Process Flexibility: A Distribution-Free Bound on the Performance of K-Chain

Abstract

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. 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 sale 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.

Keywords: Process flexibility, problem of moments, asymptotic analysis, worst-case bound