Autonomous Mobile Robots (AMRs) are increasingly deployed in smart factories and intralogistics systems, yet dynamic fleet scheduling remains challenging because of growing task complexity, multi-objective requirements, and human–robot interaction. This review examines the evolution of AMR scheduling from Mixed-Integer Linear Programming (MILP), heuristics, metaheuristics, and Reinforcement Learning (RL) toward emerging quantum and hybrid quantum–classical optimization. Particular attention is given to Quadratic Unconstrained Binary Optimization (QUBO), the Quantum Approximate Optimization Algorithm (QAOA), and quantum annealing as potential approaches for representing coupled task allocation, routing, energy management, and human-safety requirements. The industrial implications of quantum-enhanced scheduling are critically discussed in terms of operational coordination, resource efficiency, human-centric collaboration, and scalability. Sector-specific opportunities and current research maturity are further assessed from an Industry 5.0 perspective. The review identifies hybrid quantum–classical architectures, dynamic QUBO formulations, Digital Twin integration, and human-aware scheduling as key research directions for advancing scalable and adaptive multi-AMR fleet coordination.
Autonomous Mobile Robots (AMRs) are increasingly deployed in smart factories and intralogistics systems, yet dynamic fleet scheduling remains challenging because of growing task complexity, multi-objective requirements, and human–robot interaction. This review examines the evolution of AMR scheduling from Mixed-Integer Linear Programming (MILP), heuristics, metaheuristics, and Reinforcement Learning (RL) toward emerging quantum and hybrid quantum–classical optimization. Particular attention is given to Quadratic Unconstrained Binary Optimization (QUBO), the Quantum Approximate Optimization Algorithm (QAOA), and quantum annealing as potential approaches for representing coupled task allocation, routing, energy management, and human-safety requirements. The industrial implications of quantum-enhanced scheduling are critically discussed in terms of operational coordination, resource efficiency, human-centric collaboration, and scalability. Sector-specific opportunities and current research maturity are further assessed from an Industry 5.0 perspective. The review identifies hybrid quantum–classical architectures, dynamic QUBO formulations, Digital Twin integration, and human-aware scheduling as key research directions for advancing scalable and adaptive multi-AMR fleet coordination.
Autonomous Mobile Robots (AMRs) play an increasingly important role in flexible and reconfigurable production systems. Assigning heterogeneous tasks to multiple AMRs constitutes a combinatorial optimization problem that becomes computationally intractable as system complexity grows. This paper presents a Quadratic Unconstrained Binary Optimization (QUBO) model for AMR task assignment, integrating scheduling and resource allocation within a Hamiltonian formulation. The model is parameterized and evaluated using both exact and heuristic solvers to analyze scalability and validity across benchmark scenarios. Results demonstrate the trade-off between computational effort and solution optimality, confirming the feasibility of the QUBO representation for this problem class. The formulated model creates a basis for future implementation on quantum hardware for optimization using Quantum Annealing (QA) or the Quantum Approximate Optimization Algorithm (QAOA), thereby bridging the gap between classical optimization methods and new quantum computing paradigms.
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.
Industrial engineering increasingly depends on solving large-scale optimization problems involving scheduling, routing, resource allocation, inventory control, energy management, and supply-chain coordination. Classical exact methods often become computationally expensive when problem size, uncertainty, and combinatorial complexity grow rapidly. Although practical quantum computers are still developing, quantum-inspired computing approaches have emerged as powerful alternatives that adapt principles from quantum mechanics to run on classical hardware. This paper investigates quantum-inspired computing approaches for complex optimization problems in industrial engineering. It examines methodologies including simulated annealing, tensor-network optimization, Ising formulations, quantum- inspired evolutionary algorithms, digital annealers, and hybrid classical-intelligent heuristics. Applications in production scheduling, facility layout, vehicle routing, maintenance planning, portfolio optimization, warehouse operations, and smart manufacturing are analyzed. Particular attention is given to solution quality, scalability, stochastic decision-making, real-time adaptability, and integration with Industry 4.0 data systems. Benefits include faster near-optimal solutions, improved operational efficiency, reduced energy consumption, and better responsiveness under uncertainty. Major challenges include formulation difficulty, parameter tuning, benchmarking inconsistency, interpretability, and transition barriers within traditional industrial workflows. A future roadmap is proposed involving hybrid quantum-classical ecosystems, AI- guided optimization engines, digital twins, and autonomous decision platforms. The paper concludes that quantum-inspired computing can deliver practical industrial value today by bridging the gap between conventional optimization and future quantum advantage, especially in environments where speed, flexibility, and complexity management are essential.
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 The convergence of quantum optimization and autonomous agentic reasoning defines a new computational frontier in large-scale resource coordination. This work introduces Q-PACT, a Quantum-Parallel Agentic Coordination Toolkit that unifies quantum optimization, fairness-driven orchestration, and adaptive multi-agent intelligence into a reproducible hybrid framework. Q-PACT addresses a key limitation in distributed and cloud-based quantum infrastructures; inefficient, inequitable scheduling of scarce quantum resources among competing agents and tasks. The proposed architecture formulates multi-agent scheduling as a Quadratic Unconstrained Binary Optimization (QUBO) model, solved through a heterogeneous pipeline integrating quantum annealing (D-Wave), variational optimization (QAOA on IonQ/Azure), and classical meta-heuristics. A noise-aware encoder, solver-adapter layer, and agentic manager collaborate to maintain fairness, adaptability, and load balance, while the QML-AURA subsystem continuously refines solver hyperparameters through feedback-driven variational learning. Q-PACT’s hybrid orchestration layer enables dynamic re-optimization, fault-tolerant fallback execution, and secure artifact exchange across distributed backends, achieving resilience under the noise and queueing constraints of NISQ-era hardware. Empirical evaluations demonstrate significant improvements in makespan reduction, workload variance, and energy minimization compared with classical heuristics, establishing the viability of quantum-assisted agentic scheduling at scale. By bridging quantum optimization paradigms, multi-agent systems, and fairness-aware orchestration, Q-PACT provides a foundational blueprint for the next generation of autonomous, cloud-integrated, and quantum-enabled coordination systems.
The advent of quantum computing is redefining the computational landscape of industrial manufacturing, introducing new paradigms for simulation, optimization, and adaptive decision-making. This study investigates the integration of quantum computing–enhanced service ecosystems within industrial manufacturing frameworks, focusing on how quantum algorithms can accelerate workflow optimization, supply chain coordination, and process simulation in large-scale production environments. Traditional simulation and optimization techniques often struggle with the combinatorial complexity of modern manufacturing systems, leading to inefficiencies in resource allocation, scheduling, and predictive maintenance. The proposed framework leverages hybrid quantum–classical computation to simulate high-dimensional manufacturing workflows through quantum annealing, Quantum Approximate Optimization Algorithm (QAOA), and quantum-inspired reinforcement learning. These techniques enable more efficient exploration of multi-objective optimization spaces, facilitating near-real-time decision support and improved throughput under uncertain production conditions. The model also emphasizes the development of service-oriented architectures that integrate quantum computation with industrial Internet of Things (IIoT) infrastructures, digital twins, and cloud-based manufacturing services. Results from conceptual modeling and early simulation experiments suggest that quantum-enhanced service ecosystems outperform conventional digital twins and heuristic optimization methods in adaptability, precision, and energy efficiency. This convergence of quantum computing and industrial systems marks a shift toward next-generation intelligent manufacturing, capable of autonomous learning, dynamic reconfiguration, and sustainable production optimization.