Integrating Absorbing Markov Chains and Multi-Issue Bankruptcy Problems with Cross-Claims for Resource Allocation Under Production Uncertainty

Source abstract

Production systems may generate resource scarcity as products progress through production stages that are subject to deterioration, reprocessing, or failure. This study builds upon the integration of absorbing Markov chains with Multi-Issue Bankruptcy Problems with Cross-Claims (MI-MIBC) and develops a method for deriving a multi-resource estate based on the fundamental matrix of a Markov chain and state-specific multi-resource requirements. This method defines a multi-resource allocation problem with connected claims. The resulting MI-MIBC is addressed using Constrained Proportional Awards (CPA), Constrained Equal Awards (CEA), and Constrained Sequential Priority (CSP) rules. This method is illustrated with the postharvest system of Colombian plantains, which consists of money, labor, transportation, and packing resources. The three rules produce different allocation patterns when scarcity is identical. The cross-claims structure may also leave a residual estate even when claims remain unmet. This method interlinks stochastic production systems with multi-resource allocation and derives the estate from the stochastic production model rather than specifying it independently at the allocation stage.