From MINLP to QUBO: A Quantum-Inspired Approach for Bulk Carrier Routing with Time Windows

Emerging optimization paradigms like Quantum Annealing (QA) offer potential for tackling large-scale combinatorial problems, yet applications in the shipping industry remain scarce. This paper addresses the cargo routing problem for bulk carriers, where fuel consumption depends nonlinearly on vessel speed and strict time windows must be respected. We formulate the problem as a Mixed-Integer Nonlinear Program (MINLP) and derive a tractable model through velocity discretization, yielding a Travelling Salesman Problem with Time Windows (TSPTW). A Quadratic Unconstrained Binary Optimization (QUBO) model enables exploration with QA, and performance is evaluated using classical solvers and Simulated Annealing (SA).