In this paper, three production inventory models are constructed for an imperfect manufacturing system by considering a warm-up production run, shortages during the hybrid maintenance period, and the rework of imperfect items. The proportions of imperfect items produced during the warm-up and regular production runs are random and they are represented using a bivariate random variable. The shortage quantity is partially backordered and the supply of backorder quantity is planned simultaneously with regular demand satisfaction. The learning models are designed to accommodate the different learning capabilities of workers in unit production time during warm-up and regular production periods. The production and demand rates of these models are made dependent on the learning exponents. As the resulting models are highly nonlinear in the decision variable, they are optimized using a genetic algorithm. The models are illustrated using numerical examples and sensitivity studies are performed to find the influence of the key parameters.

在本文中，通过考虑预热生产运行，混合维护期间的短缺以及不完善项目的返工，为不完善的制造系统构建了三种生产库存模型。在预热和常规生产过程中生产的不完美物料的比例是随机的，并使用二元随机变量表示。短缺数量被部分延期交货，并且在定期满足需求的同时计划了延期交货的数量。学习模型旨在适应工人在预热和常规生产期间在单位生产时间内的不同学习能力。这些模型的生产率和需求率取决于学习指数。由于所得模型的决策变量高度非线性，因此使用遗传算法对其进行了优化。使用数值示例对模型进行了说明，并进行了敏感性研究以发现关键参数的影响。