类社会产生不利影响。为及时应对此类灾难做准备的一种有效策略是库存预置。持有适量的库存对于最大限度地减少社会和经济影响及成本至关重要。学者们通常假设常见的概率密度函数 （PDF），如正态、泊松和指数，对此类问题进行建模，以简化计算。继 Gumbel 关于“自然的本质”的研究并探索极端事件的性质之后，在这项研究中，我们解决了以下研究问题：首先，自然灾害的规模和时间是否遵循特定的 PDF？其次，不切实际的假设如何影响此类灾害的经济和社会成本？第三，研究人员和从业者在对清单预置进行建模时应该如何纠正他们的假设？为了回答这些问题，我们为 （S，s） 清单系统设计了一个半马尔可夫模型，该模型考虑了一般 PDF 的灾难的规模和时间。该模型是一个清单系统，它考虑了一般 PDF 的灾难规模和时间。该模型使用 1996 年至 2019 年有关佛罗里达州台风和加利福尼亚州地震的真实数据进行分析求解和测试。我们的研究结果表明，关于灾害间隔时间的正确假设远比灾难的严重程度更重要，因为由此产生的社会和经济成本。 在这方面，我们可以将我们的发现总结如下：（1） 如果最大库存水平 （S） 仅取决于平均需求，则假设的 PDF 的影响是微不足道的;（2） 如果 S 同时取决于需求的平均差和标准差 （STD），则采用的 PDF 的影响是显着的;（3） STD 是受 PDF 类型影响的主要因素。