Many modern manufacturing companies have evolved from a single production facility to a multi-factory production environment that must manage both regionally dispersed production orders and their multi-site production steps. The availability of a range of machines in different locations capable of performing the same operation and shipping times between factories have transformed planning systems from the classic Job Shop Scheduling Problem (JSSP) to the Distributed Flexible Job Shop Scheduling Problem (DFJSP). Consequently, the complexity of production planning has increased significantly. We employ Quantum Annealing (QA) to solve the DFJSP in our research. In addition to assigning production orders to production sites, production steps are also assigned to these sites. This requirement is based on a real use case of a wool textile manufacturing company. To investigate the applicability of this method to large problem instances, problems ranging from 50 variables up to 250 variables, the largest problem that could be embedded into a D-Wave quantum annealer Quantum Processing Unit (QPU), are formulated and solved. Special Attention is dedicated to determining the Lagrange parameters of the Quadratic Unconstrained Binary Optimization (QUBO) model and the QPU configuration parameters, as these factors can significantly impact solution quality. The obtained solutions are compared to solutions obtained by Simulated Annealing (SA), both in terms of solution quality and calculation time. The results demonstrate that QA has the potential to solve large problem instances specific to the industry.
Many modern manufacturing companies have evolved from a single production facility to a multi-factory production environment that must manage both regionally dispersed production orders and their multi-site production steps. The availability of a range of machines in different locations capable of performing the same operation and shipping times between factories have transformed planning systems from the classic Job Shop Scheduling Problem (JSSP) to the Distributed Flexible Job Shop Scheduling Problem (DFJSP). Consequently, the complexity of production planning has increased significantly. We employ Quantum Annealing (QA) to solve the DFJSP in our research. In addition to assigning production orders to production sites, production steps are also assigned to these sites. This requirement is based on a real use case of a wool textile manufacturing company. To investigate the applicability of this method to large problem instances, problems ranging from 50 variables up to 250 variables, the largest problem that could be embedded into a D-Wave quantum annealer Quantum Processing Unit (QPU), are formulated and solved. Special Attention is dedicated to determining the Lagrange parameters of the Quadratic Unconstrained Binary Optimization (QUBO) model and the QPU configuration parameters, as these factors can significantly impact solution quality. The obtained solutions are compared to solutions obtained by Simulated Annealing (SA), both in terms of solution quality and calculation time. The results demonstrate that QA has the potential to solve large problem instances specific to the industry.
Abstract Quantum Annealing (QA) is a metaheuristic for solving optimization problems in a time-efficient manner. Therefore, quantum mechanical effects are used to compute and evaluate many possible solutions of an optimization problem simultaneously. Recent studies have shown the potential of QA for solving such complex assignment problems within milliseconds. This also applies for the field of job shop scheduling, where the existing approaches however focus on small problem sizes. To assess the full potential of QA in this area for industry-scale problem formulations, it is necessary to consider larger problem instances and to evaluate the potentials of computing these job shop scheduling problems while finding a near-optimal solution in a time-efficient manner. Consequently, this paper presents a QA-based job shop scheduling. In particular, flexible job shop scheduling problems in various sizes are computed with QA, demonstrating the efficiency of the approach regarding scalability, solutions quality, and computing time. For the evaluation of the proposed approach, the solutions are compared in a scientific benchmark with state-of-the-art algorithms for solving flexible job shop scheduling problems. The results indicate that QA has the potential for solving flexible job shop scheduling problems in a time efficient manner. Even large problem instances can be computed within seconds, which offers the possibility for application in industry.
