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IEEE Open Journal of Intelligent Transportation Systems

An Intelligent and Sustainable Green Supply Chain Optimization of Transportation Systems Using Classical and Quantum-Powered Computing

Muhammad Makama Mahmudur Rahman Ohee, Hafiz Md. Hasan Babu

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Transportation strategists increasingly handle heterogeneous fleets under tight service levels, fluctuating costs, and stated environmental targets. This paper addresses the operational Heterogeneous Vehicle Routing Problem (HVRP) with a practical, mathematically light decision framework that treats sustainability as the main goal of the design. We introduce a Quantum-Inspired Supply Chain and Logistics Optimization Algorithm (QISCLOA), solver-independent HVRP approach for transportation system. Our proposed framework builds a curated, capacity-feasible, and diversified route pool using multi-strategy generation. In our $16\times 16$ HVRP benchmarks, our proposed algorithm reduces elapsed time by up to 98.6% compared with strong classical formulations, while matching classical distance quality and delivering higher load utilization (95–99%) under the same feasibility constraints. Compared with existing classical system, our proposed system preserves full feasibility and comparable distance, shows clear distance-per-demand gains in symmetric unit-demand cases, and attains near-zero solve time on identical Binary Quadratic Models (BQM), evidencing orders-of-magnitude speedups. The proposed model further introduces a load–carbon emission correlation with speed, road-condition, and congestion factors, and the proposed Quantum Annealing (QA) and existing Quantum Approximate Optimization Algorithm (QAOA) comparison demonstrates competitive solution quality, solver-dependent efficiency, and full logical hardware compatibility. Additionally, we extend the formulation to a multi-depot setting with depot availability, dispatch-capacity, time-window, and Electric Vehicle (EV) charging constraints, and validate it on 21 Multi-Depot Vehicle Routing Problem (MDVRP) benchmark instances to demonstrate scalable multi-depot route selection, while a reduced comparison confirms competitive solution quality and solver-dependent efficiency, with existing QAOA improving overall route distance by 0.63% and proposed QA achieving a 9.14% overall runtime advantage. In multitasking Capacitated Vehicle Routing Problem (CVRP) benchmarks used in explicit evolutionary multitasking studies, our approach achieves lower routing cost for both best and average results with a win rate of 81.48%, indicating a lower emission of CO2. Empirically, our proposed method outperforms competitive state-of-the-art approaches in our evaluation metrics while maintaining core feasibility.

