An improved heuristic approach for the interval immune transportation problem

We study the problem of determining the bounds of the optimal cost of a transportation problem when the capacity of the suppliers and the demand of the customers vary over an interval. We consider transportation costs such that the transportation paradox does not arise. We design a new heuristic approach based on some polyhedral properties of the problem and provide a novel integer linear programming mathematical formulation to solve it exactly. Our computational results, carried out on benchmark instances from the literature and on some new instances, show that our heuristic algorithm greatly outperforms the best solution approaches currently used.