An integrative location-allocation model for humanitarian logistics with distributive injustice and dissatisfaction under uncertainty

Humanitarian logistics is an integral part of disaster relief operations, which involves the phases of preparedness, disaster operations, and post-disaster operations. Integrating the planning and execution between phases minimizes the gaps in providing relief to the affected population. This paper presents a two-stage multi-objective mathematical model for integrated decision-making during the preparation and response phases. The proposed model is developed to jointly optimize the location of emergency shelters (and/or depots) and coordinate the movement of relief vehicles between the disaster site and emergency shelters. Focusing on the optimal distribution of relief supplies to the emergency shelters, the proposed model aims to minimize the operational, distributive injustice, and dissatisfaction costs. To address the computational complexity of the introduced model, two multi-objective meta-heuristics, namely multi-objective vibration damping optimization and non-dominated sorting genetic algorithm (NSGA-II), are used. A comprehensive sensitivity analysis is conducted to study the impacts of variations in key parameters on model output under different scenarios. Our results suggests that the employed solution algorithms outperform the traditional optimization methods in achieving the Pareto-Front solutions.