Process Flexibility: A Distribution-Free Bound on the Performance of k-Chain
推导了长链与完全灵活性预期销售额比值的无分布闭式界，该界仅依赖随机需求的均值和标准差，且与使用完整分布信息的结果高度吻合，证明了长链在不同需求分布下的稳健性。
Process flexibility has been widely applied in many industries as a competitive strategy to improve responsiveness to demand uncertainty. An important flexibility concept is the long chain proposed by Jordan and Graves (1995) [Jordan WC, Graves SC (1995) Principles on the benefits of manufacturing process flexibility. Management Sci. 41(4):577–594.]. The effectiveness of the long chain has been investigated via numerical as well as theoretical analysis for specific probability distributions of the random demand. In this paper, we obtain in closed form a distribution-free bound on the ratio of the expected sales of the long chain relative to that of full flexibility. Our bound depends only on the mean and standard deviation of the random demand, but compares very well with the ratio that uses complete information of the demand distribution. This suggests the robustness of the performance of the long chain under different distributions. We also prove a similar result for k-chain, a more general flexibility structure. We further tighten the bounds by incorporating more distributional information of the random demand.