Variants of transshipment problem

Abstract

In a transshipment problem all the sources and destinations can function in any direction thus transshipment is very useful to reduce the transportation cost. Sometimes, because of budget/political constraint, the total flow in transshipment problem is also specified by some external decision maker and the optimal solution of such problems is of realistic interest to the decision maker. This has motivated me to discuss impaired and enhanced flow in a transshipment problem. Algorithms are provided for solving such transshipment problems by transforming the original problem into an equivalent transportation problem by adding an additional row and a column. The optimal solution of the transformed transportation problem gives the optimal solution of the given transshipment problem having the same objective function value. I have considered both balanced as well unbalanced transshipment problems and have also discussed various situations emerging out of unbalanced capacitated transshipment problems in the form of inequalities. The algorithms and transformations are easy to understand and serve the managers by providing the solution to a variety of distribution problems. Numerical examples are solved to illustrate the theory and computational work for various higher dimensional problems is also included.