Location and Emergency Inventory Pre†Positioning for Disaster Response Operations: Min†Max Robust Model and a Case Study of Yushu Earthquake

Pre†positioning emergency inventory in selected facilities is commonly adopted to prepare for potential disaster threat. In this study, we simultaneously optimize the decisions of facility location, emergency inventory pre†positioning, and relief delivery operations within a single†commodity disaster relief network. A min†max robust model is proposed to capture the uncertainties in both the left†and right†hand†side parameters in the constraints. The former corresponds to the proportions of the pre†positioned inventories usable after a disaster attack, while the latter represents the demands of the inventories and the road capacities in the disaster†affected areas. We study how to solve the robust model efficiently and analyze a special case that minimizes the deprivation cost. The application of the model is illustrated by a case study of the 2010 earthquake attack at Yushu County in Qinghai Province of PR China. The advantage of the min†max robust model is demonstrated through comparison with the deterministic model and the two†stage stochastic model for the same problem. Experiment variants also show that the robust model outperforms the other two approaches for instances with significantly larger scales.