The Transportation Paradox Revisited

The transportation paradox is related to the classical transportation problem. For certain instances of this problem an increase in the amount of goods to be transported may lead to a decrease in the optimal total transportation cost. Thus this phenomenon has also been named the more-for-less-paradox. Even though the paradox has been known since the early days of linear programming, it has got very little attention in the literature and in teaching, and it seems to be almost unknown to the majority of the LP-practitioners. We consider the result of a recent paper which presents necessary and sufficient conditions for a transportation cost matrix to be immune against the paradox. These conditions are rather restrictive, supporting the results reported from simulations that the paradox may occur quite frequently. We also consider some postoptimal conditions for when the paradox may occur. A simple procedure for modifying an existing model to exploit the paradox is given and illustrated by examples. Finally two transportation examples from two selected textbooks are presented illustrating the appearance of the paradox.