Distributional Robustness and Inequity Mitigation in Disaster Preparedness of Humanitarian Operations

Problem definition : In this paper, we study a predisaster relief network design problem with uncertain demands. The aim is to determine the prepositioning and reallocation of relief supplies. Motivated by the call of the International Federation of Red Cross and Red Crescent Societies (IFRC) to leave no one behind, we consider three important practical aspects of humanitarian operations: shortages, equity, and uncertainty. Methodology/results : We first employ a form of robust satisficing measure, which we call the shortage severity measure , to evaluate the severity of the shortage caused by uncertain demand in a context with limited distribution information. Because shortages often raise concerns about equity, we then formulate a mixed-integer lexicographic optimization problem with nonconvex objectives and design a new branch-and-bound algorithm to identify the exact solution. We also propose two approaches for identifying optimal postdisaster adaptable resource reallocation: an exact approach and a conservative approximation that is more computationally efficient. Our case study considers the 2010 Yushu earthquake, which occurred in northwestern China, and demonstrates the value of our methodology in mitigating geographical inequities and reducing shortages. Managerial implications : In our case study, we show that (i) incorporating equity in both predisaster deployment and postdisaster reallocation can produce substantially more equitable shortage prevention strategies while sacrificing only a reasonable amount of total shortage; (ii) increasing donations/budgets may not necessarily alleviate the shortage suffered by the most vulnerable individuals if equity is not fully considered; and (iii) exploiting disaster magnitude information when quantifying uncertainty can help alleviate geographical inequities caused by uncertain relief demands.