Fair Allocation Mechanisms for Logistic Resources in Multi-Issue Bankruptcy with Cross-Claims

This study proposes a fair allocation framework for logistics settings in which multiple agents share scarce resources, routes, or operational capacities under interdependent constraints. To this end, it applies the Multi-Issue Bankruptcy Problem with Cross-Claims (MBC) model to the field of cooperative logistics. The study shows that the MBC framework provides a rigorous way to represent allocation problems arising when multiple agents simultaneously claim the same logistics capacity across multiple states. The Constrained Equal Awards (CEA) rule is adapted and implemented within this setting through an iterative linear programming procedure. The approach is illustrated through a real case study applaied in the departament of Magdalena, Colombia, and complemented with comparative analyses under Proportional-MBC, a simplified Constrained Equal Losses (CEL)-inspired benchmark, and alternative claimant-state structures. The comparative analysis shows that the proposed CEA–MBC method achieves the highest average satisfaction rate while fully utilizing all four available states. It was also found that the Proportional–MBC method allocates a slightly larger amount of resources and attains the highest Jain’s Fairness Index; nevertheless, both MBC-based approaches substantially out-perform the CEL benchmark, which leaves the highest unmet demand and fully utilizes only two states. These findings demonstrate that the proposed the proposed framework yields feasible and distributively meaningful allocations while offering a useful methodological basis for designing more equitable and collaborative logistics systems.

Allocation rules; Bankruptcy theory; Constrained equal awards rule; Constrained equal loses; Game theory; Logistics cooperation; Proportional MBC rule

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