Corporate travel procurement is a multi-objective, constraint-dense decision domain spanning strategic supplier portfolio selection, travel policy design, and operational disruption response. Classical methods—mixed-integer programming (MIP), constraint programming, metaheuristics, and machine learning—deliver strong results but face scaling and responsiveness challenges as procurement objectives broaden to include compliance, traveler experience, sustainability, and resilience. Quantum optimization methods, particularly quantum annealing and gate-based variational algorithms (e.g., QAOA), have been proposed for combinatorial problems with binary decisions and complex interaction terms. Yet empirical evidence across optimization domains often shows classical solvers match or exceed quantum approaches on meaningful instance sets, motivating a hybrid quantum–classical posture rather than replacement. This paper formalizes quantum-enhanced travel procurement as a hypothesis-driven, hybrid decision-support approach in which quantum routines contribute to solution search, diversification, or time-to-decision for selected combinatorial cores. We present canonical procurement formulations, show explicit mappings to QUBO/Ising models, and propose hybrid architectures for supplier portfolio design, airline share allocation under commitments, policy parameter tuning, and disruption re-accommodation. To strengthen accessibility and rigor, we provide (i) a worked QUBO example with explicit coefficients and variable counts; (ii) an operational benchmark protocol with representative instance sizes, solver baselines, runtime assumptions, and statistical reporting; and (iii) an enterprise governance view including post-quantum cryptography readiness across vendor integrations.
Corporate travel procurement is a multi-objective, constraint-dense decision domain spanning strategic supplier portfolio selection, travel policy design, and operational disruption response. Classical methods—mixed-integer programming (MIP), constraint programming, metaheuristics, and machine learning—deliver strong results but face scaling and responsiveness challenges as procurement objectives broaden to include compliance, traveler experience, sustainability, and resilience. Quantum optimization methods, particularly quantum annealing and gate-based variational algorithms (e.g., QAOA), have been proposed for combinatorial problems with binary decisions and complex interaction terms. Yet empirical evidence across optimization domains often shows classical solvers match or exceed quantum approaches on meaningful instance sets, motivating a hybrid quantum–classical posture rather than replacement. This paper formalizes quantum-enhanced travel procurement as a hypothesis-driven, hybrid decision-support approach in which quantum routines contribute to solution search, diversification, or time-to-decision for selected combinatorial cores. We present canonical procurement formulations, show explicit mappings to QUBO/Ising models, and propose hybrid architectures for supplier portfolio design, airline share allocation under commitments, policy parameter tuning, and disruption re-accommodation. To strengthen accessibility and rigor, we provide (i) a worked QUBO example with explicit coefficients and variable counts; (ii) an operational benchmark protocol with representative instance sizes, solver baselines, runtime assumptions, and statistical reporting; and (iii) an enterprise governance view including post-quantum cryptography readiness across vendor integrations.
Airline and space mission scheduling present complex combinatorial optimization challenges, requiring sophisticated coordination of multiple resources under stringent operational constraints. This paper introduces a novel hybrid quantum-classical framework for scheduling optimization, the Quantum Scheduling Optimization Algorithm (QSOA), addressing crew assignment, gate allocation, and trajectory planning through advanced quantum machine learning techniques. We formulate the scheduling problems as stochastic multi-objective optimization and propose three integrated solution approaches: (1) hybrid quantum optimization via QAOA with constraint-aware loss functions and problem decomposition strategies, (2) classical-quantum integration using graph partitioning and variational circuit optimization, and (3) comprehensive baselines including mixed-integer programming, genetic algorithms, and reinforcement learning formulations. For multi-objective handling, we develop Pareto-optimal sampling techniques combining quantum superposition with classical post-processing for constraint repair and solution refinement. Our experimental evaluation on realistic airline crew scheduling benchmarks and space mission simulators demonstrates significant improvements: the hybrid QSOA achieves 19.2\% cost reduction in airline scheduling compared to classical heuristics, while quantum methods provide competitive solutions for moderate-sized space mission subproblems with 15-18\% improvement in multi-objective trade-offs. The framework shows promise for scalable deployment in real-world transportation networks, with practical implications for next-generation scheduling optimization in complex operational environments.
Abstract Airline itinerary and scheduling represent some of the most difficult computational problems that exist in transportation. The problems require choosing the best flight routes while determining schedules and allocating resources through various constraints which include regulatory requirements and maintenance schedules and dynamic demand patterns. The solution of small and medium-scale instances has been achieved through mixed-integer programming and heuristic methods including simulated annealing and genetic algorithms and branch-and-price but these methods become impractical for larger real-world instances due to exponential scaling issues. Quantum computing has introduced fresh solutions which enable the resolution of these problems. Quantum mechanical phenomena particularly superposition and entanglement enable optimization algorithms to examine an exponentially expanded solution space simultaneously. Our research applies a basic airline scheduling problem to the Traveling Salesman Problem (TSP) before converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The Quantum Approximate Optimization Algorithm (QAOA) serves as a hybrid quantum-classical method to solve this formulation. The experimental evaluation of a 4-city scenario shows that quantum-based optimization generates performance levels comparable to traditional methods and indicates that improved quantum hardware development will provide computational benefits for complex airline scheduling problems. This research holds dual importance because it can minimize operational expenses and improve scheduling performance and it establishes fundamental principles for complex combinatorial problem optimization across the transportation industry. The research establishes fundamental principles for quantum-enabled applications that will revolutionize airline operations and other transportation networks by solving critical scalability and solution quality problems.
