Inventory-Allocation Distribution Models for Postdisaster Humanitarian Logistics with Explicit Consideration of Deprivation Costs

This paper develops novel mathematical models to maximize the benefits derived from the distribution of critical supplies to populations in need after a disaster. The formulations are based on welfare economics and the use of social costs, which are incurred by the segments of society involved in, and impacted by, the relief distribution strategy. The costs to the relief group are assessed as logistical costs, whereas the impacts to the beneficiaries are measured as the effects that the relief distribution has on their deprivation costs, which are the economic value of human suffering resulting from the lack of access to a good or service. The impacts on beneficiaries take into account two components: the reduction in deprivation costs for the recipients of the aid and the increase in deprivation costs for those individuals who do not receive the aid at a delivery epoch (the opportunity costs of the delivery strategy). The paper develops an inventory‐allocation‐routing model for the optimal assignment of critical supplies that minimizes social costs, designs suitable heuristic solution approaches, and assesses the performance of the heuristics using numerical experiments. The results, coupled with the insight gained from the models developed, are used to establish conclusions and policy recommendations.