关键词: 产出率, 学习效应, 生产库存, 缺货, 需求依赖库存

Abstract: To research the optimization problem of production inventory of stock-dependent products under learning effect of productivity,two functions of minimizing total cost with shortage and without shortage were established.Aiming at the high nonlinearity of these two functions,the optimal production quantity and optimal production time were obtained with Newton iterative method.To illustrate the impact of learning effect on the result,numerical and sensitive analysis was conducted.The results showed that the learning effect played an important role in the early production stage,but the productivity reached a stable state in the later period,so the learning effect was limited.In the case of without shortage,the optimal production time and optimal production quantities with learning effect were less than those without learning effect.In the case of with shortage,compared with the model without learning effect,the model with learning effect had shorter optimal shortage time and shorter optimal production time,but larger optimal production quantities.With the increasing of learning coefficient,the optimal production quantity increased rapidly,but the optimal production time decreased.

Key words: productivity, learning effect, production inventory, shortage, stock-dependent demand