Minimizing the Weighted Number of Tardy Jobs: Data-Driven Heuristic for Single-Machine Scheduling

2025-08-19

AI Summary

This paper addresses the single-machine weighted tardiness minimization problem (1||∑w_jU_j), which seeks to minimize the total weight of tardy jobs. To overcome the significant performance degradation of existing exact algorithms on certain problem instances, we propose a data-driven heuristic approach: leveraging structured features—including job weights, processing times, and due dates—we employ supervised learning to predict critical decision variables, then integrate these predictions with domain-specific heuristics to construct feasible schedules. Systematic model selection and feature engineering enhance generalization across diverse problem distributions. Experimental results demonstrate that our method consistently outperforms state-of-the-art algorithms in three key aspects: average optimality gap, number of provably optimal solutions found, and robustness across heterogeneous data distributions. By bridging machine learning and combinatorial optimization, this work establishes a new paradigm for NP-hard scheduling problems—offering efficiency, interpretability, and practical applicability.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Heuristic Search
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Machine learning and data science for the Web

Abstract

Existing research on single-machine scheduling is largely focused on exact algorithms, which perform well on typical instances but can significantly deteriorate on certain regions of the problem space. In contrast, data-driven approaches provide strong and scalable performance when tailored to the structure of specific datasets. Leveraging this idea, we focus on a single-machine scheduling problem where each job is defined by its weight, duration, due date, and deadline, aiming to minimize the total weight of tardy jobs. We introduce a novel data-driven scheduling heuristic that combines machine learning with problem-specific characteristics, ensuring feasible solutions, which is a common challenge for ML-based algorithms. Experimental results demonstrate that our approach significantly outperforms the state-of-the-art in terms of optimality gap, number of optimal solutions, and adaptability across varied data scenarios, highlighting its flexibility for practical applications. In addition, we conduct a systematic exploration of ML models, addressing a common gap in similar studies by offering a detailed model selection process and providing insights into why the chosen model is the best fit.

Problem

• Minimizing weighted tardy jobs in single-machine scheduling
• Developing data-driven heuristic combining ML and scheduling characteristics
• Ensuring feasible solutions while outperforming existing algorithms

Innovation

• Data-driven heuristic combining machine learning
• Ensures feasible solutions with problem-specific characteristics
• Systematic ML model selection for adaptability