Fuzzy bilevel programming with multiple non-cooperative followers: model, algorithm and application

Abstract

In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers’ inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.

Keywords:

• Fuzzy bilevel programming
• Stackelberg–Nash equilibrium
• particle swarm optimization
• penalty function approach
• pricing competition

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 71371141, 71001080].