Transformer-Based Flow Shop Scheduling Using MILP-Generated Training Data
Abstract
Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.
Related
- Minimizing the makespan in job shop scheduling under conflict graph constraints
- EGD–ILS: Hybrid Penalty–Energy Gradient Descent Optimization for Job Shop Scheduling
- BOLT: Multi-Bottleneck Bound-Guided Learning for Flexible Job-Shop Scheduling with Time Lags and Resource-Coupled Transport
- SLAB: Time-Lag-Aware Deep Reinforcement Learning for Flexible Job-Shop Scheduling in PPVC Module Factories
- Radial Tail Repair: Post-Training Correction for Diffusion and Flow Models
BibTeX
@misc{wallrath2026transformerbased,
title = {{Transformer-Based Flow Shop Scheduling Using MILP-Generated Training Data}},
author = {Roderich Wallrath},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29690},
eprint = {2608.29690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29690},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transformer-Based Flow Shop Scheduling Using MILP-Generated Training Data
AU - Roderich Wallrath
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29690
UR - https://arxiv.org/abs/2608.29690
AB - Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.
ER -