Abstract: When the product pass rate is randomly distributed, we build up the decision-making model of quantity putting into production, which is with total loss (insufficient production and then putting into production again charges, excess output charges and unqualified handling charges) expected value as the objective function, quantity putting into production as the decision variables. We sdve the optimal solution of the model with uniform distribution or normal distribution, and obtain equation between production and cast production, which effectively guide the production plan. Finally, we use a numerical example to prove the model is valid.

Key words: make to order, quantity putting into prodution, pass rate of product, erf(x), LambertW(x)

摘要： 当产品合格率随机分布时,建立起以投产综合损失费(欠产再投产费,过量产出费和不合格处理费)期望值为目标函数,投产量为决策变量的投产量模型。结合产品合格率随机分布不同(均匀分布和正态分布)推导求解了模型的最优解,得出了产量与投产量的等式关系,据此可有效地指导生产。最后通过数值实例分析验证了模型的有效性。

关键词: 订单式生产, 投产量, 产品合格率, 误差函数, 欧米加函数