Optimizing Collaboration: An Integrated Approach to Cost and Carbon Emission-Based Incentive Allocation in LTL Shipping

Linear programming (LP) model, in conjunction with cooperative game theory (CGT), can be utilized to allocate benefits, encompassing cost savings and reduced carbon emissions, among collaborating companies engaged in lessthan-truckload (LTL) shipping. This approach allocation adopts the nucleolus solution concept and solves it as a single joint LP, that enforces fairness with regard to completeness, marginality, and rationality, which serve as constraints. The nucleolus offers a stable and equitable solution among the participating companies, serving as the players, and showcasing all possible strategic alternatives. This ensures the rationale that no company can gain more by breaking away to form a separate group, and no player subsidizes another, guaranteeing the recognition of all marginal contributions. Additionally, it ensures the appropriate allocation of the complete benefit by maximizing the gains of the least satisfied coalition (strategic alternative) in lexicographical order, thereby minimizing the propensity for each coalition to disrupt collaboration. The order serves as an incentive structure, striking a balance between cost optimization and the reduction of carbon emissions. The proposed LP-CGT model presented in this study will function as a decision support tool for companies, demonstrating the measurable benefits of collaboration. This involves defining the characteristic function of all strategic alternatives in the cooperative game to estimate the measurable benefits. In doing so, this work provides a transparent framework for joint allocation, encouraging careful consideration among companies engaged in collaborative shipping initiatives with the proposed approach serving as an efficient allocation tool.