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

Many modern manufacturing companies have evolved from a single productionsite to a multi-factory production environment that must handle bothgeographically dispersed production orders and their multi-site productionsteps. The availability of a range of machines in different locations capableof performing the same operation and shipping times between factories havetransformed planning systems from the classic Job Shop Scheduling Problem(JSSP) to Distributed Flexible Job Shop Scheduling Problem (DFJSP). As aresult, the complexity of production planning has increased significantly. Inour work, we use Quantum Annealing (QA) to solve the DFJSP. In addition to theassignment of production orders to production sites, the assignment ofproduction steps to production sites also takes place. This requirement isbased on a real use case of a wool textile manufacturer. To investigate theapplicability of this method to large problem instances, problems ranging from50 variables up to 250 variables, the largest problem that could be embeddedinto a D-Wave quantum annealer Quantum Processing Unit (QPU), are formulatedand solved. Special attention is dedicated to the determination of the Lagrangeparameters of the Quadratic Unconstrained Binary Optimization (QUBO) model andthe QPU configuration parameters, as these factors can significantly impactsolution quality. The obtained solutions are compared to solutions obtained bySimulated Annealing (SA), both in terms of solution quality and calculationtime. The results demonstrate that QA has the potential to solve large probleminstances specific to the industry.