The maritime transportation problem was first formulated by T.C. Koopmans (1957) as a transportation problem related to specific maritime activities. Across time, several classes of Simplex-type algorithms have been developed to find the numerical solution when the problem has a non-empty set of feasible solutions. Often, the mathematical model of a real world context will provide an unbalanced and inconsistent maritime transportation problem, i.e. when the set of classical feasible solutions is empty and the least squares one must be considered. In such cases, the linear programming solutions techniques cannot be applied, and one way to find an optimal solution is to reformulate the problem as an inconsistent (incompatible) system of linear inequalities, for which several Han-type iterative algorithms have been proposed. In this paper, we attempt to solve an unbalanced and inconsistent maritime transportation problem by two approaches. One of them refers to the application of the MH algorithm, a modified version of Han’s original algorithm, previously proposed by the authors. The other one involves a soft computing technique that produces an original formulation of a genetic algorithm (GA) over a maritime transportation problem. The results are discussed and a comparative study is given, aiming to provide a cost optimized solution to some real world maritime transportation problems.
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