A goal programming strategy for bi-level decentralised multi-objective linear programming problem with neutrosophic numbers

This paper develops a goal programming (GP) algorithm to evaluate bi-level decentralised multi-objective linear programming problem (BLDMOLPP) in neutrosophic number (NN) environment. In a BLDMOLPP, a single decision maker (DM) is present at the upper level and multiple decision makers at the lower level. Here the parameters of the problem are considered to be NNs in the form of [P+QI], where P and Q are real numbers and indeterminacy is represented through the symbol I. I is expressed in the form of a real interval as agreed upon by the DMs. The BLDMOLPP with NNs then gets converted into an interval BLDMOLPP. Using interval programming, the target intervals for the objective functions are identified and subsequently, the goal achievement functions are constructed. The upper level DM provides some possible relaxation on the decision variables under his/her control to cooperate with the lower level DMs to attain a compromise optimal solution. Thereafter, goal programming (GP) models are formulated by minimising the deviational variables and thereby obtaining the most satisfactory solution for all DMs. Finally, a numerical example demonstrates the feasibility and simplicity of the proposed strategy.