Balancing a transportation problem: Is it really that simple?

Abstract

The transportation problem (TP) is discussed in all operational research textbooks. Although the TP can be formulated as a linear programme, owing to its special structure, it can be solved more efficiently than just using the standard simplex algorithm. Typically, the first step in solving a TP is to ‘balance’ the problem. If total supply is not equal to total demand, then a dummy column (supply greater than demand) or dummy row (demand greater than supply) is created. Although a few papers have discussed the importance of how the dummy column (row) is handled, this has been done only with reference to using one particular heuristic (Vogel's approximation method or VAM). Furthermore, the impact on solution quality based on how a heuristic processes the dummy column or row has not been empirically quantified. The closer an initial heuristically determined basic feasible solution is to the optimal solution, the fewer the required iterations of the modified transportation simplex to determine the optimal solution. The purpose of this article is to empirically quantify the importance of how five TP heuristics (northwest corner method, the greedy heuristic, VAM, Russell's method and the maximum demand method) process the dummy column (row) in a balanced TP.