Bi-level Linear Programming Problem with Neutrosophic Numbers

Abstract

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level and lower or second level with one objective at each level. The objective function of each level decision maker and the system constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and I represents indeterminacy. In the decision making situation, we convert neutrosophic numbers into interval numbers and the original problem transforms into bi-level interval linear programming problem. Using interval programming technique, the target interval of the objective function of each level is identified and the goal achieving function is developed. Since, the objectives of upper and lower level decision makers are generally conflicting in nature, a possible relaxation on the decision variables under the control of each level is taken into account for avoiding decision deadlock. Then, three novel goal programming models are presented in neutrosophic numbers environment. Finally, a numerical problem is solved to demonstrate the feasibility, applicability and novelty of the proposed strategy.

Keywords

• Neutrosophic set
• neutrosophic number
• bi-level linear programming
• goal programming