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Enterprise Resource Planning Using Multi-type Transformers in Ferro-Titanium Industry

Samira Yazdanpourmoghadam, Mahan Balal Pour, Vahid Partovi Nia

TL;DR

This paper addresses ERP-relevant combinatorial optimization by introducing Multi-Type Transformer (MTT), a unified transformer with heterogeneous attention designed for heterogeneous problem structures like KP and JSP. By encoding KP as a bipartite items-capacity graph and JSP as a disjunctive graph within a shared MTT backbone, the approach learns cross-domain representations and enables efficient, near-optimal solutions. Benchmark results show competitive gaps, with KP attaining about 0.001 and JSP around 0.03 relative to exact solvers, and real-world Ferro-Titanium application achieving stable gaps around 0.025–0.029 with sub-second runtimes on GPUs. The findings support the potential of multi-type attention for industrial ERP planning, while highlighting the need for more rigorous comparisons and ablations in future work.

Abstract

Combinatorial optimization problems such as the Job-Shop Scheduling Problem (JSP) and Knapsack Problem (KP) are fundamental challenges in operations research, logistics, and eterprise resource planning (ERP). These problems often require sophisticated algorithms to achieve near-optimal solutions within practical time constraints. Recent advances in deep learning have introduced transformer-based architectures as promising alternatives to traditional heuristics and metaheuristics. We leverage the Multi-Type Transformer (MTT) architecture to address these benchmarks in a unified framework. We present an extensive experimental evaluation across standard benchmark datasets for JSP and KP, demonstrating that MTT achieves competitive performance on different size of these benchmark problems. We showcase the potential of multi-type attention on a real application in Ferro-Titanium industry. To the best of our knowledge, we are the first to apply multi-type transformers in real manufacturing.

Enterprise Resource Planning Using Multi-type Transformers in Ferro-Titanium Industry

TL;DR

This paper addresses ERP-relevant combinatorial optimization by introducing Multi-Type Transformer (MTT), a unified transformer with heterogeneous attention designed for heterogeneous problem structures like KP and JSP. By encoding KP as a bipartite items-capacity graph and JSP as a disjunctive graph within a shared MTT backbone, the approach learns cross-domain representations and enables efficient, near-optimal solutions. Benchmark results show competitive gaps, with KP attaining about 0.001 and JSP around 0.03 relative to exact solvers, and real-world Ferro-Titanium application achieving stable gaps around 0.025–0.029 with sub-second runtimes on GPUs. The findings support the potential of multi-type attention for industrial ERP planning, while highlighting the need for more rigorous comparisons and ablations in future work.

Abstract

Combinatorial optimization problems such as the Job-Shop Scheduling Problem (JSP) and Knapsack Problem (KP) are fundamental challenges in operations research, logistics, and eterprise resource planning (ERP). These problems often require sophisticated algorithms to achieve near-optimal solutions within practical time constraints. Recent advances in deep learning have introduced transformer-based architectures as promising alternatives to traditional heuristics and metaheuristics. We leverage the Multi-Type Transformer (MTT) architecture to address these benchmarks in a unified framework. We present an extensive experimental evaluation across standard benchmark datasets for JSP and KP, demonstrating that MTT achieves competitive performance on different size of these benchmark problems. We showcase the potential of multi-type attention on a real application in Ferro-Titanium industry. To the best of our knowledge, we are the first to apply multi-type transformers in real manufacturing.
Paper Structure (14 sections, 5 equations, 3 figures, 2 tables)

This paper contains 14 sections, 5 equations, 3 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. METHODOLOGY
  3. COMBINATORIAL BENCHMARKS
  4. Knapsack (KP)
  5. Job-Shop Scheduling Problem (JSP)
  6. Illustrative example (3 jobs, 3 machines).
  7. Problem Similarities
  8. BENCHMARKING
  9. FERRO-TITANIUM APPLICATION
  10. Problem Definition
  11. Mapping to KP
  12. Objective Alignment
  13. Numerical Results
  14. CONCLUSION

Figures (3)

  • Figure 1: Overview of the unified MTT pipeline for ERP optimization, KP and JSP are represented using heterogeneous graphs and solved using a shared Transformer backbone with type-specific attention.
  • Figure 2: Schematic illustration of combinatorial problems studied, the visualization of KP (left panel), and JSP (right panel).
  • Figure 3: The optimality gap of the OR solver compared with MTT on KP and JSP problems, see Table \ref{['tab:bench']}.