Job Shop Scheduling is a combinatorial optimization problem of particular importance for production environments where the goal is to complete a production task in the shortest possible time given limitations in the resources available. Due to its computational complexity it quickly becomes intractable for problems of interesting size. The emerging technology of Quantum Annealing provides an alternative computational architecture that promises improved scalability and solution quality. However, several limitations as well as open research questions exist in this relatively new and rapidly developing technology. This paper studies the application of quantum annealing to solve the job shop scheduling problem, describing each step required from the problem formulation to the fine-tuning of the quantum annealer and compares the solution quality with various classical solvers. Particular attention is devoted to aspects that are often overlooked, such as the computational cost of representing the problem in the formulation required by the quantum annealer, the relative qubits requirements and how to mitigate chain breaks. Furthermore, the impact of advanced tools such as reverse annealing is presented and its effectiveness discussed. The results indicate several challenges emerging at various stages of the experimental pipeline which bring forward important research questions and directions of improvement.
Job Shop Scheduling is a combinatorial optimization problem of particular importance for production environments where the goal is to complete a production task in the shortest possible time given limitations in the resources available. Due to its computational complexity it quickly becomes intractable for problems of interesting size. The emerging technology of Quantum Annealing provides an alternative computational architecture that promises improved scalability and solution quality. However, several limitations as well as open research questions exist in this relatively new and rapidly developing technology. This paper studies the application of quantum annealing to solve the job shop scheduling problem, describing each step required from the problem formulation to the fine-tuning of the quantum annealer and compares the solution quality with various classical solvers. Particular attention is devoted to aspects that are often overlooked, such as the computational cost of representing the problem in the formulation required by the quantum annealer, the relative qubits requirements and how to mitigate chain breaks. Furthermore, the impact of advanced tools such as reverse annealing is presented and its effectiveness discussed. The results indicate several challenges emerging at various stages of the experimental pipeline which bring forward important research questions and directions of improvement.
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.
A flexible job shop scheduling problem (FJSSP) poses a complex optimization task in modeling real-world process scheduling tasks with conflicting objectives. To tackle FJSSPs, approximation methods are employed to ensure solutions are within acceptable timeframes. Quantum Annealing, a metaheuristic leveraging quantum mechanical effects, demonstrates superior solution quality in a shorter time compared to classical algorithms. However, due to hardware limitations of quantum annealers, hybrid algorithms become essential for solving larger FJSSPs. This paper investigates the threshold problem sizes up to which quantum annealers are sufficient and when hybrid algorithms are required, highlighting the distribution of computing power in hybrid methods.
A promising use of quantum computers lies in the logistics and scheduling of industrial problems, such as space mission planning, maritime management, and many others. This field is expected to provide useful applications for quantum computing at the current stage of hardware development. Quantum annealing techniques have been proposed to solve scheduling problems, along with many other optimization problems. In this work, we test quantum annealing and hybrid techniques based on the D-Wave hardware to solve scheduling problems in the framework of job shop scheduling (JSP), which consists of optimally assigning operations to certain resources, while satisfying specific constraints and minimizing the total scheduling time, known as timespan. We devised an iterative algorithm that produces valid schedules for decreasing timespan values. We implemented a refined iterative variable pruning technique, which significantly reduces the number of spin variables in the corresponding Ising model, whose low-energy configurations are sampled by using the D-Wave Hybrid Solver Service. Our novel iterative algorithm leverages a directed acyclic graph (DAG) representation of partial or complete solutions of the JSP instance, which enables an efficient update of the feasible processing time windows for each operation. This approach leads to significantly improved results compared to the standard state-of-the-art applications of quantum annealing for the JSP. Remarkably, we can often prove the absolute optimality of the obtained solution, namely that a more efficient schedule within a shorter timespan can not exist.
The Job Shop Scheduling Problem (JSSP) has always been considered as one of the most complex and industry essential scheduling problems. Optimizing the makespan of a given schedule generally involves using dedicated algorithms, local search strategies, or metaheuristics. These approaches, however, heavily rely on classical computational power, which is bounded by the physical limits of microcontrollers and power issues. Inspired by the promising results achieved for Quantum Annealing (QA) based approaches to solve JSSP instances, we propose a new approach that uses gate-model quantum architecture as an alternative to QA. We find that we can make use of the time-indexed JSSP instance representation to build a cost Hamiltonian, which can be embedded into Quantum Approximate Optimization Algorithm (QAOA) to find an optimal solution to a basic JSSP instance. We demonstrate the use of QAOA to solve the JSSP, and we evaluate its efficiency and accuracy for this problem from experimental results, as there is an increased urgency to demonstrate the applicability of quantum optimization algorithms. We also find that optimal variational parameters form patterns that can facilitate computation in bigger quantum circuits. Additionally, we compare the obtained noiseless simulation results of gate-model quantum circuits demonstrating the relationship between two evaluation criteria - makespan and energy. Finally, we analyze and present the overall performance of our approach with the increasing deadline and simulated depth of QAOA circuits.
Quantum Processing Units promise speed-ups for selected computational problems, including combinatorial optimisation, but their industrial utility remains an open challenge. We study an industrial variant of the Job-Shop Scheduling Problem using quantum, quantum-inspired, and classical methods across three platforms: IBM Quantum, the D-Wave Quantum Annealer, and the Fujitsu Digital Annealer. By tailoring formulations to hardware-specific constraints, we show that hardware-software co-design is essential for solution quality and scalability. We benchmark all approaches against an exact classical solver and a MILP formulation, evaluating runtime, solution quality, and scalability. Our results indicate that quantum and quantum-inspired optimisation can support industrial solver selection, integration in classical workflows, modelling decisions, and early proof-of-concept development, while suggesting a potential path towards improved approximations for industrial scheduling.
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.