考虑学习效应及次品率的制造商生产批量和信用期优化

Optimal Trade Period and Production Batch of Manufacturer with Learning Effects and Defect Rate

现实中销售商需要把信用期和批量一样当作决策变量。本文把卖方定位为生产过程中存在学习效应的非完美生产制造商,一是考虑需求同时受信用期和销售价格的影响;二是考虑商业信用给制造商带来机会成本和违约风险,站在制造商的视角构建了制造商的信用期和生产批量优化模型。通过定理证明了在一定条件下,模型存在唯一的最优解并用算例验证了模型的可行性和合理性。最后通过对参数进行灵敏度分析,得出制造商生产过程中的学习能力越强,给予下游购买商的信用期越长、生产批量越大、企业利润越高等结论。

Trade credit , while bringing the benefits of increasing sales to the sellers , also increases the disadvantages of opportunity cost and the default risk .The sellers should set the trade credit period as a de-cision variable as the production batch .The seller is, in this research, taken as an imperfect manufacturer who produces items with learning curve production costs and defect rate .An economic production quantity （ EPQ） model is proposed , in which there are two decision variables as the trade credit period and the pro-duction batch .The model follows two assumptions , the first being that the annual demand rate in units is determined by both the trade credit period and the production batch and the second being the trade credit brings opportunity cost and default risk to the manufacturer .Then the properties of the objective function are derived , and it is shown that there exists at most one minimum point under certain conditions , and this has been proved by a numerical example .Finally , a sensitivity analysis is conducted to understand manag-erial insights such as that the stronger the ability to learn , the shorter the credit period , the smaller the production lot size , and the lower the profit and that the higher the defective rate , the shorter the credit pe-riod, the smaller the production lot size , and the lower the profit .