Abstract
In a supply chain system, the prices with which the suppliers supply its local commodity to the retailers should satisfy the requirements of the retailers and the consumers. The supply and demand scheme satisfying these requirements is reduced into fuzzy relation inequalities (FRIs) with min-product composition. Due to the difference between the min-product composition and the classical max-t-norm one, we first study the resolution of such min-product FRI system. For optimization management in the supply chain system, we further investigate a maximin programming problem subject to the min-product FRIs. An algorithm is proposed to obtain the optimal solution based on the quasi-maximal matrix and corresponding index set. To illustrate the efficiency of our proposed algorithm, we provide a simple numerical example. The obtained optimal solution reflects an optimal pricing scheme, which maximizes the minimum prices of the commodity from the suppliers.
Highlights
The classical fuzzy relational equation (FRE) system could be formulated as A ∘ x = b, (1)in which a11 a12 ⋅ ⋅ ⋅ a1n A = [[[[[[ a21 ... a22 ... ⋅⋅⋅ ... a2n
In many practical application fields, mathematical programming with FREs or fuzzy relation inequalities (FRIs) constraint was established and investigated, for describing the corresponding optimization model. Resolution of such optimization problems is usually related to the properties and structure of the feasible domain, and related to the characteristic of the objective function
Based on such equalitarianism consideration, we propose a new type of optimal model, i.e., the maximin optimization problem subject to min-product fuzzy relation inequalities, and investigate its resolution method in this work
Summary
In many practical application fields, mathematical programming with FREs or FRIs constraint was established and investigated, for describing the corresponding optimization model Resolution of such optimization problems is usually related to the properties and structure of the feasible domain (i.e., the solution set of a FREs or FRIs system), and related to the characteristic of the objective function. Based on the specific structure of the complete solution set of min-product fuzzy relation inequalities system, Yang et al [52] further studied a lexicographic optimization problem. Based on such equalitarianism consideration, we propose a new type of optimal model, i.e., the maximin optimization problem subject to min-product fuzzy relation inequalities, and investigate its resolution method in this work.
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