A Benchmarking Environment for Worker Flexibility in Flexible Job Shop Scheduling Problems

TL;DR

The paper tackles the lack of standardized benchmarking for Flexible Job Shop Scheduling Problems (FJSSP) and its worker-flexible variant (FJSSP-W) by introducing an open-source benchmarking environment and a curated set of 402 FJSSP instances extended to FJSSP-W. It provides problem encodings for MILP, CP, and SBO paradigms, a reproducible instance extension workflow, and a comprehensive evaluation framework with statistical comparison using MiniZinc scores and Friedman/Nemenyi tests. The environment enables targeted solver development through filtering, systematic benchmarking, and visualization of makespan performance across diverse problem characteristics. The work enables reproducible, fair comparisons across solvers and lays the groundwork for extending benchmarks with additional metrics and uncertainty modeling to better reflect real-world staffing and production dynamics.

Abstract

In Production Scheduling, the Flexible Job Shop Scheduling Problem (FJSSP) aims to optimize a sequence of operations and assign each to an eligible machine with varying processing times. For integration of the workforce, each machine also requires a worker to be present to process an operation which additionally affects the processing times. The resulting problem is called Flexible Job Shop Scheduling Problem with Worker Flexibility (FJSSP-W). The FJSSP has been approached with various problem representations, including Mixed Integer Linear Programming (MILP), Constrained Programming (CP), and Simulation-based Optimization (SBO). In the latter area in particular, there exists a large number of specialized Evolutionary Algorithms (EA) like Particle Swarm Optimization (PSO) or Genetic Algorithms (GA). Yet, the solvers are often developed for single use cases only, and validated on a few selected test instances, let alone compared with results from solvers using other problem representations. While suitable approaches do also exist, the design of the FJSSP-W instances is not standardized and the algorithms are hardly comparable. This calls for a systematic benchmarking environment that provides a comprehensive set of FJSSP(-W) instances and supports targeted algorithm development. It will facilitate the comparison of algorithmic performance in the face of different problem characteristics. The present paper presents a collection of 402 commonly accepted FJSSP instances and proposes an approach to extend these with worker flexibility. In addition, we present a detailed procedure for the evaluation of scheduling algorithms on these problem sets and provide suitable model representations for this purpose. We provide complexity characteristics for all presented instances as well as baseline results of common commercial solvers to facilitate the validation of new algorithmic developments.

Figures (11)

• Figure 1: Visualization of the problem classes in the area of Production Scheduling considered in this paper. Notice that other problem types exist and the illustration does by no means claim to be comprehensive.
• Figure 2: Explanation of the standard FJSSP benchmark specifications on the basis of the 11th test instance from the collection in barnes_solving_1995.
• Figure 3: An overview over the benchmark instances on a subset of problem characteristics to show the distribution and similarities between instances. The instances are marked with respect to their original source.
• Figure 4: Explanation of the FJSSP-W benchmark specifications based on an extended FJSSP test instance.
• Figure 5: Illustration of the distribution of benchmark instances with respect to their flexibility $\beta$, duration variety $dv$, and their total amount of operations $\texttt{N}$. Note that the calculations of $\beta$ and $dv$ differs between the FJSSP (c.f. Eqs. \ref{['beta_flexibility']} and \ref{['duration_variety']}, and the FJSSP-W (c.f. Eqs. \ref{['eq:beta_fjssp-w']} and \ref{['eq:dv_fjssp-w']}), respectively.