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(F, ρ)-invexity of higher order for multiobjective fractional variational problem

Kumar P., Sharma B.

Control and Cybernetics

2018

Vol. 47, no. 2

131--146

Multiobjective fractional variational problem is considered and suﬃcient optimality conditions, characterizing eﬃciency of higher order, are obtained under the assumptions of (F,ρ)−invexity of higher order on the functionals involved. Parametric higher order dual of the above stated problem is proposed. Duality theorems are proved to relate eﬃcient solutions of higher order for primal and its dual problem using generalized class of functionals.

A multi-level decision making model for supplier selection problem in a fuzzy situation

Adhami A. Y., Muneeb S. M., Nomani M. A.

Operations Research and Decisions

2017

Vol. 27, No. 4

5--26

Supplier selection plays a vital role in evolving an effective supply chain and the overall performance of organisations. Choosing suppliers may involve different levels arranged in a hierarchical structure. Decisions are made successively starting from the first level to the last level. Decision variables are partitioned between different levels and are called controlling factors. In the paper, we propose a multilevel supplier selection problem with uncertain or fuzzy demand and supply. Since objectives may be conflicting in nature, possible relaxations in the form of tolerances are provided by the upper level decision makers to avoid decision deadlocks. We use (linear) membership functions to fuzzily describe objective functions, as well as the controlling factors, and generate satisfactory solutions. We extend and present an approach to solving multilevel decision making problems when fuzzy constraints are employed. Different scenarios are constructed within a numerical illustration, based on the selection of controlling factors by the upper level decision makers.