Facility disruptions in the supply chain often lead to catastrophic consequences, although they occur rarely. The low frequency and non-repeatability of disruptive events also make it impossible to estimate the disruption probability accurately. Therefore, we construct an uncertain programming model to design the three-echelon supply chain network with the disruption risk, in which disruptions are considered as uncertain events. Under the constraint of satisfying customer demands, the model optimises the selection of retailers with uncertain disruptions and the assignment of customers and retailers, in order to minimise the expected total cost of network design. In addition, we simplify the proposed model by analysing its properties and further linearise the simplified model. A Lagrangian relaxation algorithm for the linearised model and a genetic algorithm for the simplified model are developed to solve medium-scale problems and large-scale problems, respectively. Finally, we illustrate the effectiveness of proposed models and algorithms through several numerical examples.

High-order uncertain differential equations are used to model differentiable uncertain systems with high-order differentials, and how to solve the high-order uncertain differential equations is a core issue in practice. This paper aims at proposing a numerical method to solve the high-order uncertain differential equations based on the Runge-Kutta recursion formula, which is of high precision degree. A procedure is designed and some numerical experiments are performed to illustrate the effectiveness and efficiency of the Runge-Kutta method. In addition, this paper also presents a numerical method to calculate the expected value of a function of the solution.