Abstract/Summary

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.