Multi-choice multi-objective linear programming problem

We consider a multi-objective linear programming problem where some of the right hand side parameters of the constraints are multi-choice in nature. For some right hand side parameters of the constraints, there may exist multiple choices, out of which exactly one is to be chosen. The selection from the sets should be in such a manner that the combination of choices for each set should provide best compromise solution. In order to solve the proposed multi-choice multi-objective linear programming problem, this paper proposes an equivalent mathematical model, which can be solved with the help of existing non-linear programming method. The proposed model can accommodate a maximum of sixteen choices for a single parameter. An illustrative example is presented in support of the proposed model.