Multi-agent multi-objective coordination in humanitarian logistics

Abstract

Humanitarian crises are escalating in both frequency and complexity, placing unprecedented demands on response systems composed of government agencies, non-governmental organizations, and private actors. These entities must coordinate their operations in a decentralized manner under limited resources and often competing objectives. Existing coordination frameworks rely on centralized control or assume alignment of goals, thereby falling short in settings where autonomous decision-makers require assurances of fairness to remain engaged. Addressing this deficiency requires a formal methodology capable of reconciling multiple objectives, preserving incentive compatibility, and quantifying the concessions necessary to sustain coordination. This research advances the body of knowledge in multi-objective multi-agent humanitarian logistics through a sequence of interlinked contributions. First, it delivers a systematic literature review that maps existing work at the intersection of game theory and optimization for coordination in humanitarian contexts. The review categorizes existing studies by modeling approaches, coordination mechanisms, and decision contexts. It identifies four primary coordination mechanisms: resource sharing, information sharing, contracting, and strategic action. The review also reveals the absence of models that consider fairness in decentralized settings with conflicting objectives. Building on the review insights, a new mathematical concept Chebyshev least core is introduced and formalized, extending classical cooperative game theory, to quantify the smallest uniform concession necessary to achieve near-stable outcomes when perfect equity is unattainable. Moreover, a novel mathematical framework is developed by integrating cooperative game theory with multi-objective optimization to enable equitable and sustainable coordination by computing the Chebyshev least core. Specifically, a Cooperative Goal Optimization (CGO) model is proposed to identify fair allocations by minimizing the maximum relative shortfall each actor experiences compared to their stand-alone performance. The model also incorporates the preference core and nondominance core concepts into a single model, allowing practitioners to distinguish solutions that satisfy all imposed conditions from those that involve trade-offs. Computational experiments demonstrate that the CGO approach yields more stable, equitable, and scale-invariant outcomes than conventional allocation rules, and that it accommodates objectives expressed in disparate units without the need for commensurability assumptions. Finally, the framework is validated with a case study using real-world data on hurricane staging-area planning. The case study offers empirical evidence on how coordination mechanisms reshape operational choices in hurricane response. Joint planning alters routing, and pre-positioning decisions to make the disaster response more effective, efficient, and equitable. By applying the developed framework, it is demonstrated that equitable cost and benefit-sharing rules can be constructed so that no organization has an incentive to deviate from coordinated arrangements. Lastly, the study bridges theory and practice by quantifying the exact price of coordination for multi-objective multi-agent relief operations.