Lexicographic Maximum Solution of Min-Product Fuzzy Relation Inequalities for Modeling the Optimal Pricing With Fixed Priority Grade in Supply Chain

Abstract

Fuzzy relation inequalities composed by the min-product operation are established to model the pricing relation in a supply chain system. Basic properties of the min-product fuzzy relation inequalities are presented first, based on which the complete solution set could be characterized and obtained. In fact, each solution of the corresponding fuzzy relation inequalities is exactly a feasible price scheduling. Considering the fixed priority grade of the suppliers, the concept of lexicographic maximum solution is introduced and investigated, as an optimal price scheduling that maximizes the benefits. A detailed algorithm is developed to search the unique lexicographic maximum solution with a numerical illustrative example.