A biased-randomized matheuristic for designing physical internet supply chain networks with multiple paths

Within the current interconnected and volatile global economy, supply chain network design has become a strategic priority for organizations aiming to enhance resilience, efficiency, and sustainability. The physical internet (PI) paradigm offers a transformative approach to logistics by promoting hyperconnectivity, interoperability, and dynamic reconfiguration. However, designing PI-based supply chain networks, especially those involving multipath routing and decentralized decision-making, poses significant computational challenges that traditional optimization methods have not yet addressed. This paper introduces a series of biased-randomized matheuristic algorithms tailored to the design of PI supply chain networks. Two problem variants are considered: a basic model and a multipath model incorporating network connectivity constraints. Both are formulated as mixed-integer programming models, which become computationally inefficient for large-scale instances. Hence, scalable matheuristics are also proposed, based on greedy and biased-randomized strategies, and on an extended Dijkstra's algorithm in the case of the multipath version. Computational experiments show that these methods have strong potential for real-world logistics applications, offering robust and time-efficient tools for complex supply chain network design.