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

Lilia Toma, Markus Zajac, Uta Störl

TL;DR

This work tackles solving the Distributed Flexible Job Shop Scheduling Problem (DFJSP) in the wool textile industry using Quantum Annealing on a D-Wave Advantage 4.1 system. It extends the DFJSP to simultaneously distribute production orders and production steps, incorporating inter-site shipping times, and develops a QUBO formulation with carefully tuned Lagrange parameters to solve large, industry-relevant instances. The study compares Quantum Annealing to Simulated Annealing, analyzes embedding limits and chain-strength effects, and demonstrates QA can yield valid, consistent schedules for problem sizes up to 150 variables, with potential speedups expected as quantum hardware and tuning techniques improve. These findings highlight QA's promise for industry-scale combinatorial optimization while underscoring the current hardware constraints and the need for continued advances in embedding and parameter optimization to realize practical benefits.

Abstract

Many modern manufacturing companies have evolved from a single production facility to a multifactory 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

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

TL;DR

This work tackles solving the Distributed Flexible Job Shop Scheduling Problem (DFJSP) in the wool textile industry using Quantum Annealing on a D-Wave Advantage 4.1 system. It extends the DFJSP to simultaneously distribute production orders and production steps, incorporating inter-site shipping times, and develops a QUBO formulation with carefully tuned Lagrange parameters to solve large, industry-relevant instances. The study compares Quantum Annealing to Simulated Annealing, analyzes embedding limits and chain-strength effects, and demonstrates QA can yield valid, consistent schedules for problem sizes up to 150 variables, with potential speedups expected as quantum hardware and tuning techniques improve. These findings highlight QA's promise for industry-scale combinatorial optimization while underscoring the current hardware constraints and the need for continued advances in embedding and parameter optimization to realize practical benefits.

Abstract

Many modern manufacturing companies have evolved from a single production facility to a multifactory 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
Paper Structure (18 sections, 19 equations, 7 figures, 3 tables)

This paper contains 18 sections, 19 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Combinatorial Optimization Problems
  4. Quantum Annealing
  5. Simulated Annealing
  6. Binary Quadratic Models
  7. Related Work
  8. Modell
  9. Problem formulation
  10. QUBO model
  11. Variable pruning
  12. Lagrange parameters
  13. Experiments
  14. Problem size and dataset
  15. Solver parameters
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Quantum Annealing versus Simulated Annealing (Source: authors, based on 157:Kasirajan2021157:Kasirajan2021)
  • Figure 2: Presentation of the DFJSP consisting of A Jobs, L Operations (per Job), B Machines and C Factories (Source: authors)
  • Figure 3: Chain break analysis for problem instance of size 150 (Source: authors)
  • Figure 4: Chain strength impact on solution quality (Source: authors)
  • Figure 5: Energy of best solutions obtained with QA and SA (Source: authors)
  • ...and 2 more figures