A Robust Optimization Methodology for Multi-objective Location-transportation Problem in Disaster Response Phase under Uncertainty

This paper presents a multi-objective model for location-transportation problem under uncertainty that has been developed to respond to crisis. In the proposed model, humanitarian aid distribution centers (HADC), the number and location of them, the amount of relief goods stored in distribution centers, the amount of relief goods sent to the disaster zone, the number of injured people transferred to medical centers and the delivery of relief regarding the limits of capacity for transport, distribution centers and also available time and budget limits are all considered. This work aims at minimizing unfulfilled needs; that is meaning the number of people have not been transferred to medical centers. In order to take the inevitable uncertainty in some parameters into account, the primal deterministic model has been reformulated by applying the robust optimization approach. Also the performance of the both deterministic and robust models are investigated by solving a numerical example. The results of the study show that the robust counterpart of deterministic model will remain feasible with a high probability in reality.