Joint Optimal Design for Speed and Routing in Maritime Logistics for Green Supply Chain: A Quantum Approximate Optimization Algorithm Approach

Maritime transportation is essential for global trade but presents significant environmental challenges due to its greenhouse gas emissions. Existing studies have addressed these challenges through integrated routing and speed optimization frameworks, yet frequently lack explicit quantification of environmental impacts and exhibit limited scalability for large-scale ship routing operations. Conversely, existing quantum optimization research in vehicle routing predominantly targets land-based transportation scenarios, restricting its direct applicability to maritime logistics. Maritime logistics inherently involve distinct operational complexities, such as nonlinear interactions among speed, payload, fuel consumption, and numerous operational uncertainties. These combined limitations underscore the critical need for quantum optimization methods explicitly designed for green maritime supply chains. To bridge this gap, this article proposes an efficient quantum-centric optimization framework that uses the quantum approximate optimization algorithm (QAOA) to jointly optimize ship routing and speed management within sustainable maritime supply chains. Specifically, we formulate an NP-hard cost minimization problem integrating critical maritime parameters, including fuel consumption, payload constraints, and operational speeds. We further develop a hybrid quantum-classical alternating optimization approach that iteratively addresses routing decisions through quantum computing techniques and optimizes ship speed using an analytical solution. Simulation results and real quantum hardware experiments demonstrate that our quantum-centric methodology achieves substantial cost reductions and highlights the potential for practical applicability in realistic maritime operations, significantly outperforming classical optimization benchmarks.