Resource-Constrained Multi-objective Optimization Model for Global Warming Resilient Emergency Response and Welfare Networks

Abstract

This study introduces an uncertain multi-objective, multi-commodity, multi-period, and multi-vehicle
mixed-integer programming model with social equity designed for the critical response phase of
humanitarian operations. The framework strategically addresses the complexities of disaster relief by
integrating five key echelons: affected regions, distribution centers, hospitals, temporary
accommodation facilities, and temporary care centers. The model is driven by four primary objectives:
the minimization of overall costs associated with facility location, resource allocation, social equity and
crucially, the reduction of relief supply shortages. Uncertainty inherent in disaster scenarios is robustly
managed through a probabilistic scenario-based approach. Significant strategic decisions facilitated by
the model encompass the optimal siting of temporary care and accommodation centers, the efficient
allocation of affected populations to designated centers and hospitals, and the effective distribution of
supplies from major hubs to temporary shelters. Furthermore, the model determines optimal flows for
injured individuals and commodities between facilities, specifies the required number of vehicles for
inter-facility transport, and manages both shortage and inventory levels at all centers. A comprehensive
set of constraints ensures practical applicability, covering aspects such as demand fulfillment, relief
commodity flow, facility capacities, transportation logistics for both people and goods, and the
utilization of backup centers across multiple planning periods.
The developed model’s efficacy was demonstrated through its application to a real-world case
study: the city of Warri and its environs in Nigeria, a region significantly impacted by floods exacerbated
by global warming. To solve this complex problem, three distinct methods were employed: the epsilon-
constraint method, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), and a modified multi-
objective particle swarm optimization (MMOPSO). Perfor- mance analysis, utilizing various multi-
objective evaluation metrics, confirmed the superior performance of MMOPSO. A significant
innovation of this model is its inherent integration of social equity principles, ensuring that the allocation
of resources and services prioritizes the most vulnerable populations within the affected area. A
preferred solution, selected from the MMOPSO-generated non-dominated set based on these equity
considerations and expert judgment, was thoroughly analyzed to exemplify the model’s practical
implications for resilient and equitable disaster response.