Uncertain random bilevel programming models and their application to shared capacity routing problem

Bilevel programming is frequently used to resolve decentralized decision-making problems in a hierarchical system. In practice, these problems usually contain indeterminacy parameters because of volatile factors or emergencies. As two sorts of indeterminacies, randomness and uncertainty may appear in a same system simultaneously, which produces uncertain random phenomena. For resolving decentralized decision-making problems containing uncertain random factors, this study serves to construct the uncertain random expected value, chance-constrained and dependent-chance bilevel programming models. And these models are all transformed into their corresponding equivalent forms via rigorous derivation. Furthermore, a metaheuristic algorithm is employed to obtain the Stackelberg-Nash equilibrium solutions of proposed models. Finally, the established models are applied to a shared capacity routing problem in the context of omni-channel retailing.