Multi-objective two-stage grey transportation problem using utility function with goals

Multi-Objective Goal Programming is applied to solve problems in many application areas of real-life decision making problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.