A class of bi-level vector extremum models with hybrid uncertain coefficients and its application to supply chain planning problems

Abstract

Decision-making optimization for supply chain planning under uncertain environment is of vital importance since it determines the reliability and efficiency of whole system. In this paper, a bi-level supply chain planning model is established in which the core company is the leader and the suppliers and retailers are the followers in the hierarchal process. Considering the hybrid uncertainty of randomness and fuzziness in the bi-level vector extremum models, a class of linear combination between fuzzy coefficients and decision variables is studied and its crisp equivalent transformation under the given possibilistic level is proposed. Furthermore, the fuzzy decision is applied to separate the two-planner Stakelberg-Nash equilibrium and the Genetic Algorithm (GA) is developed to solve the bi-level multi-objective model with hybrid variables. A practical case is provided to illustrate robustness and practicality of the proposed methodology, and algorithm comparison is then given to prove the efficiency of the GA. The computational results indicate that the proposed model and techniques can provide appropriate tools to tackle the other supply chain planning problems with hybrid variable in uncertain decision-making environment.