Effective Cost Allocation in Agricultural Production Systems Using Absorbing Markov Chains and Bankruptcy Rules

Agricultural production systems are frequently affected by uncertainty, processing cycles, quality variability, and irreversible losses, leading to discrepancies between planned and actually available operational resources. This study proposes an integrated framework combining absorbing Markov chains and bankruptcy allocation theory to address endogenous scarcity in stochastic production systems. The production process is modeled using an absorbing Markov chain, where transient states represent operational stages and absorbing states represent successful completion or irreversible loss. The fundamental matrix is used to estimate the effective expected resource availability induced by the stochastic dynamics of the system. When this availability is insufficient to satisfy nominal operational requirements, the problem is reformulated as a bankruptcy allocation problem. Four classical allocation rules are evaluated and compared: proportional, constrained equal awards, constrained equal losses, and the Talmud rule. A stylized cocoa production system illustrates the proposed framework. The results show that the constrained equal awards and Talmud rules better preserve operational continuity under scarcity conditions. The main contribution lies in linking stochastic production modeling with normative resource allocation under endogenous scarcity.