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This paper aims to introduce a novel structure for the physical internet (PI)–enabled sustainable supplier selection and inventory management problem under uncertain environments.

To address hybrid uncertainty both in the objective function and constraints, a novel interactive hybrid multi-objective optimization solution approach combining Me-based fuzzy possibilistic programming and interval programming approaches is tailored.

Various numerical experiments are introduced to validate the feasibility of the established model and the proposed solution method.

Due to its interconnectedness, the PI has the opportunity to support firms in addressing sustainability challenges and reducing initial impact. The sustainable supplier selection and inventory management have become critical operational challenges in PI-enabled supply chain problems. This is the first attempt on this issue, which uses the presented novel interactive possibilistic programming method.

Modular capacity units enable rapid reconfiguration, providing tactical flexibility to efficiently meet customer demand during disruptions and ensuring sustainability. Moreover, the Physical Internet (PI) enhances the potential of modular capacity in addressing efficiency, sustainability, and resilience challenges. To evaluate the sustainability and resilience advantages of the PI-enabled reconfigurable modular system (PI-M system), this paper studies a PI-enabled sustainable and resilient production-routing problem with modular capacity.

We develop a multi-objective optimization model to assess the sustainability and resilience benefits of combining PI and modular capacity in a chemical industry case study. A hybrid solution approach, combining the augmented e-constraint method, construction heuristic, and hybrid adaptive large neighborhood search, is developed.

The experimental results reveal that the proposed solution approach is capable of obtaining better solutions than the Gurobi and the existing heuristic in a shorter running time. Moreover, compared with the traditional system, the PI only and traditional with modular capacity systems, PI-M system has significant advantages in both sustainability and resilience.

To the best of our knowledge, this study is the first to integrate the PI and modular capacity and investigate sustainability and resilience in the production-routing problem.