Optimal Deployment of Emergency Supply Inventory for Recurring Disasters with a Humanitarian Relief Objective

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We consider the pre-positioning of emergency supply inventories (ESIs) for recurring disasters such as floods and hurricanes, and investigate the optimal allocation policy with the objective of minimizing the expected total unmet demand. Different from the previous literature that has considered only the static processes of ESI requirements and deployment, in this study, we model them as dynamic processes: the arrival epochs of the ESI at the disaster-affected location(s) from the supply network are part of a dynamic process and the corresponding demand for the ESI is a time-dependent stochastic process. We characterize the matching process between the delivery of the ESI after the landfall of the disaster and the corresponding demand arrival process to derive the total unmet demand.Based on a stylized two-location example, we show that it can be optimal to pre-position more ESI at locations with a smaller disaster-affected population size and/or with a smaller inventory survival rate. The optimal allocation depends on the demand arrival process, lead time and pre-positioned inventory survival rate. We then apply our model to a large-scale humanitarian relief operation case, as in Rawls and Turnquist (2010). Based on the data provided, we compute the optimal pre-positioning decisions for three types of ESIs: water, food, and medical supplies. We find that both the optimal ESI pre-positioned at a particular location and the number of locations that pre-position a positive amount of ESI may decrease with the level of total available ESI. We also find that the optimal ESI pre-positioned at a location can decrease in its own inventory survival rate. Last, we compare our case results with those computed via the static model. We find that our model and algorithms can substantially improve the effectiveness of the ESI pre-positioning.