Interval-valued trapezoidal neutrosophic bi-level multiobjective linear programming numbers: algorithm and its application to pharmaceutical production planning problem

This paper describes solution methodology for bi-level multiobjective programming problems (BL-MOPPs) with interval-valued trapezoidal neutrosophic numbers (IVTrNNs) and its application in solving bi-level multi-objective production planning problem of pharmaceutical organizations. In this paper, the author proposed a simple and straight algorithm based on accuracy function for solving BL-MOPP under neutrosophic environment. Each interval-valued trapezoidal neutrosophic coefficient/parameter of the problem is converted into their respective equivalent crisp vales with the use of accuracy function of NNs. Thereafter, in order to handle decision deadlock situations due to bi-level multi-objective structure of the problem, separate membership function are created for each objective function of the problem as well as decision variables of the top level. Then goal programming is used to formulate solution models to obtain a satisfactory solution of BL-MOPP under a neutrosophic environment. A numerical example is illustrated with the proposed solution methodology to describe its computational simplicity and efficiency in solving BL-MOPPs with IVTrNNs. Besides this, a hypothetical case study related to production planning problem of a pharmaceutical company with two level hierarchical production units and multiple objectives at each level under vague information is discussed. The proposed technique is then applied to solve this industrial problem to show its applicability.