Worst-Case Analysis of Process Flexibility Designs

Theoretical studies of process flexibility designs have mostly focused on expected sales. In this paper, we take a different approach by studying process flexibility designs from the worst‐case point of view. To study the worst‐case performances, we introduce the plant cover indices (PCIs), defined by bottlenecks in flexibility designs containing a fixed number of products. We prove that given a flexibility design, a general class of worst‐case performance measures can be expressed as functions of the design’s PCIs and the given uncertainty set. This result has several major implications. First, it suggests a method to compare the worst‐case performances of different flexibility designs without the need to know the specifics of the uncertainty sets. Second, we prove that under symmetric uncertainty sets and a large class of worst‐case performance measures, the long chain, a celebrated sparse design, is superior to a large class of sparse flexibility designs, including any design that has a degree of two on each of its product nodes. Third, we show that under stochastic demand, the classical Jordan and Graves (JG) index can be expressed as a function of the PCIs. Furthermore, the PCIs motivate a modified JG index that is shown to be more effective in our numerical study. Finally, the PCIs lead to a heuristic for finding sparse flexibility designs that perform well under expected sales and have lower risk measures in our computational study.