An Aligned Constraint Programming Model For Serial Batch Scheduling With Minimum Batch Size

2025-11-20

AI Summary

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.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Programming
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

Abstract

In serial batch (s-batch) scheduling, jobs from similar families are grouped into batches and processed sequentially to avoid repetitive setups that are required when processing consecutive jobs of different families. Despite its large success in scheduling, only three Constraint Programming (CP) models have been proposed for this problem considering minimum batch sizes, which is a common requirement in many practical settings, including the ion implantation area in semiconductor manufacturing. These existing CP models rely on a predefined virtual set of possible batches that suffers from the curse of dimensionality and adds complexity to the problem. This paper proposes a novel CP model that does not rely on this virtual set. Instead, it uses key alignment parameters that allow it to reason directly on the sequences of same-family jobs scheduled on the machines, resulting in a more compact formulation. This new model is further improved by exploiting the problem's structure with tailored search phases and strengthened inference levels of the constraint propagators. The extensive computational experiments on nearly five thousand instances compare the proposed models against existing methods in the literature, including mixed-integer programming formulations, tabu search meta-heuristics, and CP approaches. The results demonstrate the superiority of the proposed models on small-to-medium instances with up to 100 jobs, and their ability to find solutions up to 25% better than the ones produces by existing methods on large-scale instances with up to 500 jobs, 10 families, and 10 machines.

Problem

• Optimizes serial batch scheduling with minimum batch size constraints
• Eliminates predefined virtual batch sets to reduce model complexity
• Improves solution quality for semiconductor manufacturing scheduling problems

Innovation

• CP model without predefined virtual batch sets
• Uses alignment parameters for same-family job sequences
• Enhanced with tailored search and constraint propagators