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

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.