This study investigates optimal inventory positioning in multi-stage supply chains by utilizing a mixed-integer nonlinear programming model that incorporates a scenario-based disruption delay, and the subsequent expediting to mitigate inventory shortages. The goal is to determine the amount and positioning of inventory in the supply chain to minimize the total inventory and expediting costs, subject to meeting customer service requirements. Discretization techniques are applied to linearize non-convex objective functions and reformulate the problem as an equivalent mixed-integer linear programming, which can be solved by the standard solvers. To demonstrate the model, numerical experiments are conducted to determine the optimal solution under different disruption scenarios. These experiments provide interesting insights regarding inventory decisions that can serve as guidelines for building resilience in the supply chain.

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.

Background: Blockchain has emerged as a promising enabler for improving transparency, trust, and operational efficiency in logistics systems. In PI-oriented logistics environments, where openness, interoperability, and streamlined information exchange are emphasized, blockchain offers a decentralized alternative to conventional coordination methods. However, its economic feasibility remains uncertain due to substantial system development and operational costs. Existing literature largely isolates qualitative benefits from quantitative cost structures. Methods: This study proposes a quantitative–qualitative evaluation framework to assess blockchain adoption in PI-oriented logistics systems. Two Mixed-Integer Linear Programming (MILP) cost-minimization models were constructed to represent alternative coordination approaches: PI–BC (blockchain-enabled coordination) and PI–Human (traditional human-centered coordination). The results of the optimization analysis were integrated into an Analytic Hierarchy Process (AHP) evaluation alongside qualitative criteria such as interoperability, reliability, and transparency. Results: Numerical findings show that although PI–BC incurs higher operational costs, it performs considerably better in qualitative dimensions related to information visibility and robustness. Conclusions: These results suggest that blockchain provides particular value in PI-oriented contexts at the adoption stage. However, the framework does not provide a universal recommendation, as the relative advantage of PI–BC is highly contingent on decision-makers’ subjective criterion weight assignments, as revealed by the sensitivity analysis.