Multi-level linear programming problem with neutrosophic numbers: A goal programming strategy

Abstract

In the paper, we propose an alternative strategy for multi-level linear programming (MLP) problem with neutrosophic numbers through goal programming strategy. Multi-level linear programming problem consists of k levels where there is an upper level at the first level and multiple lower levels at the second level with one objective function at every level. Here, the objective functions of the level decision makers and constraints are described by linear functions with neutrosophic numbers of the form [u + vI], where u, v are real numbers and I signifies the indeterminacy. At the beginning, the neutrosophic numbers are transformed into interval numbers and consequently, the original problem transforms into MLP problem with interval numbers. Then we compute the target interval of the objective functions via interval programming procedure and formulate the goal achieving functions. Due to potentially conflicting objectives of k decision makers, we consider a possible relaxation on the decision variables under the control of each level in order to avoid decision deadlock. Thereafter, we develop three new goal programming models for MLP problem with neutrosophic numbers. Finally, an example is solved to exhibit the applicability, feasibility and simplicity of the proposed strategy.