Cost-Sharing Optimization in Competitive Manufacturing Supply Chains: Integrating Learning–Forgetting Dynamics and Environmental Costs

This study proposes an enhanced model for optimizing cost-sharing strategies in competitive manufacturing supply chains, integrating the effects of learning, forgetting, and sustainable green practices. Building on the foundational framework of a monopolistic competition environment, the research extends the traditional cost allocation between an incumbent manufacturer and a midstream assembly plant by incorporating environmental costs, such as carbon emissions taxes, into the total cost function. The model accounts for learning and forgetting dynamics in both setup and production stages, influencing setup costs, production costs, and inventory holding costs, alongside defensive costs against competitors. A novel sustainability extension introduces an environmental cost component, reflecting the impact of demand-driven emissions under varying cost-allocation rates. Sensitivity analyses demonstrate that a higher rate of competitor entry, reduced dispersion in defensive costs, and elevated learning/forgetting rates increase the optimal cost-allocation rate and total expected cost, with production-stage effects dominating setup-stage impacts. Furthermore, the inclusion of green practices reveals a trade-off, where higher environmental taxes and emission rates lower the optimal allocation to mitigate emissions, albeit at an increased overall cost. Numerical simulations validate the model, offering insights for managers to balance economic efficiency with environmental sustainability in dynamic supply chain contexts.