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Updating Lower and Upper Bounds for the Job-Shop Scheduling Problem Test Instances

Marc-Emmanuel Coupvent des Graviers, Lotfi Kobrosly, Christophe Guettier, Tristan Cazenave

TL;DR

The paper tackles updating bounds for the Job-Shop Scheduling Problem and its Flexible variant by employing a Constraint Programming approach via OR-Tools. It defines a CP model for JSSP/FJSSP, applies two bound-search methods (OPT and SAT), and reports new numerical lower bounds for multiple benchmarks, including closing Taillard ta33, as well as improved upper bounds for ta26, ta45, 05a, and 06a, along with optimal solutions for ta45 and car5. While the results do not constitute formal proofs of the bounds, they offer practically valuable benchmarks for evaluating scheduling algorithms and provide detailed solutions and Gantt diagrams. The work highlights the effectiveness of a straightforward CP framework on open benchmarks and contributes new reference bounds to the scheduling community. The annex consolidates the improved bounds across datasets, supporting future comparative analyses.

Abstract

The Job-Shop Scheduling Problem (JSSP) and its variant, the Flexible Job-Shop Scheduling Problem (FJSSP), are combinatorial optimization problems studied thoroughly in the literature. Generally, the aim is to reduce the makespan of a scheduling solution corresponding to a problem instance. Thus, finding upper and lower bounds for an optimal makespan enables the assessment of performances for multiple approaches addressed so far. We use OR-Tools, a solver portfolio, to compute new bounds for some open benchmark instances, in order to reduce the gap between upper and lower bounds. We find new numerical lower bounds for multiple benchmark instances, up to closing the Taillard's ta33 instance. We also improve upper bounds for four instances, namely Taillard's ta26 & ta45 and Dauzere's 05a & 06a. Additionally we share an optimal solution for Taillard's ta45 as well as Hurink-edata's car5.

Updating Lower and Upper Bounds for the Job-Shop Scheduling Problem Test Instances

TL;DR

The paper tackles updating bounds for the Job-Shop Scheduling Problem and its Flexible variant by employing a Constraint Programming approach via OR-Tools. It defines a CP model for JSSP/FJSSP, applies two bound-search methods (OPT and SAT), and reports new numerical lower bounds for multiple benchmarks, including closing Taillard ta33, as well as improved upper bounds for ta26, ta45, 05a, and 06a, along with optimal solutions for ta45 and car5. While the results do not constitute formal proofs of the bounds, they offer practically valuable benchmarks for evaluating scheduling algorithms and provide detailed solutions and Gantt diagrams. The work highlights the effectiveness of a straightforward CP framework on open benchmarks and contributes new reference bounds to the scheduling community. The annex consolidates the improved bounds across datasets, supporting future comparative analyses.

Abstract

The Job-Shop Scheduling Problem (JSSP) and its variant, the Flexible Job-Shop Scheduling Problem (FJSSP), are combinatorial optimization problems studied thoroughly in the literature. Generally, the aim is to reduce the makespan of a scheduling solution corresponding to a problem instance. Thus, finding upper and lower bounds for an optimal makespan enables the assessment of performances for multiple approaches addressed so far. We use OR-Tools, a solver portfolio, to compute new bounds for some open benchmark instances, in order to reduce the gap between upper and lower bounds. We find new numerical lower bounds for multiple benchmark instances, up to closing the Taillard's ta33 instance. We also improve upper bounds for four instances, namely Taillard's ta26 & ta45 and Dauzere's 05a & 06a. Additionally we share an optimal solution for Taillard's ta45 as well as Hurink-edata's car5.

Paper Structure

This paper contains 8 sections, 2 figures, 16 tables.

Table of Contents

  1. Introduction
  2. The Job-Shop Scheduling Problem
  3. Problem description
  4. The Flexible Job-Shop Scheduling Problem
  5. Review of lower bounds computation
  6. Implementing the Job-Shop Scheduling Solver
  7. Results
  8. Conclusion

Figures (2)

  • Figure 1: Gantt's diagram of the optimal solution for the instance car5 of Hurink's vdatahurink1994tabu. Operations of the same colour belong to the same job, and white spaces represent inactivity on a machine. For this specific instance machines are used continuously without interleave between tasks.
  • Figure 3: Lower bound for Dauzere dauzere1995solving instance 16a, along solving time (log scale in seconds). Previously best known lower bound is 2193 in red. This previously known value is in the regime area where adding computational time is sufficient to find new values.