Flexible Job Shop Scheduling (FJSSP) is a challenging optimization problem with multiple conflicting objectives used to model and compute real-world process scheduling tasks. In order for a manufacturing system to remain competitive, it is necessary to compute such optimization problems quickly and efficiently. The limitations of conventional optimization methods frequently stem from a delicate balance between solution quality and computation time. Consequently, a pressing need for solution algorithms arises that can effectively transcend these limitations. This paper presents a novel Quantum Annealing-based solving algorithm (QASA) for computing FJSSP, leveraging the power of Quantum Annealing combined with classical techniques. The proposed approach aims to optimize a multi-criterial FJSSP considering makespan, total workload, and job priority simultaneously. QASA employs a Hamiltonian formulation with Lagrange parameters to integrate the problem's constraints and objectives. By assigning appropriate weights to the objectives, the method allows the prioritization of certain objectives over others. To handle the computational complexity of large FJSSP instances, the problem is decomposed into smaller subproblems, and a decision logic based on bottleneck factors is employed to select critical jobs for computation combined with variable pruning techniques. To evaluate the effectiveness of the proposed approach, experiments are conducted on benchmark problems, considering makespan, total workload, and priority objectives. Therefore, QASA combining tabu search, simulated annealing, and Quantum Annealing is used for efficient computation and is compared with a classical solving algorithm (CSA) combining tabu search and simulated annealing. The results demonstrate that QASA outperforms CSA in terms of solution quality, as measured by set coverage and hypervolume ratio metrics. Furthermore, computational efficiency analysis reveals that QASA achieves superior Pareto solutions compared to the classical approach, with a reasonable increase in computation time.
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.
The flexible job shop scheduling problem (FJSSP) is a challenging optimization problem arising in small-batch and single-unit manufacturing, where high product variety and short planning cycles impose strict demands on both schedule quality and computation time. Prior work has indicated the potential of an iterative hybrid quantum–classical solver (IHQPU) for multi-objective FJSSP, covering makespan, tardiness, priority, and workload objectives as well as reactive rescheduling. However, transferring this approach to industrial practice requires reliable parameter calibration and validation on real production data, both of which remain open. This paper targets both aspects. A time share analysis characterizes at which problem size the QPU branch loses time dominance to classical branches. A systematic parameter calibration using the Optuna framework evaluates 10,000 solver configurations per Brandimarte instance and objective function, yielding size-class-dependent recommendations for 21 bottleneck weighting coefficients and constraint-to-objective weight ratios. A reproducibility study across 96 parameter combinations identifies the operations-per-iteration count as the dominant source of solution variance and establishes that sub-problem sizes of at most 30 operations with at least three outer repetitions achieve a coefficient of variation below 2.5%. The calibrated configurations are transferred without modification to an industrial validation on six planning instances comprising 283 to 1386 operations and 30 to 67 machines, yielding makespan reductions of up to 1.7% and priority-weighted completion time improvements of up to 78% over existing industrial schedules, with all instances solved within 15 min. Reactive rescheduling completes in 227 to 242 s and reduces planning disruption by 93.7 to 96.0% compared to full plan revision.
Abstract The advent of quantum computing has introduced transformative potential for solving complex optimization problems, particularly in the field of manufacturing. This paper presents the Quantum-Adaptive Flex Scheduler (QAFS), a hybrid algorithm that leverages Quantum Annealing (QA) to address the Flexible Job Shop Scheduling Problem (FJSSP) with multiple objectives. QAFS integrates quantum mechanics with traditional heuristic methods to efficiently navigate the vast solution space of FJSSP, overcoming the computational limitations faced by classical algorithms. Our computational study demonstrates that QAFS significantly improves key performance metrics: it reduces makespan by 10–15%, enhances workload distribution by 5–10%, and achieves priority adherence 10–20% more effectively than Classical Scheduling Algorithms (CSA). Moreover, QAFS achieves superior solution quality, attaining an 85% C-metric coverage and a HyperVolume Ratio (HVR) of 0.92, underscoring its capability to generate Pareto-efficient solutions in multi-objective scenarios. These findings highlight the practical potential of QAFS to revolutionize production planning and control in manufacturing, offering a scalable and adaptive solution that responds effectively to real-time constraints and fluctuating market demands.
This study evaluates a nonlinear model (NLM) formulation for flexible job shop scheduling problems (FJSSP) using a hybrid nonlinear solver and compares achieved makespan and computing times against established binary quadratic model (BQM) approaches. The NLM formulation enables non-iterative computation across all tested problem instances, eliminating the need for decomposition required by BQM-based methods. However, solution quality remains inferior to both iterative hybrid BQM and quantum processing unit (QPU) approaches. Computational analysis reveals that the NLM approach exhibits higher computation times for smaller instances compared to iterative hybrid BQM methods but demonstrates more favorable scaling behavior between smallest and largest instances. The results suggest potential application of NLM formulations for generating initial solutions in large-scale scheduling problems. Additional findings indicate that minimal BQM energy does not necessarily correspond to minimal makespan solutions, and chain breaks in QPU implementations can occasionally yield feasible solutions.