A mathematical model for simultaneous personnel shift planning and unrelated parallel machine scheduling

This paper addresses a production scheduling problem derived from an industrial use case, focusing on unrelated parallel machine scheduling with the personnel availability constraint. The proposed model optimizes the production plan over a multi-period scheduling horizon, accommodating variations in personnel shift hours within each time period. It assumes shared personnel among machines, with one personnel required per machine for setup and supervision during job processing. Available personnel are fewer than the machines, thus limiting the number of machines that can operate in parallel. The model aims to minimize the total production time considering machine-dependent processing times and sequence-dependent setup times. The model handles practical scenarios like machine eligibility constraints and production time windows. A Mixed Integer Linear Programming (MILP) model is introduced to formulate the problem, taking into account both continuous and district variables. A two-step solution approach enhances computational speed, first maximizing accepted jobs and then minimizing production time. Validation with synthetic problem instances and a real industrial case study of a food processing plant demonstrates the performance of the model and its usefulness in personnel shift planning. The findings offer valuable insights for practical managerial decision-making in the context of production scheduling.

Deep reinforcement learning for machine scheduling: Methodology, the state-of-the-art, and future directions

Machine scheduling aims to optimize job assignments to machines while adhering to manufacturing rules and job specifications. This optimization leads to reduced operational costs, improved customer demand fulfillment, and enhanced production efficiency. However, machine scheduling remains a challenging combinatorial problem due to its NP-hard nature. Deep Reinforcement Learning (DRL), a key component of artificial general intelligence, has shown promise in various domains like gaming and robotics. Researchers have explored applying DRL to machine scheduling problems since 1995. This paper offers a comprehensive review and comparison of DRL-based approaches, highlighting their methodology, applications, advantages, and limitations. It categorizes these approaches based on computational components: conventional neural networks, encoder-decoder architectures, graph neural networks, and metaheuristic algorithms. Our review concludes that DRL-based methods outperform exact solvers, heuristics, and tabular reinforcement learning algorithms in terms of computation speed and generating near-global optimal solutions. These DRL-based approaches have been successfully applied to static and dynamic scheduling across diverse machine environments and job characteristics. However, DRL-based schedulers face limitations in handling complex operational constraints, configurable multi-objective optimization, generalization, scalability, interpretability, and robustness. Addressing these challenges will be a crucial focus for future research in this field. This paper serves as a valuable resource for researchers to assess the current state of DRL-based machine scheduling and identify research gaps. It also aids experts and practitioners in selecting the appropriate DRL approach for production scheduling.