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

TL;DR

This paper explores using Quantum Annealing to solve complex distributed job shop scheduling problems in the wool textile industry, demonstrating potential advantages over classical methods for large-scale instances.

Contribution

It introduces a quantum annealing approach tailored for large-scale distributed flexible job shop scheduling problems based on real industry data.

Findings

QA can solve larger problem instances than classical methods.

Quantum annealing shows promising solution quality and speed.

The study provides insights into QUBO parameter tuning for industry applications.

Abstract

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.