This paper introduces a groundbreaking hybrid quantum-classical algorithm for the socioeconomically weighted warehouse facility location problem, addressing critical challenges in modern supply chain optimization. We present a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation with rigorously derived penalty parameters, automated constraint repair mechanisms, and theoretically proven performance guarantees. Our hybrid approach integrates demand-weighted kmedoids clustering with quantum annealing, achieving an 7.92% reduction in total weighted distance over classical baselines while maintaining 95% feasibility rates. Key innovations include: (1) mathematically rigorous penalty parameter bounds ensuring constraint satisfaction, (2) automated quantum solution repair algorithms with bounded objective deterioration, (3) intelligent hybrid merging strategies leveraging complementary classicalquantum strengths, and (4) empirical 95% repair bound and a sufficient computable penalty condition. Experimental validation on real Hyderabad socioeconomic data demonstrates superior performance with approximation ratio 1.11 compared to pure quantum approaches (1.22) and classical methods (1.05), establishing practical quantum advantage for logistics optimization,
This paper introduces a groundbreaking hybrid quantum-classical algorithm for the socioeconomically weighted warehouse facility location problem, addressing critical challenges in modern supply chain optimization. We present a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation with rigorously derived penalty parameters, automated constraint repair mechanisms, and theoretically proven performance guarantees. Our hybrid approach integrates demand-weighted kmedoids clustering with quantum annealing, achieving an 7.92% reduction in total weighted distance over classical baselines while maintaining 95% feasibility rates. Key innovations include: (1) mathematically rigorous penalty parameter bounds ensuring constraint satisfaction, (2) automated quantum solution repair algorithms with bounded objective deterioration, (3) intelligent hybrid merging strategies leveraging complementary classicalquantum strengths, and (4) empirical 95% repair bound and a sufficient computable penalty condition. Experimental validation on real Hyderabad socioeconomic data demonstrates superior performance with approximation ratio 1.11 compared to pure quantum approaches (1.22) and classical methods (1.05), establishing practical quantum advantage for logistics optimization,
Managing inventory in large-scale supply chains necessitates quick, cost-effective decisions that adhere to constraints such as storage limits and variable demand. This paper describes a novel hybrid approach that uses both quantum and classical computers to tackle inventory problems structured as Quadratic Unconstrained Binary Optimization (QUBO). Each choice variable, such as restocking a product, is represented in binary form, with related costs and penalties built into the objective function. Business constraints are communicated indirectly using adjustable weights, allowing the model to remain unconstrained while discouraging unrealistic conclusions. Optimization is carried out using both classical methods like simulated annealing and quantum solvers such as D-Wave and QAOA, where a hybrid strategy selects the most viable solution. The results indicate that the hybrid system consistently produces lower total costs and better constraint compliance compared to individual solvers, especially for complex, high-dimensional datasets. To ensure secure, automated execution of these optimized decisions, a blockchain layer is introduced. Inventory actions—such as placing orders or updating stock—are carried out through smart contracts that provide tamper-proof, verifiable enforcement. By employing a lightweight Proof of Authority (PoA) mechanism, transaction validation remains fast while maintaining transparency across all nodes in the network. This integration of quantum optimization with blockchain automation enables a responsive and trustworthy framework for modern inventory management.
This paper establishes a theoretical framework for constraint-preserving quantum optimization that maintains problem structure throughout quantum algorithm execution, addressing a fundamental challenge in translating real-world optimization problems to quantum hardware. We develop mathematical formulations that embed hard constraints directly into quantum circuit design rather than relying solely on penalty methods, proving that certain constraint classes can be exactly enforced through quantum state space restriction. Our theory characterizes the complexity of constraint preservation across different problem classes including facility location, network optimization, and resource allocation, deriving conditions under which quantum algorithms can explore only feasible solution spaces. We introduce automated repair mechanisms with theoretical guarantees on convergence to valid solutions and establish bounds on the additional quantum resources required for constraint maintenance. The framework provides rigorous analysis of trade-offs between constraint flexibility, quantum circuit depth, and solution quality, identifying problem structures amenable to efficient constraint-preserving quantum formulations. We extend the theory to socioeconomic weighting and multi-objective scenarios, proving that preference structures can be incorporated without compromising feasibility guarantees. This theoretical foundation advances practical quantum optimization by ensuring quantum algorithms produce implementable solutions while maintaining provable performance characteristics across diverse constrained optimization domains including logistics, energy systems, and infrastructure planning.
