constraint-based scheduling

To address suboptimal scheduling in resource-constrained project scheduling caused by overly restrictive constraints, this paper proposes a framework that automatically identifies critical bottleneck constraints and precisely locates relaxable ones. Methodologically, it integrates job-shop heuristics, constraint sensitivity analysis, iterative re-optimization, and two relaxation strategies—targeted and non-targeted. A key contribution is the empirical finding that non-targeted relaxation achieves performance comparable to targeted relaxation in reducing project tardiness, challenging the conventional intuition that explicit optimization direction is necessary. Experiments across multiple case studies demonstrate significant reductions in task delays, validate the accuracy of bottleneck identification, and confirm the effectiveness of constraint relaxation. The framework provides interpretable and actionable constraint tuning support for Advanced Planning and Scheduling (APS) systems.

This work investigates the reasoning reliability of large language models (LLMs) on the highly constrained NP-complete Resource-Constrained Project Scheduling Problem (RCPSP). We propose R-ConstraintBench, a novel evaluation framework that generates synthetic RCPSP instances of controllable difficulty using directed acyclic graphs, systematically incorporating non-redundant precedence, downtime, time-window, and mutual-exclusion constraints. Our feasibility analysis and error-mode diagnosis reveal that constraint interaction—not individual constraint complexity—is the primary bottleneck causing LLM failure. Experiments across diverse LLMs show near-optimal performance under single precedence constraints but sharp feasibility degradation under composite constraints; moreover, strong synthetic-data performance fails to generalize to real-world domain instances. This is the first study to quantitatively characterize the detrimental impact of constraint interaction on LLM reasoning for scheduling. The work establishes a scalable, diagnostic benchmark and methodology for developing trustworthy AI-driven scheduling systems.

This paper addresses the multi-machine serial-batch (s-batch) scheduling problem with a minimum batch size constraint, incorporating practical complexities including non-identical job weights, release times, and sequence-dependent setup times across job families. We propose the first exact Constraint Programming (CP) model for this problem—overcoming prior reliance solely on dynamic programming and metaheuristics. By introducing batch-group-based modeling and an efficient encoding scheme for sequence-dependent setup times, our CP formulation significantly outperforms two state-of-the-art Mixed-Integer Programming (MIP) models on benchmark instances: it reduces solution time substantially and yields superior solutions on large-scale instances. Extensive experiments demonstrate its strong adaptability and engineering practicality, establishing a novel, efficient modeling paradigm for real-world applications—such as semiconductor manufacturing and metal processing—where minimum batch requirements are strictly enforced.

For serial batch scheduling with minimum batch size constraints (e.g., semiconductor ion implantation), existing constraint programming (CP) models rely on predefined dummy batches, leading to the curse of dimensionality and high modeling complexity. This paper proposes a novel CP model that eliminates dummy batches entirely: it directly encodes contiguous sequences of jobs from the same family via critical alignment parameters, thereby avoiding combinatorial explosion; it further integrates a customized search strategy and enhanced constraint propagation to improve solving efficiency. Experiments on nearly 5,000 instances demonstrate that the approach significantly outperforms baseline methods on small-to-medium-scale problems and improves average solution quality by 25% for large-scale instances. The core contribution is the first compact, dummy-batch-free CP formulation and efficient solving framework for minimum batch size-constrained scheduling.

This study addresses the Resource-Constrained Project Scheduling Problem (RCPSP) by proposing a modeling approach based on timed Petri nets, wherein scheduling decisions are represented as transitions in the state space triggered by relative delay tokens. Building upon this formulation, the authors design an admissible A* heuristic that integrates critical path information with resource-constrained lower bounds to enable efficient optimal search. Experimental results on the PSPLIB benchmark suite demonstrate that the proposed method outperforms state-of-the-art mixed-integer programming solvers such as SCIP and CBC in both solution success rate and computational time. Furthermore, the findings reveal a complementary performance relationship between heuristic search and mixed-integer programming approaches across varying problem scales.

This work addresses the inefficiency of traditional scheduling approaches in handling cumulative constraints, which often neglect interactions among multiple resources. The authors propose a novel preprocessing method that systematically integrates cover-set identification with inequality lifting techniques to model cumulative constraints as linear inequalities over occupation vectors. This approach automatically infers and injects new constraints that explicitly capture multi-resource coupling relationships—without requiring additional search or probing. By significantly enhancing constraint propagation, the method effectively identifies incompatibilities among tasks that preclude parallel execution. Evaluated on standard RCPSP and RCPSP/max benchmark instances, the technique not only markedly improves solving performance but also establishes 25 new lower bounds—eight of which directly result from the inferred constraints—and yields five new optimal solutions.

This study systematically evaluates the faithfulness and consistency of large language models (LLMs) in adhering to constraints when solving natural language scheduling problems that are semantically equivalent but differ in surface form. To this end, we introduce SCHEDBench, the first natural language benchmark for combinatorial scheduling tasks, encompassing diverse problem types such as job shop scheduling (JSP), resource-constrained project scheduling (RCPSP), workforce rostering, and timetabling. We generate varied surface formulations through lexical-syntactic rewrites and constraint reordering. Using scheduling solvers for validation and domain-specific templates for generation, our evaluation across 13 state-of-the-art LLMs reveals a critical lack of invariance: surface-level variations significantly degrade solution feasibility, with constraint reordering most frequently causing violations of hard constraints. This work is the first to expose the pronounced sensitivity of LLMs to linguistic surface form in scheduling reasoning.

This work addresses the challenge of maximizing end-to-end success probability in structured agent workflows under hard constraints on budget and deadline. The authors propose Monte Carlo Combinatorial Planning (MCPP), a lightweight closed-loop planner that dynamically replans during execution in response to observations. MCPP employs a finite-horizon stochastic online allocation model with parallel sampling and leverages Monte Carlo simulation to estimate, in real time, the probability of successful task completion under the given constraints. Experimental results demonstrate that MCPP significantly outperforms strong baseline methods on the CodeFlow and ProofFlow benchmarks, consistently achieving higher task completion rates across diverse budget–deadline configurations. These findings validate MCPP’s effectiveness and robustness in resource-constrained scenarios.

This work addresses the lack of native support in PyCSP3 for high-level abstractions such as interval variables, sequence variables, and resource functions commonly used in scheduling problems, which often leads to complex and error-prone models. To bridge this gap, the paper introduces, for the first time, a systematic set of scheduling-specific modeling primitives into PyCSP3. These primitives—comprising 53 constraints and 27 expressions—enable the construction of high-level scheduling models that are automatically compiled into standard XCSP3 format, thereby decoupling modeling from solving. The approach provides high-level interfaces encapsulating global constraints like NoOverlap and Cumulative. Evaluation on 261 instances demonstrates that eight model classes preserve their structure after compilation, 72 instances yield identical optimal solutions under dual verification, and selected instances achieve up to a 5.8× speedup, all while maintaining full compatibility with the existing PyCSP3 ecosystem.