Abstract: Shared manufacturing is a new type of production model based on cloud manufacturing technology to share free capacity. This model not only reduces the cost of equipment for user enterprises but also makes up for the lack of capacity of small and medium-sized enterprises due to the surge in orders. However, with the development of the market, manufacturing features such as socialization of manufacturing capacity, interconnection and integration are gradually emerging, which brings many challenges to the production scheduling problem under the shared manufacturing model. For example, scheduling under capacity sharing is mostly collaborative scheduling across enterprises; the production capacity and technology of different manufacturing enterprises are very different; the tasks and needs of customers have become more complex and variable; in addition, the reliability of the products delivered by manufacturing enterprises and the dynamic variability of the production process need to be taken into account. In this environment, it is of great theoretical and practical significance to efficiently integrate the scattered idle production capacity of various manufacturing enterprises, effectively carry out supply and demand matching and production scheduling, and maximize the interests of relevant stakeholders.
   Currently, few studies have focused on the time window of capacity available to enterprises and the effective flow between production and logistics. As for the solution algorithm, the traditional Non-dominated Sorting Genetic Algorithm (NSGA-II) has some limitations, such as the low-quality initial population that leads to slow convergence of the algorithm, the fixed cross-variation probability that reduces the accuracy of the search, which restricts the exploratory ability of the algorithm, and the simple cross-variation operation that cannot realize the evolutionary iteration of the solution, which leads to the algorithm's poor local searching ability.
   In this context, this paper establishes a distributed production scheduling model under cross-enterprise idle capacity sharing by taking into account the limited capacity time window, heterogeneous production performance and inter-enterprise transport collaboration of manufacturing enterprises, aiming at time, cost and quality. Then an improved NSGA-II algorithm is designed to solve the model according to its characteristics. The proposed algorithm uses three-type-population initialization strategies, adaptive cross-variation strategies and variable neighborhood search strategies combined with five operations to strengthen and balance the exploration and development abilities of the algorithm.
   To verify the effectiveness and superiority of the proposed algorithm, we extract three sets of data of different sizes in the example for experiments. The effectiveness experiment of the improved strategy and the algorithm comparison experiment are designed, respectively. Each group of data is independently tested 10 times, and the best results are taken to analyze the performance of the algorithm. Finally, a real case study compares the difference between the proposed algorithm and the traditional scheduling methods of the company in terms of improving capacity utilization.
   The experimental results show that: (1) The proposed improvement strategy is effective, and the proposed algorithm has obvious superiority. (2) The proposed model can be effectively applied to the production scheduling of idle capacity sharing, and the proposed algorithm can make fuller use of the idle resources of the enterprise and improve the capacity utilization rate.
   This study provides some new modeling ideas and algorithmic insights for shared manufacturing. However, in real shared manufacturing environments, where equipment and capacity or order information may often be subject to numerous anomalies, how to build models based on the characteristics of the problem and find efficient solutions in complex and uncertain environments will be an urgent issue to be explored in the future.

Key words: capacity sharing, distributed scheduling, idle capacity time window, different production performance, INSGA-II

摘要： 随着共享制造模式的发展,制造产能社会化和互联集成化的制造业特征逐渐显现。如何高效整合零散的闲置产能,打通生产与物流间的有效流转成为生产调度领域亟需解决的问题。本文综合考虑制造企业有限的产能时间窗,异质的生产性能和企业间的运输协作,以工期、成本和质量为目标,建立了跨企业空闲产能共享下的分布式生产调度模型。其次,为解决传统NSGA-II收敛缓慢和易陷入局部最优的情况,本文根据模型特点设计了改进的NSGA-II算法进行求解。所提算法通过3种种群初始化策略、自适应交叉变异策略和结合5种操作的变邻域搜索策略以加强和平衡算法的探索与开发能力。最后通过多组不同规模的算例实验表明:所提改进策略和所提算法具有显著的有效性和优越性;所提模型能够显著提高制造企业的产能利用率。

关键词: 产能共享, 分布式调度, 空闲产能时间窗, 异质的生产性能, INSGA-II