This paper has a full-scale reference architecture for hybrid quantum-classical learning to include the integration of classical representation models with quantum neural networks (QNN), quantum support vector machines (QSVM), quantum principal component analysis (qPCA), variational quantum circuits (VQC), and QAOA-based combinatorial optimization to create next-generation predictive business intelligence and complex decision optimization subject to all real world operating constraints. The proposed structure has a layered system consisting of; (1) Quantum aware data encoding techniques through Amplitude, Basis and Angle Mapping; (2) Differentiable Hybrid Learning Pipelines optimized using Parameter Shift Gradient Methods across Simulators and Managed Quantum Processing Units; (3) Prescriptive Workflows that reformulate Multi-Objective Business Problems such as Supply Chain Coordination, Routing with Time Windows and Portfolio Construction into QUBO Representations Supported by Convex Warm Starts and Classical Post-Processing to Guarantee Feasibility and Explainability. An End-To-End Orchestration Layer will manage Circuit Templates, Data Hashes, Model Versions and Backend Execution Metadata to Provide Reproducibility, Traceability, Governance Compliance Across All Enterprise Pipelines. A Systematic Evaluation Protocol Will be Defined to Isolate Quantum Contribution Through Systematic Ablation Analysis of Classical-Only, Quantum-Only, and Hybrid Configurations Combined With Rolling Window Validation, Latency Profiling, Cost Efficiency Analysis, and Carbon Impact Accounting. Industry Standard Time Series and Probabilistic Accuracy Measures Including sMAPE, MASE, CRPS and Calibration Consistency Will Be Used to Evaluate the Performance of Predictive Models. Optimization Quality Will Be Evaluated Using Optimality Gap, Constraint Violation Rates, Time to Feasible Solution and Downstream Business Impact on Profit Margins and Service Levels. An Interpretability Layer Will Provide Transparency by Mapping Quantum Feature Spaces, Circuit Observables, and Kernel Alignment Structures to Domain-Specific Reasoning to Build Stakeholder Trust, Auditability and Regulatory Alignment. In Addition, The Framework Will Incorporate Adaptive Decision-Making Via Quantum Reinforcement Learning to Allow Continuous Optimization Under Dynamic and Uncertain Business Environments. An Energy Aware Execution Layer Will Dynamically Route Workloads Between Classical Simulators and Quantum Hardware According to Predefined Energy Budgets, Carbon Thresholds, and Performance Demands. The Overall Framework Provides a Scalable, Auditable and Ethically Aligned Blueprint for Deploying Hybrid Quantum-Classical Intelligence Within Existing Enterprise Ecosystems for Applications Such as Financial Forecasting, Retail Analytics, Dynamic Pricing, Market Risk Modeling, and Supply Chain Optimization.
E-commerce platforms face ever more complex dimensional SKU portfolios, demand volatility, returns, seasonality and cost pressures. Traditional optimization approaches (integer programming, heuristics, meta-heuristics) increasingly strain under scale, real-time demands and combinatorial explosion. Meanwhile, quantum-inspired optimization leveraging methods such as quantum annealing, coherent Ising machines, variational circuits and QUBO (Quadratic Unconstrained Binary Optimization) mapping offer near-term practical approaches to combinatorial logistics and inventory problems. This paper proposes a comprehensive framework for applying quantum-inspired optimization to e-commerce supply-chain logistics and inventory management: we provide an extended literature review of classical and quantum-inspired methods; we derive full mathematical formulations for logistics/inventory problems and map them into QUBO/quantum-inspired frameworks; we design a benchmarking/implementation methodology; we discuss industry architecture and deployment issues (data pipelines, latency, hybrid classical/quantum-inspired workflows, interpretability, cost benefit); we present use cases and discuss practical adoption in ecommerce. Our findings suggest that while fully fault-tolerant quantum computing remains some years away, quantum-inspired optimization can deliver meaningful improvements in logistics and inventory decisions today, particularly for large-SKU e-commerce, multi-warehouse networks and time-sensitive delivery.
Advanced Quantum Annealing for the Bi-Objective Traveling Thief Problem: An ε-Constraint-based Approach
This paper addresses the Bi-Objective Traveling Thief Problem (BI-TTP), a challenging multi-objective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the ε-constraint method. Specifically, we reformulate the bi-objective problem into a single-objective formulation by restricting the second objective through adjustable ε-levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, enabling direct solution via a quantum annealing (QA) solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance overall performance. By leveraging the flexibility in selecting ε parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.
Quantum computing offers transformative potential for addressing complex combinatorial optimization challenges in logistics and supply chain management. This paper presents a comprehensive investigation of quantum annealing and hybrid quantum-classical algorithms applied to unit load device (ULD) configuration and disruption management in air cargo and multimodal logistics networks. We formulate the ULD loading and placement problem as a Quadratic Unconstrained Binary Optimization (QUBO) model that incorporates weight, volume, center-of-gravity, structural stress, and compatibility constraints. A stratified hybrid architecture spanning physical quantum hardware, algorithmic middleware, and decision-support layers is proposed. Through extensive numerical experiments and comparison with classical solvers, we demonstrate superior payload utilization (up to 96.5%), favorable computational scaling, and rapid disruption recovery. Real-world industry pilots, including quantum-assisted route optimization achieving substantial carbon emission reductions and hybrid solutions at major ports, are analyzed. Results indicate that while noisy intermediate-scale quantum (NISQ) hardware limitations persist, hybrid approaches already deliver measurable gains in operational efficiency, cost reduction, and supply-chain resilience. The work provides a practical roadmap for near-term adoption of quantum technologies in high-stakes logistics environments. Keywords— Quantum annealing, Unit load device (ULD), QUBO, Logistics optimization, Disruption management, Hybrid quantum-classical algorithms, Air cargo, Supply chain resilience