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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 2870420, 10 pages
https://doi.org/10.1155/2017/2870420
Research Article

A New Method for Solving Multiobjective Bilevel Programs

1Business School, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, China
2College of Science, University of Shanghai for Science and Technology, Shanghai, China

Correspondence should be addressed to Ying Ji; moc.621@1891_gniyij

Received 14 May 2016; Revised 15 August 2016; Accepted 28 December 2016; Published 23 March 2017

Academic Editor: Kamel Barkaoui

Copyright © 2017 Ying Ji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a class of multiobjective bilevel programs with the weights of objectives being uncertain and assumed to belong to convex and compact set. To the best of our knowledge, there is no study about this class of problems. We use a worst-case weighted approach to solve this class of problems. Our “worst-case weighted multiobjective bilevel programs” model supposes that each player (leader or follower) has a set of weights to their objectives and wishes to minimize their maximum weighted sum objective where the maximization is with respect to the set of weights. This new model gives rise to a new Pareto optimum concept, which we call “robust-weighted Pareto optimum”; for the worst-case weighted multiobjective optimization with the weight set of each player given as a polytope, we show that a robust-weighted Pareto optimum can be obtained by solving mathematical programing with equilibrium constraints (MPEC). For an application, we illustrate the usefulness of the worst-case weighted multiobjective optimization to a supply chain risk management under demand uncertainty. By the comparison with the existing weighted approach, we show that our method is more robust and can be more efficiently applied to real-world problems.