What is Pareto-Optimal Solution

The multi-objective solid transportation problem is a special class of vector-minimum linear programming problems in which the objectives are often in conflict. Furthermore, the supply, demand, and conveyance constraints in MSTP may not be only of equality type but also of inequality type. The fuzzy programming approach is one of the most common solution methods for multi-objective programming problems. In this approach, linear membership functions are generally used in the literature. In this study, the fuzzy programming approach is applied by utilizing a special type of non-linear (exponential) membership functions to solve the multi-objective capacitated solid transportation problem (MCSTP) and a Pareto-optimal solution is obtained. Finally, an application from the literature is provided to illustrate the efficiency of the exponential membership function. Also, a comparison is presented with the solution obtained by using a linear membership function.