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<p>In the era of Industry 4.0, cloud manufacturing (CMfg) systems face the challenge of processing massive service requests under real-time constraints. Task scheduling plays a critical role in enhancing the overall profitability and responsiveness of such systems. This study investigates a complex task scheduling problem considering the conflicting interests of three key stakeholders: (1) customers (meeting demands), (2) suppliers (maximizing subtask allocation), and (3) the cloud provider (optimizing profit). We developed a mixed-integer programming model to satisfy these objectives simultaneously. Given the NP-hard nature and the high computational complexity of the problem on large-scale instances, traditional exact methods are insufficient for real-time applications. To address this, we propose two scalable algorithms: a Heuristic based on Lagrangian relaxation (HLR) and a three-phase loop heuristic (H3PL). The performance of these methods was rigorously evaluated against CPLEX, as well as state-of-the-art metaheuristics including genetic algorithm (GA) and simulated annealing (SA). The results indicate that HLR offers superior solution quality, achieving a gap of at most 7.98% from the optimum while reducing computation time by 79%, outperforming GA and SA in terms of convergence stability. Conversely, the H3PL algorithm is designed for high-speed processing, reducing solution time by over 99% compared to the optimal approach, making it suitable for real-time decision-making, albeit with an average optimality gap of approximately 15–20%. These findings demonstrate that HLR is ideal for high performance computing-based planning, while H3PL facilitates instant response in dynamic cloud environments.</p>

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A Lagrangian heuristic for task scheduling in cloud manufacturing considering the interests of different stakeholders

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Seyed Ali Iranmanesh,
  • Majid Sheikhmohammady,
  • Ali Husseinzadeh Kashan

摘要

In the era of Industry 4.0, cloud manufacturing (CMfg) systems face the challenge of processing massive service requests under real-time constraints. Task scheduling plays a critical role in enhancing the overall profitability and responsiveness of such systems. This study investigates a complex task scheduling problem considering the conflicting interests of three key stakeholders: (1) customers (meeting demands), (2) suppliers (maximizing subtask allocation), and (3) the cloud provider (optimizing profit). We developed a mixed-integer programming model to satisfy these objectives simultaneously. Given the NP-hard nature and the high computational complexity of the problem on large-scale instances, traditional exact methods are insufficient for real-time applications. To address this, we propose two scalable algorithms: a Heuristic based on Lagrangian relaxation (HLR) and a three-phase loop heuristic (H3PL). The performance of these methods was rigorously evaluated against CPLEX, as well as state-of-the-art metaheuristics including genetic algorithm (GA) and simulated annealing (SA). The results indicate that HLR offers superior solution quality, achieving a gap of at most 7.98% from the optimum while reducing computation time by 79%, outperforming GA and SA in terms of convergence stability. Conversely, the H3PL algorithm is designed for high-speed processing, reducing solution time by over 99% compared to the optimal approach, making it suitable for real-time decision-making, albeit with an average optimality gap of approximately 15–20%. These findings demonstrate that HLR is ideal for high performance computing-based planning, while H3PL facilitates instant response in dynamic cloud environments.