短期促销下存在缺陷品的零售商订货和检验速率决策模型

Optimal Lot Sizing and Screening Rate Decision Model for Items with Imperfect Quality under Sales Promotion

考虑到订货批量中存在缺陷产品,在短期促销背景下零售商可能出现检验能力不足的问题,分析了零售商的最优订货与检验速率决策。根据检验速率与促销期内需求率的关系,分别建立3种情形下零售商的利润函数。在情形1下,检验速率不足,且零售商投资增大检验速率,但产生额外的投资成本;在情形2下,检验速率不足,且零售商保持检验速率不变,但发生缺陷品退货;在情形3下,检验速率能满足促销期的需求率。分析每种情形下目标函数的性质,证明了情形1下目标函数关于订货量与检验速率的驻点存在且唯一,并且得到了在情形2和情形3下目标函数关于订货量的性质,进而设计求解方法。采用离散化方法将模型扩展到考虑促销价格决策的情境,并结合算例得到管理启示。

Considering that defective items might exist in each lot size during the production operations and that the retailer′s screening rate might become insufficient under sales promotion,the retailer′s optimal lot sizing and screening rate were determined. According to the relationship between the screening rate and the promotional demand rate,the retailer′s profit functions were formulated under 3 cases. In Case 1,when the screening rate was insufficient,the retailer increased the screening rate through investments,but incurred extra investment cost. In Case 2,when the screening rate was insufficient,the retailer kept the screening rate unchanged,but incurred defect sales returned. In Case 3,the screening rate was sufficient to meet the promotional demand rate. Then under each case,the properties of the objective function were derived. It was proved that in Case 1,the objective function had a unique stationary point with respect to lot sizing and screening rate,and the properties of the optimal lot sizing for Case 2 and Case 3 were obtained. A solution procedure was proposed to solve the problem. Using the discrete method,the model was further extended to the situation where the sale price was the decision variable. Numerical examples were provided to gain managerial insights.