Uncertain multilevel programming with application to omni-channel vehicle routing problem

Multilevel programming is widely applied to solve decentralized decision-making problems. In practice, indeterminacies are presented in these problems due to volatile factors or emergencies. As a type of indeterminacy, uncertainty is introduced in multilevel programming. For resolving multilevel programming problems with uncertain parameters, this paper constructs the uncertain expected value multilevel programming model and chance-constrained multilevel programming. Then, these models are converted to their equivalent forms. Moreover, the Stackelberg-Nash equilibrium solutions are obtained by using a genetic algorithm. Finally, these models are applied to the omni-channel vehicle routing problem, and a numerical experiment is given. The numerical experiment shows that the established models can optimize the distribution efficiency by coordinating the interests of decision-makers.