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 optimization provides a promising approach for solving large-scale combinatorial problems through quadratic unconstrained binary optimization (QUBO) formulations. However, integrating QUBO-based solvers into structured optimization frameworks while preserving solution guarantees remains a fundamental challenge. This paper develops a hybrid quantum-classical column-and-constraint generation (QCCG) framework for solving two-stage adaptive robust optimization problems with binary first-stage decisions and linear recourse under polyhedral uncertainty. The proposed approach reformulates the restricted master problem as a QUBO and solves it approximately using a quantum optimizer, while retaining a classical adversarial subproblem to compute worst-case recourse and certify solution quality. We construct a constraint-preserving QUBO encoding for inequality-constrained master problems using slack variables and penalty terms, enabling general mixed-integer structures to be mapped to quantum-compatible representations. To address inexactness arising from discretization, penalty modeling, and quantum optimization, we introduce a bound-adjustment mechanism that yields valid lower and upper bounds and provides a certified stopping criterion. We show that the proposed framework generalizes classical column-and-constraint generation and retains its convergence properties when the master problem is solved exactly. Numerical experiments on two-stage robust location-transportation problems demonstrate that the proposed hybrid approach achieves solution quality comparable to classical methods while reducing the computational burden associated with solving mixed-integer master problems, highlighting the potential of hybrid quantum-classical optimization for scalable decision-making under uncertainty.
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary Optimization (QUBO) formulation provides a unifying modeling framework for a broad class of NP-hard problems and is naturally suited to quantum computing and quantum-inspired algorithms. Location science, network design, and logistics represent core application domains of discrete optimization, combining high practical impact with substantial computational challenges. In this work, we develop QUBO formulations for several fundamental problems in these domains, including a nonlinear integer formulation of the Discrete Ordered Median Problem (DOMP). Beyond their modeling relevance, these QUBO formulations serve as representative benchmark problems for assessing quantum algorithms and quantum hardware. We further derive a tight bound for the penalty parameter ensuring equivalence between the QUBO formulation and its underlying integer program. Finally, we conduct a comprehensive computational study using QAOA, WS-QAOA, and classical heuristics for QUBO instances of the p-Median Problem and the Fixed-Charge Facility Location Problem (FCFLP), and introduce two effective warm-start strategies for WS-QAOA based on its linear programming relaxation.
• First use of QAOA for Facility Location (FL) and Load Balancing (LB) in supply chains optimisation. • QAOA successfully solves FL and LB using compact unbalanced-penalisation QUBO models. • Hardware-calibrated QAOA retrieves optimal FL solutions even under realistic gate and readout errors. • Provides reproducible QUBO–to–Ising transformations and full QAOA implementations in PennyLane and Qiskit. Quantum computing is emerging as a promising paradigm for solving combinatorial optimisation problems that are intractable for classical methods. Among the most prominent quantum algorithms is the Quantum Approximate Optimisation Algorithm (QAOA), which has demonstrated potential in addressing NP-hard problems using shallow circuits compatible with Noisy Intermediate-Scale Quantum (NISQ) devices. While QAOA has been applied to logistics and scheduling tasks, foundational supply chain problems such as Facility Location (FL) and Load Balancing (LB) remain largely unexplored. This paper addresses this gap by formulating FL and LB as Quadratic Unconstrained Binary Optimisation (QUBO) models and solving them using QAOA under both noiseless and hardware-calibrated noisy conditions. Two encoding methods are compared: the conventional slack-variable approach and the unbalanced penalisation technique. Results show that unbalanced penalisation consistently outperforms the slack-variable method by achieving higher feasibility and optimality rates and by avoiding the qubit inflation that limits slack-based encodings. FL instances, modelled as minimum dominating sets, exhibit strong performance in both noiseless and noisy simulations, whereas LB instances suffer from depth-induced noise due to their denser constraints. Furthermore, we outline the QUBO-to-Ising transformation process, with open-source implementations in PennyLane and Qiskit. To the best of our knowledge, this work represents the first application of QAOA to FL and LB, bridging the gap between quantum algorithm design and practical supply chain optimisation.