On the fixed-charge transportation problem

In many distribution problems, the transportation cost consists of a fixed cost, independent of the amount transported and a variable cost, proportional to the amount shipped. In such fixed-charge transportation problems, is it possible to find a solution with less (or equal) cost than the optimal solution by shipping more units, under the condition that at least the same amount is shipped from each supply point and to each market? This question has not received any attention in the literature, and no algorithm (either analytical or heuristic) is known to address this problem. The more-for-less analysis could be useful for managers in decisions such as increasing warehouse/plant capacity, analyzing company acquisitions, mergers, consolidations or downsizing. In this paper we develop a quick sufficient condition to identify candidate markets and supply points to ship more for less in fixed-charge transportation problems.