A signomial programming-based approach for multi-echelon supply chain disruption risk assessment with robust dynamic Bayesian network

Disruption risk assessment is a primary and crucial step before taking measures to mitigate the negative impact of disruptions propagating along supply chains (SCs). Recently, robust dynamic Bayesian network (DBN) provides a valid tool for disruption risk estimation under the ripple effect in a data-scarce environment. However, existing literature has not considered such disruption risk assessment for multi-echelon SCs that are usually structurally complicated and thus vulnerable to disruptions with ripple effects. Motivated by this fact, we study the disruption risk assessment problem under the ripple effect for a multi-echelon SC with several suppliers and one manufacturer, in which only probability intervals of the suppliers' states and those of the related disruption propagations are known. The aim is to acquire a robust risk estimation, measured by the worst-case total weighted probabilities for the manufacturer in the disrupted state over a time horizon. For the problem, a nonconvex nonlinear programming model is established to obtain the worst-case risk estimation. To efficiently solve the problem, a novel signomial programming (SP)-based approach is developed for finding near-optimal solutions. Numerical experiments on instances in the literature and our randomly generated instances are conducted to evaluate the efficiency of the proposed method. Besides, managerial insights are drawn.