Neutrosophic programming approach to multilevel decision-making model for supplier selection problem in a fuzzy situation

In supply chain management, the selection of supplier is of vital importance, and plays a valuable role in the performance of organizations. A hierarchical structure, with different levels in the selection of suppliers, is employed, wherein sequential decisions are made from the highest to the lowest level. Decision variables, called controlling factors, are divided into several categories. In the decision-making process, often because of the lack of confidence or uncertainty, It becomes hard for decision-makers to give explicit/crisp values to any parameter, resulting in uncertainty in the problem. In this paper, we address a multi-level supplier selection problem with fuzzy supply and demand. To avoid decision conflicts, superior or upper-level decision makers give tolerances that could be used as a possible relaxation. Thus, the problem is employed with fuzzy constraints. Based on a neutrosophic decision set, the Neutrosophic Compromise Programming Approach (NCPA) is used as a solution technique with the idea of indeterminacy degree as well as different objectives for membership and non-membership degree. Membership functions (Linear-type) are used to develop satisfactory solutions by fuzzily describing objective functions as well as controlling factors. A numerical illustration is provided to demonstrate the validity and appropriateness of NCPA.