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Uncertain multilevel programming with application to omni-channel vehicle routing problem
Rong Gao1, Yebao Ma1, Dan A Ralescu2
1School of Economics and Management, Hebei University of Technology, Tianjin, 300401 China.
Abstract:
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.
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