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

2025-04-17

AI Summary

This work addresses the Job-Shop Scheduling Problem (JSSP) and its flexible variant (FJSSP), targeting the reduction of optimality gaps—particularly for long-standing open benchmark instances. We propose a boundary reinforcement framework that synergistically integrates Google OR-Tools’ exact optimization with problem-specific heuristic search to systematically tighten both lower and upper bounds on the makespan. Our approach achieves the first complete closure of the optimality gap for the Taillard instance ta33; establishes new provably valid lower bounds—and verifies optimality—for ta45 and car5; improves upper bounds for ta26, ta45, 05a, and 06a; and significantly narrows gaps for multiple historically unsolved instances. These results yield more rigorous theoretical benchmarks for JSSP/FJSSP evaluation, thereby advancing standardized benchmarking and algorithmic validation in scheduling optimization.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Solvers and Tools
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Reducing makespan in Job-Shop Scheduling Problem (JSSP) instances
• Computing new upper and lower bounds for benchmark instances
• Improving bounds for Taillard's and Dauzere's test cases

Innovation

• Using OR-Tools solver for bound computation
• Closing gap in Taillard's ta33 instance
• Improving upper bounds for four instances