A bi-objective mixed-integer non-linear programming model with Grasshopper Optimization Algorithm for military-based humanitarian supply chains

Military systems have many components, such as garrisons, border guards, and industries with a large population that may be affected by disasters. Garrisons, hospitals, clinics, and other facilities in military systems are needed to reduce human casualties. However, these facilities may not have enough resources to handle the disruption. There is no mathematical model to manage disasters with military systems including garrisons and border guards as relief forces interacting with non-military medical centers. This study develops a model for coordinating humanitarian supply chains and logistics within the military system. The affected military sites (AMSs) are military hospitals, clinics, industries, airports, military organizational settlements, garrisons, and border guards. A bi-objective mixed integer non-linear programming model is developed to minimize total costs during pre- and post-disaster planning, a weighted average of injury time in military vehicles, and total delay in relief items (RIs) distribution and rescue operations. For small and medium test problems, GAMS software is used, and for large test problems, the Grasshopper Optimization Algorithm (GOA) is proposed. We conducted some numerical examples to demonstrate the proposed model's efficiency and feasibility and evaluate the metaheuristic. Sensitivity analyses are conducted to evaluate model behavior under various conditions.