Efficiency and Fairness in Physical Internet Logistics Coordination Under Shared Capacity Constraints

Background: The Physical Internet (PI) promotes resource sharing among independent firms. This can improve logistics efficiency, but shared route capacity and limited compensation may also create unequal outcomes among firms. Methods: This study develops a framework for coordinated logistics planning under shared route capacity constraints. The framework includes two coordination rules. Model 3.3 is an efficiency-oriented participation-guaranteeing rule with individual rationality constraints. Model 3.4 is a fairness-oriented rule that minimizes the maximum firm-level disadvantage under a limited compensation budget. Numerical experiments are conducted using a stylized Japanese domestic consumer goods distribution network. Results: Coordinated planning reduces total logistics cost compared with decentralized sequential allocation. Model 3.3 achieves the lowest system cost but gives benefits unevenly. Model 3.4 gives more balanced firm-level outcomes and improves the worst-off firm in the tested scenarios. The results also show that substantial fairness improvements can be obtained through small route-allocation changes. Conclusions: The study shows how two coordination rules can be used in PI-oriented logistics coordination. Model 3.3 is useful when firms need a no-loss guarantee, especially in an early stage. Model 3.4 is useful in a mature or repeated coordination stage, where the platform needs to avoid excessive disadvantage.