Optimal depot locations for humanitarian logistics service providers using robust optimization

When a disaster strikes an area, often international assistance is requested to help responding to and recovering from the disaster. The response is often characterized by the dispatch of relief items to the affected regions via depots from Humanitarian Logistics Service Providers (HLSPs). One of the challenges an HLSP faces is how to organize its network of depots. Important questions are how many depots should be opened and what should their locations be? We develop a method that uses historical data to determine depot locations that minimize the cost of transportation and minimize the maximum response time to a disaster. We examine the trade-off between the two objectives using the Pareto front. Furthermore, we use robust optimization to find solutions that are robust against uncertainty in the location and scale of future disasters. We provide a case study of the United Nations Humanitarian Response Depot (UNHRD), a large globally operating HLSP. Among other things, we compute potential cost savings that could be obtained when expanding the network with additional depots. Also, we show the need for using robust optimization when looking for solutions that are robust against the location and scale of future disasters. We generalize the approach by applying it to the independent disaster database EM-DAT, in which we focus on examining the added value of using a robust optimization framework. The first result holds for all Uncapacitated Facility Location Problems (UFLP) with uncertain demand, which are used to find the optimal number of depots. We conclude that incorporating the likely advantage of larger networks having less uncertainty in the expected cost of transportation, enhances the decision-making regarding the optimal number of depots. Even if at some point increasing the number of depots allowed to be opened may not decrease the expected cost of transportation significantly, it is likely to reduce the uncertainty in this expected cost of transportation. For the second result, we consider UFLP used for finding optimal locations of a given number of depots. We conclude that solutions based on nominal and robust optimization may perform similar on individual years that are not included in the optimization, but robust solutions guarantee a smaller cost of transportation for worst case scenarios. This uncertainty reduction is especially valuable when the solution has to be robust against extreme scenarios.