Robust Optimization of Facility Location Models and Fundamental Resource Estimations under Demand Uncertainty: A Case Study of Relief Distribution

Humanitarian logistics are recognized as significant issues of natural disaster operations and management. This study considers the vital item distribution network models to relieve the large number of surviving victims under their uncertainty by the reason that the post-disaster undergoes fluctuation of demand and imprecise prediction. The purpose of this study is to handle this demand uncertainty with the facility location model and to compare their sensitivity with the deterministic model. The expected results are to explore the location of facilities and optimize transportation link flows in order to minimize total delivery cost, which includes travel, facility and transhipment costs. We propose three distinct network models based on their hierarchy structures and truck sizes to determine the most efficient model with high robustness for both deterministic demand and uncertainty demand. We determine a single hierarchy and double hierarchies of the facility sites; each hierarchy is then distributed by the distinct truck sizes. The two hierarchies with the large truck’s delivery offered preferable objectives; they are robust when demand becomes uncertain or unknown. We solve the problem by the ellipsoidal uncertainty set, which is a novel approach that has never been fully applied so far to solve the facility location. We also estimate the fundamental resource requirements, including the number of trucks and total working time of drivers. Therefore, this study can help the decision maker to plan for post-disaster distribution network and their systems when demand uncertainty occurs.