DOI
10.1109/ojits.2026.3726768

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Transportation strategists increasingly handle heterogeneous fleets under tight service levels, fluctuating costs, and stated environmental targets. This paper addresses the operational Heterogeneous Vehicle Routing Problem (HVRP) with a practical, mathematically light decision framework that treats sustainability as the main goal of the design. We introduce a Quantum-Inspired Supply Chain and Logistics Optimization Algorithm (QISCLOA), solver-independent HVRP approach for transportation system. Our proposed framework builds a curated, capacity-feasible, and diversified route pool using multi-strategy generation. In our 16×1616\times 1616×16 HVRP benchmarks, our proposed algorithm reduces elapsed time by up to 98.6% compared with strong classical formulations, while matching classical distance quality and delivering higher load utilization (95–99%) under the same feasibility constraints. Compared with existing classical system, our proposed system preserves full feasibility and comparable distance, shows clear distance-per-demand gains in symmetric unit-demand cases, and attains near-zero solve time on identical Binary Quadratic Models (BQM), evidencing orders-of-magnitude speedups. The proposed model further introduces a load–carbon emission correlation with speed, road-condition, and congestion factors, and the proposed Quantum Annealing (QA) and existing Quantum Approximate Optimization Algorithm (QAOA) comparison demonstrates competitive solution quality, solver-dependent efficiency, and full logical hardware compatibility. Additionally, we extend the formulation to a multi-depot setting with depot availability, dispatch-capacity, time-window, and Electric Vehicle (EV) charging constraints, and validate it on 21 Multi-Depot Vehicle Routing Problem (MDVRP) benchmark instances to demonstrate scalable multi-depot route selection, while a reduced comparison confirms competitive solution quality and solver-dependent efficiency, with existing QAOA improving overall route distance by 0.63% and proposed QA achieving a 9.14% overall runtime advantage. In multitasking Capacitated Vehicle Routing Problem (CVRP) benchmarks used in explicit evolutionary multitasking studies, our approach achieves lower routing cost for both best and average results with a win rate of 81.48%, indicating a lower emission of CO2. Empirically, our proposed method outperforms competitive state-of-the-art approaches in our evaluation metrics while maintaining core feasibility.
Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We show that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime.
Quantum annealing (QA) is a quantum computing algorithm that works on the principle of Adiabatic Quantum Computation (AQC), and it has shown significant computational advantages in solving combinatorial optimization problems such as vehicle routing problems (VRP) when compared to classical algorithms. This paper presents a QA approach for solving a variant VRP known as multi-depot capacitated vehicle routing problem (MDCVRP). This is an NP-hard optimization problem with real-world applications in the fields of transportation, logistics, and supply chain management. We consider heterogeneous depots and vehicles with different capacities. Given a set of heterogeneous depots, the number of vehicles in each depot, heterogeneous depot/vehicle capacities, and a set of spatially distributed customer locations, the MDCVRP attempts to identify routes of various vehicles satisfying the capacity constraints such as that all the customers are served. We model MDCVRP as a quadratic unconstrained binary optimization (QUBO) problem, which minimizes the overall distance traveled by all the vehicles across all depots given the capacity constraints. Furthermore, we formulate a QUBO model for dynamic version of MDCVRP known as D-MDCVRP, which involves dynamic rerouting of vehicles to real-time customer requests. We discuss the problem complexity and a solution approach to solving MDCVRP and D-MDCVRP on quantum annealing hardware from D-Wave.
Background: This paper investigates hybrid quantum–classical optimization approaches for addressing core supply chain management (SCM) problems. A unified hybrid framework is implemented and evaluated across five representative domains: vehicle routing, scheduling, facility location, inventory optimization, and demand forecasting. Methods: The framework integrates quantum algorithms—namely the Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing (QA), and the Variational Quantum Eigensolver (VQE)—with classical constraint-handling and local refinement procedures in an iterative workflow. Quantum solvers are employed for global solution exploration, while classical optimization ensures feasibility and convergence stability. Results: Experiments conducted on standardized synthetic benchmarks demonstrate that the proposed hybrid framework consistently outperforms classical-only and quantum-only baselines, achieving 12–18% reductions in operational costs and 20–35% faster convergence. In routing and fulfilment tasks, quantum-generated candidate solutions provide effective warm starts for classical refinement. Robustness analysis based on stochastic SCM simulations further indicates lower performance variance under uncertainty. Conclusions: These results demonstrate that hybrid quantum–classical optimization constitutes a practical and scalable strategy for near-term SCM decision-making under current Noisy Intermediate-Scale Quantum (NISQ) hardware constraints.
