A Comprehensive Benchmark of Constraint Programming Solvers for the Makespan-Minimisation Job Shop Scheduling Problem

The Job Shop Scheduling Problem (JSSP) is a paradigmatic and strongly NP-hard combinatorial optimisation problem that underpins production planning in modern manufacturing systems, and constraint programming (CP) has become one of the leading methodologies for tackling it. However, comparative studies of CP solvers for the JSSP have so far been restricted to a single benchmark family, a single instance-size range, or a single hardware setting, which limits the practical guidance they offer to both researchers and practitioners. This paper presents a controlled empirical evaluation of four state-of-the-art CP solvers—IBM ILOG CP Optimizer, Google OR-Tools (CP-SAT), Hexaly, and OptalCP—on the makespan-minimisation JSSP. The four engines are run with default parameters and a uniform 600-second wall-clock time budget on 332 instances drawn from nine canonical benchmark families (Fisher–Thompson, Lawrence, Adams–Balas–Zawack, Applegate–Cook, Yamada–Nakano, Storer–Wu–Vaccari, Taillard, Demirkol–Mehta–Uzsoy, and Da Col–Teppan), spanning sizes from 6 × 5 up to 1000 × 1000 operations. OptalCP emerges as the most robust engine overall, certifying optimality on 57.5% of the instances with the smallest average optimality gap (3.55%), while Hexaly dominates on industrial-scale problems and produces the bulk of 31 new best-known upper bounds and one new best-known lower bound reported here. Solver competitiveness depends sharply on instance size and on the n/m ratio, with square instances confirmed as the hardest case. These findings support an instance-aware approach to CP solver selection in industrial scheduling.