Worst-Case Analysis of Process Flexibility Designs

Theoretical studies of process flexibility designs had mostly focused on average-case analysis. In this paper, we take a different approach by studying process flexibility designs from a worst-case point of view. To study the worst-case performances, we introduce the so-called plant cover index, an index defined by a constrained bipartite vertex cover problem associated with a given flexibility design. We show that the plant cover index allows for a comparison between the worst-case performances of two flexibility designs based only on the design structures and is independent of the choice of the uncertainty set or the choice of the performance measure. More precisely, we show that if all of the plant cover indices of one design are greater than or equal to the plant cover indices of the other design, then the first design is more robust than the second one, i.e. performs better in worst-case under any symmetric uncertainty set and a large class of performance measures. Applying the plant cover index result, we show that the long-chain flexibility design, an important design in the study of process flexibility, is more robust than any flexibility design that has degree two on each of its product nodes, or any connected flexibility design with 2n arcs, where n is the number of products. Finally, motivated by the theoretical findings, we apply the plant cover index to propose a heuristic for generating effective flexibility designs. Numerical studies show that our heuristic performs well in both average-case and worst-case performance measures.