Quantum computing (QC) stands at the cusp of revolutionizing computation, yet its near-term potential, constrained by Noisy Intermediate-Scale Quantum (NISQ) devices, remains underexplored. This dissertation investigates how hybrid quantum-classical algorithms can address combinatorial optimization challenges in logistics, focusing on vehicle routing and drone delivery—NP-hard problems with exponential solution spaces that defy classical exhaustive methods. Amidst NISQ limitations like limited qubits and high noise, we confront key challenges: encoding complex constraints, e.g., time windows, battery capacity, into quantum models, balancing quantum and classical components for scalability, and accessing scarce quantum resources. By integrating quantum annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) with classical heuristics, this work demonstrates QC’s practical utility, advancing both optimization theory and real-world logistics applications. The dissertation unfolds across four core contributions. First, the Hybrid Quantum Tabu Search (HQTS) optimally solves the 50-location Capacitated Vehicle Routing Problem (CVRP), achieving a 4.72% optimality gap. Secondly, we refine HQTS to reach a 2.15% gap with enhanced QA utilization, outperforming prior hybrids on standard datasets. Third, adapting HQTS for the CVRPTWwith D-Wave’s Constrained Quadratic Model solver yields a 3.85% gap on 100-location instances, leveraging a novel heuristic to ensure time-window feasibility where quantum outputs falter. Lastly, QUADRO, a pioneering framework for drone delivery, employs QAOA-driven routing and hybrid scheduling, minimizing transit time and makespan for fleets of 2–11 drones needing fewer than 100 qubits, rivaling classical benchmarks on adapted Augerat datasets. These advances, tested via D-Wave’s Advantage system and Qiskit simulations, showcase hybrid strategies that mitigate NISQ constraints, delivering scalable, feasible solutions to logistics challenges. This work establishes near-term QC’s viability for combinatorial optimization, bridging theoretical promise with practical impact. Synthesizing quantum exploration with classical refinement achieves competitive performance, e.g., matching or surpassing Google ORTools in select CVRPTW cases, while illuminating NISQ limits, such as feasibility degradation beyond small scales. These hybrid strategies deliver scalable, feasible solutions, from a 2.15% optimality gap for CVRP to effective drone fleet management with fewer than 100 qubits, illuminating quantum computing’s potential despite its current constraints. Ultimately, this dissertation positions hybrid QC as a transformative tool for optimization challenges, offering a robust foundation for scaling quantum optimization into operational reality.
We investigate the potential of the Quantum Approximate Optimization Algorithm (QAOA) for reducing energy consumption in route planning, a key challenge in logistics due to the NP-hard nature of the Traveling Salesman and Vehicle Routing Problems. By encoding route optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implementing QAOA circuits at depth p = 3-5 alongside classical baselines of Simulated Annealing (SA) and Genetic Algorithms (GA), we perform systematic benchmarks on Euclidean graphs of sizes N = 5, 10, and 20. Our results demonstrate that QAOA attains higher solution quality with approximation ratios of 0.953 (N = 5), 0.921 (N = 10), and 0.903 (N = 20), outperforming SA and GA by 2.7-4.4%. Wall-clock runtimes for QAOA are 2-3x faster than SA across all tested sizes, and energy consumption measurements reveal a three-order-of-magnitude reduction, remaining in the picojoule range versus nanojoules for classical methods. Translating these gains to real-world logistics suggests an 8.2% improvement in routing efficiency could save approximately 2.62 EJ of fuel annually in the U.S., avoiding nearly 1.94 x 10^8 tonnes of CO2 emissions. These findings highlight QAOA's promise as a fast, energy-efficient optimizer for sustainable logistics applications and underscore its potential role in next-generation fleet-management systems.
We present a quantum optimization framework for the Shipment Selection Problem (SSP) in electric freight logistics, developed jointly by IonQ and Einride. Idle gaps arising from stochastic shipment cancellations reduce fleet utilization and revenue; filling them optimally requires solving a combinatorial assignment problem with quadratic inter-gap dependencies. We formulate the SSP as a Mixed-Integer Quadratic Program, map it to an Ising cost Hamiltonian, and solve it using Iterative-QAOA, a non-variational warm-start extension of the Quantum Approximate Optimization Algorithm (QAOA) with a fixed linear-ramp parameter schedule. An end-to-end hybrid workflow integrates Einride's vehicle routing problem (VRP) solver with IonQ's quantum simulations, enabling evaluation on real, anonymized logistics data spanning up to 130 qubits. We assess solution quality through application-level performance metrics, including Shipments Delivered (SD), Schedule Compatibility Score (SCS), and Total Drive Distance (TDD). When the quantum assignment is passed to the classical solver as a warm start, the resulting hybrid workflow achieves improvements of up to 12% in SD and a reduction of up to 6% in total drive distance per shipment for specific instances, while total operational cost remains effectively unchanged. For the subset of instances within reach of current devices (20-35 qubits), the workflow is additionally executed on IonQ trapped-ion quantum hardware, where the hardware results closely reproduce the noiseless simulations. These results show that Iterative-QAOA can generate compatibility-aware assignments that become operationally valuable when embedded in a hybrid logistics optimization workflow.