Optimizing a Linear Function Over the Efficient Set of a Multi-Objective Transportation Problem

In this study, we propose an exact method for optimizing a linear function over the efficient set of a multi-objective transportation problem (MOTP). This type of problem arises when a decision maker needs to optimize a preference function across numerous efficient solutions. We developed a cutting plane method that iteratively adds efficient cuts to the relaxation of the original problem until a feasible and optimal solution is achieved. The method is enhanced by a lower bound, enabling a more efficient search for the optimal solution.