Key Takeaways & Executive Findings
- •• Formulates a cold rolling scheduling problem as a mixed integer linear program (MILP) with an economic objective, incorporating practical constraints like due dates, batch attributions, and parallel heterogeneous machines. • Proposes a modified genetic algorithm (GA) with heuristic initialization, three heuristic mutation operators, and parallel computing to efficiently solve the MILP. • Simulation results confirm the method's effectiveness in generating optimized scheduling schemes for cold rolling, improving operational efficiency and profitability. • Addresses unique challenges in steel cold rolling, including batch size preferences and job compatibility constraints, which are often overlooked in existing literature.
Abstract
A well-designed production schedule for cold rolling can enhance steel enterprises’ operational efficiency and profitability. Nevertheless, the intricate constraints and numerous steps involved in cold rolling pose challenges to devising a rational scheduling plan. Therefore, considering the practical production constraints, this paper investigates a cold rolling scheduling problem for processing jobs with specific due dates and batch attributions on parallel heterogeneous machines with continuous production requirements. Firstly, the scheduling problem is formulated as a mixed integer linear program (MILP) model with an economic objective. Then, a modified genetic algorithm (GA) is proposed to search for the optimal solution to the MILP problem. Specifically, this method includes a heuristic initialization mechanism to generate feasible initial solutions, three heuristic mutation operators to generate promising candidate solutions, and a parallel computing mechanism to accelerate the evaluation process of the GA. The simulation results demonstrate that the proposed method can be effectively implemented to generate optimized scheduling schemes in the cold rolling process.
1. Introduction
Cold rolling plays a crucial role in the production of steel products, and its output is widely utilized in various industries such as packaging, automotive manufacturing, electrical engineering, and others [1]. The demand for steel products from customers is characterized by a diverse range of products, small production batches, and individualized requirements due to the constantly evolving application scenarios [2]. Therefore, cold rolling is characterized by a lengthy production process and intricate constraints. The transformation of a steel coil into a finished cold-rolled steel product involves multiple processes, each requiring various pieces of parallel equipment [3]. Each process is subject to unique constraints, resulting in the cold rolling scheduling problem being exceedingly complex in large-scale production [4].
The flexible job-shop scheduling problem (FJSP) provides a general mathematical model for planning and scheduling cold rolling production [5, 6]. Although the FJSP has been extensively researched as a classic complex scheduling issue, the steel cold rolling production scheduling problem has distinct characteristics and requirements [7]. On the one hand, in addition to the standard production costs, cold rolling scheduling also needs to consider setup costs, tardiness penalties, and other factors. For instance, a setup is required whenever there is a need for the machine to switch operating modes or for job transfers between different machines. Therefore, cold rolling scheduling presents a multi-objective optimization problem. On the other hand, in addition to the time constraints in the typical FJSP, the cold rolling process requires consideration of batch production constraints and job compatibility constraints. Prior to being processed by the machine, all jobs to be produced must undergo batching together based on their similarity. There is a certain limit to the batch size, typically preferable when larger. This preference arises from larger batch sizes enhancing material continuity and minimizing switching times between different production processes, optimizing equipment’s effective capacity. Compatibility constraints pertain to the necessity for the specifications of adjacent jobs to be compatible, ensuring uninterrupted machine production. For instance, the difference in width between successive steel coils is referred to as width deviation. When the deviation exceeds the threshold, a transition coil needs to be inserted at this position. However, using a transition coil also occupies a certain capacity, which will reduce equipment utilization. To the best of our knowledge, these particular issues have not been considered in the existing literature.
Furthermore, numerous specialized optimization methods have been developed for intricate scheduling optimization models. These methods can be classified into three categories: mathematical programming approaches, heuristic methods, and evolutionary algorithms.
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Hairong Yang, Yangyi Du, Yonggang Li, Weidong Qian, Bing Hu (2025). A Heuristic Mutation Based Genetic Algorithm for Fast Parallel Scheduling of Steel Cold Rolling. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01271-1
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Frequently Asked Questions
What is the main contribution of this paper?
The paper proposes a modified genetic algorithm with heuristic initialization, three heuristic mutation operators, and parallel computing to efficiently solve a cold rolling scheduling problem formulated as a MILP model, addressing practical constraints like batch and compatibility.
What are the key constraints considered in the cold rolling scheduling problem?
The problem considers due dates, batch attributions, parallel heterogeneous machines, continuous production requirements, setup costs, tardiness penalties, batch size limits, and job compatibility constraints such as width deviation.
How does the proposed genetic algorithm improve scheduling efficiency?
The algorithm uses a heuristic initialization to generate feasible solutions, three heuristic mutation operators to explore promising candidates, and a parallel computing mechanism to accelerate fitness evaluation, leading to faster and better scheduling.
What is the significance of the simulation results?
The simulation results demonstrate that the proposed method can effectively generate optimized scheduling schemes for cold rolling, enhancing operational efficiency and profitability in steel enterprises.
Why is cold rolling scheduling considered complex?
Cold rolling scheduling is complex due to lengthy production processes, intricate constraints, multi-objective optimization (costs, tardiness), batch production requirements, and job compatibility constraints, making traditional methods insufficient.
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