针对随机供需条件下装配商的订购与定价联合决策这一难题，运用随机非线性规划方法，以装配商期望利润最大化为目标，建立零部件订购量与最终产品定价的多维优化模型。刻画了给定价格时的最优订购量和给定订购量时的最优价格，最后给出关于最优订购-定价的必要条件。通过数值算例验证了模型结论并进一步探讨随机供需的影响，为装配商的订购-定价决策以及供应商改进提供有益的管理启示。
The optimal joint ordering-pricing decisions are studied in an assembly system consisting of n components in a single period setting. Demand for the end-product is random and component supply capacities are uncertain due to unexpected breakdowns, repairs and reworks, etc. The assembler jointly decides components ordering amounts and end-product price before the supply capacities and the demand are realized. Using stochastic nonlinear programming, a multidimensional optimization model in which the object is to maximize the assembler's expected profit is presented. It is showed that the optimal ordering policy is to order equally despite the supply uncertainties, and then the n+1-dimensional model can be reduced tobe of two dimensions (i.e., a unified ordering decision and a pricing decision). One decision is fixed and the corresponding optimal path of another decision is derived, and then the global optimal solution along the path is solved. Numerical experiments are conducted to justify the model and to further explore the effect of random supply and demand. For the random supply, the increase of the mean is related to investments in new production line or promises of overtime work, the decrease of variance is related to enhancements of preventive maintenance for manufacturing equipments or enhancements of training and education for workers to avoid misoperations, etc., the simultaneous increase of mean andvariance is related to supplier outsourcing its work to multiple second-tier suppliers. Based on these relations with practice, logical explanations are came up with and managers are offered with useful suggestions and insights.
[1] Erhardt G., Langlinais T., Ratta V. The call to become customer smart[J]. Technical Report Accenture, 2010.
[2] Kazaz B., Webster S. Price-setting newsvendor problems with uncertain supply and risk aversion[J]. Operations Research, 2015, 63(4):807-811.
[3] Pan Wenting, So K C. Optimal product pricing and component production quantities for an assembly system under supply uncertainty[J]. Operations Research, 2010, 58(6):1792-1797.
[4] Bollapragada R, Rao U S, Zhang Jun. Managing inventory and supply performance in assembly systems with random supply capacity and demand[J]. Management Science, 2004, 50(12):1729-1743.
[5] Whitin T. M. Inventory control and price theory[J]. Management science, 1955, 2(1):61-68.
[6] 张菊亮, 章祥荪, 王耀球. 一般需求函数下报童模型的定价与库存控制[J]. 系统工程理论与实践, 2008, 28(9):20-28.
[7] Chen Xin, Simchi-Levi D. Pricing and inventory management[M]. Oxford:Oxford University Press, 2012:784-824.
[8] 李贵萍. 基于前景理论的单周期定价与订购联合决策模型[J]. 中国管理科学, 2013,21:502-507.
[9] 段永瑞,李贵萍,霍佳震. 有限时域内部分缺货的变质品生产-定价策略研究[J]. 中国管理科学, 2014, 22(1):94-103.
[10] Yan Xiaoming, Wang Yong. An EOQ model for perishable items with supply uncertainty[J]. Mathematical Problems in Engineering, 2013, 2013.
[11] Wang Yunzheng, Gerchak Y. Periodic review production models with variable capacity, random yield, and uncertain demand[J]. Management Science, 1996, 42(1):130-137.
[12] Hwang J., Singh M. R. Optimal production policies for multi-stage systems with setup costs and uncertain capacities[J]. Management Science, 1998, 44(9):1279-1294.
[13] Hu Xinxin, Duenyas I, Kapuscinski R. Optimal joint inventory and transshipment control under uncertain capacity[J]. Operations Research, 2008, 56(4):881-897.
[14] Erdem A S, Fadiloglu M M, Özekici S. An EOQ model with multiple suppliers and random capacity[J]. Naval Research Logistics (NRL), 2006, 53(1):101-114.
[15] Ji Qingkai, Wang Yunzeng, Hu Xiangpei. Optimal production planning for assembly systems with uncertain capacities and random demand[J]. European Journal of Operational Research, 2016, 253(2):383-391.
[16] Bollapragada R, Kuppusamy S, Rao U S. Component procurement and end product assembly in an uncertain supply and demand environment[J]. International Journal of Production Research, 2015, 53(3):969-982.
[17] Wang Yimin, Gilland W, Tomlin B. Mitigating supply risk:Dual sourcing or process improvement?[J]. Manufacturing & Service Operations Management, 2010, 12(3):489-510.
[18] 钱佳, 骆建文. 产能随机下的零售商最优订购策略[J]. 系统管理学报, 2014, 23(03):351-358.
[19] 马士华, 李毅鹏. 产能不确定环境下多供应商横向协同问题研究[J]. 工业工程与管理, 2011, 16(1):37-40.
[20] Xiao Yongbo, Chen Jian, Lee C Y. Optimal decisions for assemble-to-order systems with uncertain assembly capacity[J]. International Journal of Production Economics, 2010, 123(1):155-165.
[21] Petruzzi N C, Dada M. Pricing and the newsvendor problem:A review with extensions[J]. Operations Research, 1999,47(2):183-194.
[22] Kocabiyikoglu A., Popescu I. An elasticity approach to the newsvendor with price-sensitive demand[J]. Operations Research, 2011, 59(2):301-312.
