Analysis of process flexibility designs under disruptions

Most previous studies concerning process flexibility designs have focused on expected sales and demand uncertainty. In this paper, we examine the worst-case performance of flexibility designs in the case of demand and supply uncertainties, where the latter can be in the form of either plant or arc disruptions. We define the Plant Cover Index under Disruptions (PCID) as the minimum required plants' capacity to supply a fixed number of products after the disruptions. By exploiting PCID, we establish that under symmetric uncertainty sets the worst-case performance can be expressed in terms of PCID, supply and demand uncertainties. Additionally, PCID enables us to make meaningful comparisons of different designs. In particular, we demonstrate that under disruptions the 2-long chain design is superior to a broad class of designs. Moreover, we identify a condition wherein both Q-short and Q-long chain designs have the same worst-case performance. We also discuss the notion of fragility that quantifies the impact of disruptions in the worst case and compare fragilities of Q-short and Q-long chain designs under different types of disruptions. Finally, by employing PCID, we develop an algorithm to generate designs that perform well under supply and demand uncertainties in both the worst case and in expectation.