Solving Distributed Flexible Job Shop Scheduling Problems in the Wool Textile Industry with Quantum Annealing

2024-03-11

arXiv.org

AI Summary

This study addresses the distributed flexible job-shop scheduling problem (DFJSP) in the wool textile industry, jointly optimizing order allocation, inter-factory operation assignment, and logistics constraints. We propose the first application of quantum annealing—specifically, D-Wave’s quantum processing unit (QPU)—to a real-world industrial DFJSP, formulating a hardware-embeddable quadratic unconstrained binary optimization (QUBO) model. To overcome scalability limitations, we develop a co-optimization method for Lagrangian penalty parameters and QPU configuration, enabling reliable embedding and solution of instances with up to 250 binary variables. On the largest embeddable instance, quantum annealing yields higher-quality solutions than simulated annealing (SA) while reducing computation time significantly. These results demonstrate both the feasibility and superiority of quantum annealing for large-scale industrial DFJSPs, establishing a practical, deployable pathway for quantum optimization in manufacturing systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

Abstract

Many modern manufacturing companies have evolved from a single production site to a multi-factory production environment that must handle both geographically 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 Distributed Flexible Job Shop Scheduling Problem (DFJSP). As a result, the complexity of production planning has increased significantly. In our work, we use Quantum Annealing (QA) to solve the DFJSP. In addition to the assignment of production orders to production sites, the assignment of production steps to production sites also takes place. This requirement is based on a real use case of a wool textile manufacturer. 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 the determination of 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.

Problem

• Solving distributed flexible job shop scheduling in wool textile industry
• Applying quantum annealing to optimize multi-site production assignments
• Comparing quantum annealing performance against simulated annealing methods

Innovation

• Quantum Annealing solves Distributed Flexible Job Shop Scheduling
• QUBO model optimizes production assignment across multiple factories
• D-Wave quantum processor handles up to 250 variable problems