零部件产能不确定下装配商的订购-定价联合优化模型

Optimal Joint Ordering-Pricing Decisions for an Assembler under Uncertain Components Production Capacities

针对零部件供应商产能不确定条件下装配商的订购与定价联合优化这一难题,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。通过求解给定价格时的最优订购量,将多维模型化为一维定价模型,随后给出关于最优定价的充分条件与必要条件,最终推导出订购与定价的最优决策。通过数值算例验证了模型结论并进一步探讨不确定产能的影响。研究结果表明,最优价格大于某个门槛价格,而尽管存在产能不确定性,装配商将按等比例订购零部件,并且其订购量等于最优价格对应的需求量。

For the joint ordering and pricing problem in an assembly system where the components＇ production capacities are uncertain, we formulate a stochastic multidimensional nonlinear programming model in which the objective function is to maximize the assembler＇s expected profit and the decision variables is to jointly determine the optimal components ordering quantities and the optimal end-product pricing. Using a two-stage approach, the multidimensional model is reduced to one-dimension model by first characterizing the optimal order quantities given any price, and then the optimal pricing decision can be derived under certain sufficient conditions and necessary conditions, in order to obtain the final optimal joint decision. Numerical experiments are conducted to justify the model and to further explore the effect of uncertain capacities. The results show that when the optimal price is higher than some threshold, and the assembler always orders equal amount of each component, which happens to be same as the expected demand value at the optimal price.