Goal programming approach for multi-objective optimization to the transportation problem in uncertain environment using fuzzy non-linear membership functions

The ultimate goal of the decision maker (DM) is to take right decisions to optimize the profit or loss of the organization when the parameters of the transportation problem are ambiguous because of some uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions and the inverse uncertain normal distribution has been used to eliminate the uncertainty in the parameters which will help the DM to find a compromise solution of the uncertain multi-objective transportation problem (UMOTP) and to achieve the desired goals for a chosen level of confidence for the uncertain parameters. The compromise solutions of the uncertain multi-objective transportation problem are presented to obtain the DM satisfaction if the problem becomes achievable for this preferred confidence level of the parameters. Numerical illustration is given where Linear Programming Problems (LPPs) are resolved with LINGO and the graphs are designed with the help of MATLAB 18.00. J. Bangladesh Acad. Sci. 46(1); 101-115: June 2022