Vehicle routing problems, a comprehensive problem category that originated from the seminal Chinese postman problem (first investigated by Chinese mathematician Mei-Gu Guan), entail strategic and tactical decision making for efficient scheduling and routing of vehicles. While the Chinese postman problem is aimed at finding the minimum length cycle for a single postman, the broader challenges encompass scenarios with multiple postmen. Making cost-effective decisions in such cases depends on various factors, including vehicle sizes and types, vehicle usage time, and road tax variations across routes. In this work, we delve into a class of such problems wherein Bell nonlocal correlations provide advantages in optimizing the costs for non-communicating postmen and, thus, establish a nascent utilization of quantum entanglement in traffic routing problems. Our investigation unveils promising applications for nonlocal correlations within combinatorial optimization and operational research problems, which otherwise have predominantly been explored within the quantum foundation and quantum information theory communities.
