Processing time of each processing task.

Multi-objective production scheduling faces the problems of inter-objective conflicts, many uncertainty factors and the difficulty of traditional optimization algorithms to deal with complexity and ambiguity, and there is an urgent need to introduce the theory of fuzzy mathematics in order to improve the scheduling efficiency and optimization effect. Aiming at the shortcomings of existing kernel allocation methods, the proportional gain, weighted marginal, and average cost-saving allocation methods are innovatively proposed, all proven to be effective kernel allocation strategies. This paper analyzes the existing conditions of fuzzy mathematical scheduling solutions and probes into their relationship with fuzzy mathematical kernel allocation. It compares the similarities and differences between fuzzy mathematical scheduling solutions and other scheduling solutions. The experimental results show that the fuzzy mathematics theory reaches equilibrium when it evolves to 22 generations, and the maximum satisfaction degree is 2.345. The hybrid algorithm achieves equilibrium in the third generation, increasing the maximum satisfaction to 2.445. This shows that competitive strategy improves customer satisfaction and significantly accelerates the achievement of evolutionary equilibrium.

多目标生产调度（Multi-objective production scheduling）面临着目标间冲突频发、不确定性因素繁多，且传统优化算法难以处理复杂性与模糊性的问题，亟需引入模糊数学（fuzzy mathematics）理论以提升调度效率与优化效果。针对现有内核分配（kernel allocation）方法的固有缺陷，本文创新性地提出了比例增益分配法、加权边际分配法与平均成本节约分配法，经证实三者均为行之有效的内核分配策略。本文分析了模糊数学调度方案的现有研究现状，并探讨了其与模糊数学内核分配的内在关联，同时对比了模糊数学调度方案与其他调度方案的异同之处。实验结果表明，模糊数学理论在进化至第22代时达到均衡状态，其最大满意度为2.345；混合算法则在第3代即达成均衡，将最大满意度提升至2.445。由此可见，竞争策略可有效提升客户满意度，并显著加速进化均衡的实现。