Process Flexibility Analysis for Production Systems with Differentiated Margins Under Supply Risk

To mitigate supply and demand uncertainties, firms often design highly flexible production networks. This study investigates process flexibility in production systems subject to supply disruptions and stochastic demands with differentiated profit margins. In particular, we model supply disruptions as failures of arcs in the network, with node-based disruptions treated as a special case in which all arcs connected to a node simultaneously fail. To address the cost implications of such disruptions, we investigate the design of process flexibility under a robust optimization framework. We first develop a greedy algorithm under deterministic demand to efficiently evaluate the worst-case disruption scenario, and demonstrate the significant advantage of the alternate long-chain design under such disruptions. Subsequently, under stochastic demand, by introducing the marginal profit group index under disruption (MPGID), we characterize the worst-case total profit as a function of both the flexibility design and demand uncertainty, modeled through a partwise independently symmetric perturbation set. This representation enables direct performance comparisons across different flexibility configurations under disruption risk. For the case involving two products with distinct profit margins under supply disruption risk, we demonstrate that the alternate long-chain design outperforms all other long-chain configurations in terms of worst-case profitability. In addition, in certain cases, arc-based disruptions can be just as devastating as plant-node disruptions, particularly when they lead to the loss of high-margin demand. However, our fragility analysis reveals that this design becomes increasingly vulnerable as disruption risks intensify. To address this issue, we propose an MPGID-based heuristic that systematically generates flexible designs to mitigate both supply and demand uncertainties.