ABSTRACT
The ‘Four Axial Sums’ Transportation Problem minimizes the cost of shipping homogeneous goods from various sources to markets through various agencies, using different modes of transport (rail, sea, air etc.), where the availability at each source, requirement at each market, the total quantity handled by each agency and carrying capacity of each mode of transport are known. This paper studies the truncation of flow in any Four Axial Sums Transportation Problem. For any impared flow, the problem is shown to be equivalent to a Four Axial Sums problem, the solution method of which is given in the Appendix. The equivalence is established only for specially defined solutions (referred to as M-feasible solutions) of the standard problem. It is also proved that an optimal solution of the truncated flow problem corresponds to such an M-feasible solution.
